Prasanna

Kerala Plus One Physics Model Question Paper 3

Time: 2 Hours
Cool off time: 15 Minutes
Maximum: 60 Scores

General Instructions to candidates

• There is a ‘cool off time’ of 15 minutes in addition to the writing time.
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read the instructions carefully.
• Read questions carefully before you answering.
• Calculations, figures, and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• Give equations wherever necessary.
• Electronic devices except non-programmable calculators are not allowed in the Examination Hall.

Questions 15 carry 1 score each. Answer any I four questions.

Question 1.
The branch of Physics which deals with the study of phenomena related to light.

a. Optics
b. Thermodynamics
c. Mechanics
d. Electronics

Question 2.
State the theorem of perpendicular axes on a moment of inertia.

Question 3.
Select a true statement from the following.
a. The distance traveled by light in one year through vacuum or air is an astronomical unit.
b. The range of time in Physics varies from 10^-14 sec to 10^-25 sec.
c. Lightyear is the largest practical unit of length.
d. Chandra Shekhar Limit (C.S.L) is the largest practical unit of mass.

Question 4.
When two objects collide, after collision they could move together, the collision is ……………………
(elastic, completely elastic, inelastic, completely inelastic)

Question 5.
List any two conditions for a motion of a body to be simple harmonic.

Questions 6 to 11 carry 2 scores each. Answer any 5 questions.

Question 6.
The possibility of falling backward with the ladder is more when you are high up on the ladder than when you just begin to climb. Explain why.

Question 7.
The displacement of y (in cm) of an oscillating particle varies with time t (in a sec) according to the equation. y = 2 cos (0.5 πt + π/3) Find the amplitude and period of the particle

Question 8.
Draw the stress-strain graph of a loading wire. Mark the following points:

1. Elastic limit
2. Fracture point
3. Plastic region
4. Elastic region.

Question 9.
Calculate the work done in lifting a body of mass 10 kg to a height of 10 m above the ground. 10 kg

Question 10.
a. Which among the following possess the highest specific heat capacity?

1. Water
2. Silver
3. Copper
4. Steel

b. You are in a restaurant waiting for your friend and ordered coffee. It has arrived. Do you add sugar to your friend’s coffee and then wait for him or do you add sugar after he arrives? Explain with respect to the concept of cooling.

Question 11.
A collision between two particles need not be the physical contact of two particles as in the case of scattering of the particle by a nucleus.
a. What is the quantity that remains conserved in all types of collisions?
b. Suppose an electron and a proton are projected with equal kinetic energy, What will be the ratio of their linear momentums if the proton is 1830 times heavier than an electron?

Questions 12 to 17 carry 3 scores each. Answer any five questions.

Question 12.
Motion along a plane is called two-dimensional motion. A body moving in two dimensions is found to have an acceleration in one dimension.

a. Identify the motion.

b. A ball thrown by a player reaches another player in 2s. What is the maximum height attained by the ball above the point of projection? (Take g= 10ms^-2)

c. In the figure, the point P on a wheel of radius R is in contact with the ground. What is the displacement of the point, when the wheel rolls a half revolution?

Question 13.
All physical quantities can be expressed in terms of dimension.
a. Write the physical quantities of the following dimensions:
i. [M¹L¹T¹ ]
ii. [M²L ²T²]
b. Check whether the equation T = \(T=2\pi \sqrt { \frac { m }{ g } }\) is dimensionally correct
T → Time period of a simple pendulum
m → mass of the bob
g → acceleration due to gravity

Question 14.
Kinetic theory of gases is based on the molecular picture of matter.
a. Write any two postulates of kinetic theory of gases.
b. Write short notes on:

1. Equipartition of energy
2. Mean free path

Question 15.
The stress-strain graph for wires of two materials A and B are given below.

a. Which material is more ductile?
b. When spring balances are continuously used for a long time, they show a wrong reading. Explain why?

Question 16.
Force is required to lift a body from the ground to a height h and work is measured as the product of force and magnitude of displacement.
a. Name the energy possessed by the body at maximum height. Write an equation for it.
b. A man of mass 60 kg carries a stone of mass 20 kg to the top of a multi-story building of height 50m. Calculate the total energy spent by him? (g = 9.8 m/s²)

Question 17.
The acceleration due to gravity o,n the surface of the moon is 1.7 m/s². what is the time period of a simple pendulum on the moon, if its time period on Me earth is 3.5 second?

Questions 18 to 22 carry 4 scores each. Answer any 4 questions.

Question 18.
A stone is thrown with the help of a sling with initial velocity V_Q at an angle θ from the horizontal.

a. Working of a sling is based on a law of vector addition.
b. With the help of a vector diagram, state this law.
c. Derive the expression for the maximum height reached by the

Question 19.
The velocity of sound depends on density (p) and modulus of elasticity (E). (The dimensional formula of E is ML^-1 T^-2)
a. State the principle of homogeneity.
b. Using the above principle, arrive at an expression for the velocity of sound. (Take K = 1).

Question 20.
Hooke’s law states that stress a strain.
a. What is the necessary condition for the above law to be valid?
b. Explain with the help of a graph, the relation between stress and strain for a given solid material under increasing tensile stress.

Question 21.
a. The figure shows the position-time graph of a body moving along a straight line.

1. Draw the velocity-time graph of the body.
2. From the graph, find the displacement in 20 seconds.

b. From the velocity-time graph of a body moving with uniform acceleration, deduce the velocity-time relation and the velocity displacement relation.

Question 22.
The motion represented by the equation, y(t) = A cos (ωt + Φ) is called simple harmonic motion (SHM).
a. Which one of the following examples ‘ closely represents SHM? Substantiate your answer.

1. The rotation of the earth about its axis.
2. Oscillations of a swing.

b. A vibrating simple pendulum of period T is placed in a lift which is accelerating downwards. What is the effect of this on the time period of the pendulum?

Questions from 23 to 26 carry 4 scores. Answer any 3 questions.

Question 23.
According to Newton’s law of motion, the force depends on the rate of change of momentum.
a. Name the law that helps to measure force.
b. Using the above law, deduce an expression for a force.
c. A man jumping out of a moving bus falls with his head forward. What should he do in order to land safely?

Question 24.
The flow of an ideal fluid in a pipe of a varying cross-section is shown.

a. Differentiate between streamline flow and turbulent flow.
b. State and prove Bernoulli’s principle.

Question 25.
The figure given below depicts the schematic representation of an engine.

a. Which type of engine is this, a heat engine or a refrigerator?
b. Write the 4 steps of operation in the Carnot cycle.
c. A Carnot engine is working with a temperature of 27°C and 327°C. Find its efficiency (η).

Question 26.
In a hammer throw event, a solid sphere of mass 16 kg is tied to a light 50 cm long chain. A sportsman gives it a constant moment of 30 Nm for 10 seconds and then throws the sphere. Consider the sphere as a point mass.
a. Find the moment of inertia about the axis of rotation.
b. If ‘L’is the angular momentum and τ is the torque. Show that τ = \(\frac { dL }{ dt }\)
c. Write an example for the motion in which an angular momentum remains constant.

Answers

Answer 1.
Optics

Answer 2.
This theorem is good for flat bodies which means, thickness much less than length and breadth. The theorem states that “the moment of inertia of a plana body about an axis perpendicular to its plane is equal to the sum of moments of inertia about two mutually perpendicular axes passing through the same point, lying on the plane”.

Answer 3.
d

Answer 4.
Completely inelastic.

Answer 5.
1. acceleration is directly proportional to displacement. i.e., a α y
2. Periodic motion.

Answer 6.

As the distance from the axis of rotation (r) increases, the torque also increases. When we are high on the ladder the, r is greater and so a small force in the perpendicular direction can cause a large torque. So there is a greater chance of falling.

Answer 7.
A pendulum whose period is 2 seconds is called seconds pendulum. y = A cos (ωt + ∅)

1. x = 20 cos (62.Bt + π/14) Amplitude = 20 icm
2. Frequency a> = 62.8
3. Initial phase = 14 Strain

Answer 8.

Answer 9.
Work was done = Force × displacement
W = mg × h = 10 × 9.8 × 10 = 980 J

Answer 10.
a. Water.
b. Add sugar as soon as the coffee arrives and then wait. This is Newton’s law of cooling. Thus when sugar is added to coffee, the temperature of coffee decreases. Hence the rate of cooling also decreases.

Answer 11.
a. Momentum is conserved
b. The kinetic energy of an electron

Answer 12.
a. Projectile motion

Answer 13.
a.

1. Momentum or impulse
2. Work, energy, torque

So the equation is wrong

Answer 14.
a. AverageThe average energy of a molecule of an ideal gas is proportional to the absolute temperature. PV = nRT at all pressure and temperature.
b.

1. According to equipartition theorem, total energy of a system is equally distributed among various degree of freedom.
2. Mean free. a path is the mean distance traveled by the molecules between two successive collisions.

Answer 15.
a. Material A is more ductile.
b.This is due to a phenomenon known as fatique. Due to continuous use for a long time, the elasticity of materials decreases. So they show a wrong reading.

Answer 16.
a. Potential energy U = mgh
b. m = 60 + 20 = 80 kg;
h = 50m; g= 9.8 m/s²
U= mgh = 80 × 9.8 × 50
= 39200J

Answer 17.
g_m = 1.7 m/s², T_m = ? T= 3.5 s

Answer 18.
a. Parallelogram law of vector addition.
b. It states that “if two vectors are represented both in magnitude and direction by the adjacent sides of a parallelogram drawn from a point, then the resultant vector is represented both in magnitude and direction by the diagonal of the parallelogram passing through the same point”.
c. Horizontal range (R). It is the horizontal distance covered by a projectile from the point of projection on the ground to the point on the ground where the projectile returns again. R = horizontal velocity x time of flight (The horizontal velocity v cosQ of the projectile will be a constant)

The above equation shows that R is maximum when sin 20 is maximum, ie., when 0 = 45°
The maximum horizontal range Rmax = \({ R }_{ max }=\frac { { u }^{ 2 } }{ g }\)

Answer 19.
a. Acca ordering to a principle of homogeneity, the dimensions of the same fundamental quantity must be the same on both sides of the equation.

Answer 20.
a. Hooke’s law states that within elastic limit stress is directly proportional to strain.

Consider a uniform wire suspended freely from a fixed point. The face end is subjected to a stress and strain is noted. In the above graph, stress is on Y-axis, and strain on X-axis.

In the initial stages as stress increases strain also increases linearly from 0 to A. Till A stress a brain. For the all-region AB the proportionality is lost but even in this region, the wire will partially recover its initial state.

Beyond B (B is called the elastic limit). The strain increases very rapidly and it is seen that the wire retains the law dimension’s on the removal of the force. Now its behavior is plastic.

Beyond this point, even without increasing the stress any further the wire extends and ultimately at D, it breaks. This point D is called Breakpoint or yield point.

Answer 21.
a. A slope of a displacement-time graph (x-t) gives velocity. Velocity in the interval 0 – 5 sec.

When we draw a velocity-time graph, we get a graph as shown in the figure

ii. An area under the velocity-time graph gives displacement. Area A = 2 × 5 + 2 × 5 = 0 displacement = 0
b. Consider a body moving with uniform acceleration ‘a’. Let u be the initial velocity at a time t = 0 and v be the final velocity at time t.

But from equation (1), we get t = \(\frac { v-u }{ a }\)

Answer 22.
a. A simple harmonic motion is special type of motion which is periodic and takes place continuously at regular intervals of time in which a body moves to and fro on a straight line about a fixed point under a restoring force which is directed always towards the fixed point and directly proportional to displacement at that instant from the fixed point.

An ideal simple pendulum is made of a heavy point mass body suspended from rigid support by an inextensible, weightless and perfectly flexible string. The body is free to oscillate in a vertical plane. When an undisturbed pendulum is in the position ‘SO’. ‘S’ is the point of suspension and ‘O’ is the center of gravity of the bob.

The position SO is the equilibrium position. If the bob is slightly pulled aside and released, the pendulum oscillates between Q and P. Q & P represents the position of a center of gravity of the bob in the displaced position during the oscillation, then the force at P is shown in the figure.

1. Weight, mg of the bob acting vertically downwards.
2. The tension along the string T.

Resolving mg we get mg sinθ and mg cosθ as shown in the figure. Here mg cosθ balances the tension and mg sinθ acts tangentially at P hence it acts as the restoring force.
Let SO = SQ = SP = L
Let OP = x
Restoring force F = mg sin θ (Restoring force tends to reduce angular displacement θ hence the ve sign).
If the displacement ‘x’ is small compared to 1 θ is small hence sinθ = θ Restoring force F = – mg θ

Answer 23.
a. Newton’s 2^nd law of motion.
b. The law state that the rate of change of linear momentum is directly proportional to the applied force and it takes place in the direction of applied force. According to the second law,


c. A man jumping out of a moving bus falls with his head forward because his body gets a forward momentum and has a tendency to continue in the state of motion (inertia of motion) so in order to land safely he should not stand stationary but continue in the state of motion by running for a while.

Answer 24.
a. Streamline flow is defined as a flow in which all the liquid particles that pass any given point follow the same path at the same speed.

When the velocity of flow exceeds the critical velocity, the flow becomes Turbulent. The flow of a liquid is said to be turbulent flow if the speed and direction of the liquid particles passing any point change with time.

b. According to Bernoulli’s theorem, the steady flow of an ideal liquid, the total energy per unit volume remains constant throughout the flow. France by Bernoulli’s theorem, kinetic energy + potential energy + pressure energy = a constant throughout the flow

Consider the steady flow of a liquid through a nonuniform tube as shown in the figure. The pressure area of cross-section and speed at A are P₁, a₁, v₁ and P₂, a₂, v₂, at B. A and B are at height h₁ and h₂ from the horizontal. Let in time at liquid near

Total energy at A = Total energy at B Thus Bernoulli’s Theorem is proved.

Answer 25.
Heat engine.

Adiabatic expansion → BC
Isothermal compression → CD
Adiabatic compression → DA
c. The efficiency of a Carnot engine working between two temperature T₁ and T₂ of hot and cold reservoir is given by

Answer 26.

c. A motion of the earth around the sun.

Plus One Physics Previous Year Question Papers and Answers

Kerala Plus One Physics Model Question Paper 2

Time: 2 Hours
Cool off time: 15 Minutes
Maximum: 60 Scores

General Instructions to candidates

• There is a ‘cool off time’ of 15 minutes in addition to the writing time.
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read the instructions carefully.
• Read questions carefully before you answering.
• Calculations, figures, and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• Give equations wherever necessary.
• Electronic devices except non-programmable calculators are not allowed in the Examination Hall.

Questions 1 – 5 carry 1 score each. Answer any four questions.

Question 1.
What is the range of weak nuclear force?

Question 2.
During isothermal expansion the internal energy of gas became ………………

Question 3.
The main mode of transmission of heat by which the sun heats the surface of the earth is ……………

1. Conduction
2. Convection
3. Radiation
4. None of these

Question 4.
A constant force of 200 N displaces a body through 5 m in the direction of the force. Find the work done on the body.

Question 5.
Say true/false: “ All the false conductors are electrical conductors also”.

Questions 6 to 11 carry 2 scores each. Answer any 5 questions.

Question 6.
A physical quantity is given by A = \(h=\frac { { Fv }^{ 2 } }{ L }\). F is the force, v is the velocity and L is the angular momentum. Find the dimensions of h.

Question 7.
Position time graph of a body is given.

a. Estimate the velocity during the time interval t = 2s to t = 3s.
b. Displacement of an object is proportional to t³. Show that its acceleration is increasing with time.

Question 8.
One mole of an ideal gas expands from volume V₁ to Volume V₂ at a constant temperature T. Derive an expression for the work done.

Question 9.
The stress-strain graphs for two materials A and B are shown below (the graphs are drawn using the same scale) Which of the two is the stronger material?

Question 10.
A brass tumbler feels much colder than a wooden tray on a chilly day. Why?

Question 11.
Three vessels of different shapes are filled with water to the same height ‘h’ and their bottom parts are connected to manometers measuring the pressure. The water levels in ail the vessels remain the same.

a. Identify the above phenomenon.
b. Predict the pressure level shown by the manometers.

Questions 1217 carry 3 scores each. Answer any five questions.

Question 12.
a. The error in the measurement of the radius of a circle is 0.6%. Find the percentage error in the calculation of the area of the circle.
b. What is the number of significant figures in 0.00820 J?

Question 13.
A simple pendulum is an object suspended by a weightless and inextensible string fixed rigidly to support.

1. Under what conditions for the amplitude, are the oscillations of the pendulum simple harmonic?
2. The period of oscillation of the pendulum is T. What will be the period if the pendulum is suspended in a lift moving down with an acceleration equal to g/3.2

Question 14.
a. Will the passenger experience a decrease or an increase in his weight? Explain.2
b. What will be the effect if the cable is cut and the lift falls freely?

Question 15.
Elasticity is the property of matter that is characterized by atomic packing. For an elastic solid, stress applied is directly proportional to the strain produced in it. The stress versus strain graph for three materials A, B and C is shown below.

a. Which is more elastic A, B or C? Justify your answer.
b. If the bulk modulus of water is 2 × 10⁸ Nnr^-2. Find its compressibility.

Question 16.
When a mass is suspended on a metallic wire, the length of the wire increases slightly.
a. Name and state the law that relates to the restoring force developed in the wire and its deformation.
b. Draw the stress-strain graph of a loading wire. Mark the following points:

1. Elastic limit
2. Fracture point
3. Plastic region
4. Elastic region.

Question 17.
Gases have two specific heat capacities, C and Cv. Why?
b. Laplace pointed out that when sound is propagating through a gaseous medium, the change is adiabatic. Show that adiabatic bulk modulus is yΔp.

Questions 18 to 22 carry 4 scores each. Answer any 4 questions.

Question 18.
A rigid body is a body with a perfectly unchanging shape under the influence of an external force.


a. What do you mean by the center of mass of a rigid body?
b. A rigid beam of length L, breadth band depth d is supported near its ends as shown in the figure. A load W is suspended at its center of mass. Write the expression for the amount of sagging.
c. A steel beam of length 5 m is kept at a temperature of 20°C. On a hot day, the temperature rises to 40°C. What is the change in its length due to thermal expansion? (Coefficient of linear expansion of steel is 1.2 × 10^-5/°C).

Question 19.
Our earth has several artificial satellites. But the moon is the only natural satellite.
a. If acceleration due to gravity at the surface of the earth is ‘g’, arrive at the expression for acceleration due to gravity at a depth’.
b. Distance to the moon from the earth is 3.84 × 10⁸ m and the time period of the moon’s revolution is 27,3 days. Obtain the mass of the earth. (g = 6.67 × 10^-11 Nm²/kg²)

Question 20.
The rotational analog of force is a moment of force, also called torque.
a. The turning effect of the force is maximum when the angle between? and p is …………..
b. A wheel starting from rest acquires an angular velocity of 10 rad/s in two seconds. The moment of inertia of the wheel is 0.4 kg m². Calculate the torque acting on it.

Question 21.
When a horse suddenly starts moving, the rider falls backward.
a. Name and state the law used to explain the above theorem.
b. State the law of conservation of linear momentum and prove it on the basis of the second law of motion.

Question 22.
Viscosity is the frictional force in fluids.
a. When a small metal ball is falling through a viscous medium, what are the various forces acting on it? Using this arrive at an expression for terminal velocity.
b. Raindrops falling under gravity do not acquire very high velocity. Why?

Questions from 2326 carry 4 scores. Answer any 3 questions.

Question 23.
a. A heat engine is a device used to convert energy into energy.
b. Name the four processes taking place in the Carnot cycle. Draw indicator diagram of the Carnot cycle.
c. A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27°C. What is the change in diameter of the hole when the sheet is heated to 227° C? (Coefficient of linear expansion of copper = 1.7 x 10^-5/°C)
d. Write four postulates of kinetic theory of gases.

Question 24.
The antiseptics used for cuts and wounds in human flesh have low surface tension. Due to low surface tension, they spread over the wounds easily.

a. In the following figure, the angle of contact 0 is
b. Surface tension causes capillarity. Define capillarity and arrive at the expression for a capillary rise in terms of surface tension.
c. In a capillary tube, water rises to a height. If the capillary tube is inclined at an angle 60° with the vertical, what will be the length of the water column in the tube?

Question 25.
Moment of inertia is the analog of mass in rotational motion. But unlike mass, it is not a fixed quantity.
a. Moment of inertia can be regarded as a measure of rotational inertia. Why?
b. Write any two factors on which the moment of inertia of a rigid body depends.
c. The moments of inertia of two rotating bodies A and B are lAand lB, (lA > lB) and their angular momentum is equal. Which one has greater kinetic energy? Explain.

Question 26.
The outer side of a circular track of radius 200 m is raised to make an angle of 15°
a. Which force provides the necessary cen tripetal force for a car taking the circular track?
b. Name the process by which the outer side of a curved track is raised a little above the inner side.
c. Using the data provided in this case, determine the maximum permissible speed to avoid skidding. (Given ps = 0.25)

Answers

Answer 1.
The range of a nuclear force is of the order of 10^-16m.

Answer 2.
Zero

Answer 3.
Radiation.

Answer 4.
Force = 200 N displacement = 5m
Work done = Force × displacement = 200 × 5 = 1000 J

Answer 5.
False

Answer 6.

Answer 7.


i.e., a α t, Hence acceleration increases with time.

Answer 8.
PV = nRT; here n = 1
We have a small amount of work done when volume changes through tv at pressure p. Let volume change from V₁ to V₂ isothermally,

Answer 9.
Material A is stronger than material B because it can withstand more load without breaking for material A, the break-even point (D) is higher.

Answer 10.
The thermal conductivity of brass tumbler is larger than a wooden tray. Hence a brass tumbler feels much colder than a wooden tray.

Answer 11.
a.Hydrostatic paradox.
b. Pressure at the same height is the same.

Answer 12.

b. 3

Answer 13.
1. Amplitude should be small.
2. The period of simple pendulum \(T=2\pi \sqrt { \frac { 1 }{ g } }\)
When a lift is moving down with an acceleration g/3.

Answer 14.
a. The passenger experiences a decrease in weight.

b. The passenger experiences weightlessness W’ = m (g – g) = 0

Answer 15.
a. Material A is more elastic. Because the strain of material A is smaller than that other and slope of A is more. Soan extension of A will be less than B and C. When they are subjected to same reforming force F.

Answer 16.
a. Hooke’s law. Hooke’s law states that when elastic limit stress is directly proportional to strain.

Answer 17.
a. Heat can be given to gas in two ways.
1. By keeping the pressure constant.
2. By keeping volume constant. In (1) gas expands, additional heat is needed to work.

Answer 18.
a. Centre of a mass of a rigid body in the point where the whole mass of the body is assumed to be concentrated.

Answer 19.

Answer 20.

Answer 21.
a. Newton’s 1st Law of motion. The law states that “ everybody continues in its state of rest or of uniform motion in a straight line unless compelled by some external unbalanced force to change that state”,
b. The law states that “ If no external force acts on a system of several particles, the total linear momentum of the system remains constant”.

Answer 22.
a. The constant speed of the object falling through a viscous medium is called terminal velocity. The vicious force, F = 6xr|rv Considering the motion of the body, viscous force = apparent weight of the object in the fluid. where 5 is the density of the material of the solid and a that of the fluid.

b.Rain drop falling under gravity is acted upon by weight, upthrust and viscous force. Hence it attains constant velocity.

Answer 23.
a. Heat energy into mechanical energy.
b. Isothermal expansion AB Adiabatic expansion BC Isothermal compression CD Adiabatic compression DA

d.
1. Gas molecules randomly move all the time and collide with each other and with walls of a container.
2. Size of molecules is negligible compared to the average distance between molecules.
3. Molecules are rigid spheres with no attraction or repulsion between themselves or container and so, all the internal energy is kinetic.
4. A collision between molecules and wall are elastic. In between collisions they move in straight lines with uniform velocity. Time of collision is very small compared to time available for free motion.

Answer 24.
a. Obtuse or θ > 90°

The capillary action is a result of both adhesion and surface tension. If a capillary tube is held vertical in a liquid which has a concave meniscus. There always exists an excess pressure equal to 2s/R on the concave side of liquid are interphase. Where ‘S’ is the surface tension and R is the radius of curvature of a meniscus. Pressure just below the meniscus is p 2s/R, where P is the atmospheric pressure. The pressure outside the tube at a level of the meniscus is the atmospheric pressure’P’. Since the pressure at points in the same level of liquid must be the same, the liquid is pushed up in the tube to the height ‘h’ as shown in fig(a). In this position, the pressure of liquids column of height ‘h’ becomes equal to 2s/R. ∴ \(hpg=\frac { 2s }{ R }\) where p is the density and ‘g’ is an acceleration due to gravity.
From fig (b)


l = 2h or length increases.

Answer 25.
a. Just as inertia resists translatory motion, when a rigid body rotates about an axis, there is a tendency to resist changes in uniform rotational motion. Moment of inertia resists change in rotational motion of the body.
b. Moment of inertia of a rigid body depends on the mass of particles and the distribution of particles about the axis of rotation, size, and shape.

Answer 26.
a. It is provided by the force of friction between the tires of the car and the road.
b. Banking of roads.

Plus One Physics Previous Year Question Papers and Answers

Kerala Plus One Physics Model Question Paper 1

Time: 2 Hours
Cool off time: 15 Minutes
Maximum: 60 Scores

General Instructions to candidates

• There is a ‘cool off time’ of 15 minutes in addition to the writing time.
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read the instructions carefully.
• Read questions carefully before you answering.
• Calculations, figures, and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• Give equations wherever necessary.
• Electronic devices except non-programmable calculators are not allowed in the Examination Hall.

Answer any four questions from question numbers 1 to 5. Each carries one score.

Question 1.
State TRUE or FALSE, “weak nuclear force is the weakest fundamental force.

Question 2.
Two vectors \(\bar { A }\) and \(\bar { B }\) are such that \(\left| \bar { A } \times \bar { B } \right| =\bar { A } ,\bar { B }\) Then the angle between the two vectors is ……………

a. 45°
b. 90°
c. 60°
d. 180°

Question 3.
A satellite is revolving around the earth with a kinetic energy E. The minimum addition of kinetic energy needed to make its escape from its orbit is ………………………

Question 4.
A particle executing SHM is an example of

1. acceleration of constant magnitude and direction.
2. acceleration of changing magnitude and direction.
3. acceleration of changing magnitude but constant direction.
4. acceleration of constant magnitude but changing direction.

Question 5.
The young’s modulus Young’smaterial of a wire is equal to the

a. The stress required to increase its length four times
b. The stress required to produce unit strain
c. The strain produced in it
d. half the strain produced in it

Answer any four questions from question numbers 6 to 10. Each carries two scores.

Question 6.
When brakes are applied on a moving vehicle, it stops after traveling a distance. This distance is called stopping distance.
a. Write an expression of stopping distance in terms of initial velocity (u) and retardation (a).
b. If the initial speed is doubled keeping the retardation same, by how much will the stopping distance change?

Question 7.
A parallelogram law helps to find the mag
nitude and direction of the resultant of two forces.
a. State the law.
b. If the magnitude of the two vectors and their results are the same, what is the angle between the two vectors?
Parallelogram

result-

Question 8.
Select the CORRECT alternative.
a. When a force is applied to a moving body, its motion is retarded. Then the work is done; is

1. positive
2. negative
3. zero

b. In the stable equilibrium position, a body has

1. maximum potential energy
2. minimum potential energy

c. The rate of the kinetic energy versus position vector gives the rate of change of

1. momentum
2. velocity
3. force

d. According to a work-energy theorem, the work done by the net force on a particle is equal to the change in its

1. kinetic energy
2. potential energy

Question 9.
The wire has an unstretched length of 2.40 m and an area of a cross-section of 3.90 × 10^-7 m². Determine Young’s modulus Y of the material.

Question 10.
According to the kinetic theory of gases, gas molecules are always in random motion.
a. State the law of equipartition of energy.
b. What do you mean by ‘mean free path’? Give an equation for the mean free path.

Answer any four questions from question numbers 11 to 15. Each carries three scores.

Question 11.
Acceleration time graph of a body starts from rest as shown below:

a. What is the use of the accelerationtime graph?
b. Draw the velocity time graph using the above graph?
c. Find the displacement in the given interval of time from 0 to 3 seconds.

Question 12.
Ramesh observes the motion of an insect in a circle. He finds that it travels 6 revolutions in an anticlockwise direction for a time of 31.4 sec.
a. Find the angular velocity of the insect?
b. If the insect travels 4 revolutions in the clockwise direction for a time of 8.6 sec. What will be the angular speed averaged over the total time?

Question 13.
A circular racetrack of radius 300 m is banked at an angle of 150. The coefficient of friction between the wheels of a race car and the road is 0.2. Find :

1. The optimum speed of the race car to avoid wear and tear on its tires.
2. Maximum permissible speed to avoid slipping.

Question 14.
Rotational inertia is the tendency of a rotating body to resist any change in its state of rotational motion.

a. What do you mean by the radius of gyration of a rolling body?

b. The figure shows two different spinning poses of a ballet dancer.

In which spinning pose does the ballet dancer have less angular velocity? Justify! your answer.

Question 15.
A and B are two objects moving with velocities V_A and V_B?
a. What is the velocity of A relative to B?
b. Rain is falling vertically with a speed of
35 m/s. A woman rides a bicycle with a speed of 12 m/s in the east to west direction. What is the direction in which she should hold her umbrella?

Answer any four questions from question numbers 16 to 20. Each carries four scores.

Question 16.
a. The value of acceleration due to gravity is maximum at the

1. Poles
2. Equator ;
3. Centre of the earth

b. Find the height at which ‘g’ is reduced to g/2. 2 I

c. A rat and a horse are to be projected from earth into space. State whether the veloc ity is the same or different in projecting; each animal. Justify.

Question 17.
A person in an artificial satellite of the earth experiences weightlessness. The moon is a natural satellite of the earth.
a. Can a person on the moon experience weight? Why?
b. A satellite is revolving very close to the earth. What is the percentage increase in velocity needed to make it escape from the gravitational field of the earth?
c. Acceleration due to gravity ‘g’ depends on the distance ‘r’ from the center of the earth. Draw a graph showing the variation of‘g’with r’.

Question 18.
a. A solid sphere falling through a viscous
medium attains a constant velocity called terminal velocity after some time of its fall. What are the different forces acting, on the sphere? Derive an epression for terminal velocity in terms of the coefficient of viscosity of the medium. 3 b. Water kept in earthern pots gets cooled. Why?

Question 19.
Mechanical power is represented by P = FV +
Av3p; where F is the force, v is the velocity; A ! is the area and p is the density.
a. The dimensional formula of power is
b. Check the dimensional validity of the above , equation.
c. Which of the following equations can’t be obtained by the dimensional method?

Question 20.
While conducting a resonance column experiment in the laboratory, you can hear the maximum sound at a certain height.
a. Explain the phenomenon of sound.
b. Show that in a closed pipe at one end, the frequencies of the first three harmonics; are in the ratio of vt: v2: v3 = 1: 3: 5. 2!
c. Open pipes are preferred to closed ones in musical instruments. Why?

Answer any four questions from question numbers 21 to 25. Each carries 5 scores.

Question 21.
Raising the outer edge of a curved road a little above the inner edge is called banking of curves.
a. Derive an expression for the safe speed with which a car can negotiate a banked road by taking into account the friction between the tires and the road.
b. A machine gun fires bullets of mass 40g each with a speed 1200 ms1. The person can hold the gun with a maximum force of 144 N. What is the maximum number of bullets that can be fired per second from the gun?

Question 22.
Earth satellites are objects which revolve around the earth. Consider a satellite at a ‘ height ‘h’ from the surface of the earth.
a. Give an equation for its orbital velocity.
b. Obtain an equation for the period of the above satellite.
c. Distinguish between geostationary satellites and polar satellites.

Question 23.
The pressure of the atmosphere at any point is the weight of the air column of a unit cross-sectional area. Its unit is a bar.

a. Identify the diagram and write its use.
b. State Pascal’s law for transmission of fluid pressure and explain the principles j of working of a hydraulic lift.
c. The above arrangement is placed in an ; elevator which is accelerating upwards, i What happens to the possible height of ; the liquid column in the tube? Justify.

Question 24.
Aheatengineisadevicewhichconvertsheatenergy into work.
a. What is the working substance in an ideal heat engine?
b. Draw the Carnot cycle and explain its working.
c. Calculate the efficiency of an engine working between steam point and ice point.

Question 25.
a. Wave motion is the propagation of energy through a material medium due to repeated periodic motion.

1. Transverse waves cannot be propagated through gases. Why?
2. What was the condition assumed by Laplace in correcting Newton’s equation for the velocity of sound in a gas? Write the newton Laplace equation.

b. A source of the sound of frequency 256 Hz is in between a listener and a wall. If the source is moving towards the wall with a velocity of 5ms1, how many beats per second will be heard if the sound travels with a speed of 330ms’1?

Answers

Answer 1.
False. Gravitational force is the weakest fundamental force.

Answer 2.
45°

Answer 3.
E

Answer 4.
2

Answer 5.
The stress required to produce unit strain

Answer 6.
a. When vehicle comes to rest v = 0, a = a
substituting these values in

b. When a body comes to rest, work is done = change in kinetic energy

The stopping distance becomes 4 times the original distance.

Answer 7.
a. Parallelogram states that if two vectors
are represented both in magnitude and direction by the adjacent sides of a parallelogram drawn from a point, then the resultant vector is represented both in magnitude and direction by the diagonal of the parallelogram passing through the same point.
b. R = A + B + 2AB cosθ

Answer 8.
a. negative
b. minimum potential energy
c. momentum
d. kinetic energy

Answer 9.

[slope from graph may vary slightly and mark may be granted to possible correct answers irrespective of variations.]

Answer 10.
Law of equipartition energy:
It states that in any dynamical system in thermal equilibrium, the energy is equally distributed amongst its various degrees of freedom and the energy associated with each degree of freedom per molecule is 1/2k_BT, where k_B is Boltzmann’s constant and T is the absolute temperature of the system.

b. The average distance traveled by the molecules between two successive collisions is called the mean free path. Mean free path \(=\frac { l }{ \sqrt { 2n\pi { d }^{ 2 } } }\) (‘n’ is the number of molecules per unit volume’ is the diameter of the molecule).

Answer 11.
a.

1. The area of the acceleration time graph gives change in velocity.
2. From a 1 graph, we can find instantaneous acceleration.
3. Slope of a 1 graph gives rate of change of acceleration.

c. Displacement = Area under graph
= Area of DOAB
= 14 × 3 × 12 = 18m

Answer 12.
a. Angular velocity \(\omega =\frac { 2\pi n }{ t } =\frac { 2\pi \times 6 }{ 3.14 } =1.2rad/s\)
b. Period of rotation in clockwise,

Answer 13.

Answer 14.
a. A radius of gyration of a body about an axis of rotation is defined as the distance from the axes to a point at which the whole mass of the body is assumed to be concentrated. It is denoted by K. \(K\sqrt { \frac { I }{ M } }\)
b: Fig (a), in this pose, a moment of inertia is larger than the fig (b).

Answer 15.

Answer 16.
a. Poles
b. Let ‘h’ be the height from the surface of the earth where the value of g is g/2.

c. Velocity is same ie, V_e = \(\sqrt { 2gR }\) Escape velocity is independent of the mass of the body that projected into space.

Answer 17.
a. Yes. Moon attracts every body towards its center.
b. Orbital velocity V₀ = \(\sqrt { Rg }\)
Escape velocity V_e = \(\sqrt { 2Rg } =\sqrt { 2 } { V }_{ 0 }\) % change in velocity

18. a. The forces acting on the sphere are

1. The weight of the sphere acting downward
2. A viscous force acting upward
3. Buoyant force acting upward.

An expression for terminal velocity:
Consider a small sphere of radius Y and mass placed on a surface of a highly viscous liquid contained in a jar. According to Stoke’s formula, a viscous force on the sphere moving with a terminal velocity ‘V and radius Y is given by F = 6πrnv where ‘n’ is the coefficient of viscosity of the fluid. Apparent weight of the sphere in a fluid is [ltex]\frac { 4 }{ 3 } \pi { r }^{ 2 }pg-\frac { 4 }{ 3 } \pi { r }^{ 3 }og[/latex]Where p is the density of the material of sphere a and that of the liquid At terminal velocity, \(\frac { 4 }{ 3 } \pi { r }^{ 3 }\left( p-\sigma \right)\)

b. Due to evaporation.

Answer 19.

Answer 20.
a. If a wave is produced at the open end of a tube it travels through the gas column and gets reflected at the closed end. At a certain height of tube the incident wave and reflected wave superpose each other and produce stationary wave and a sound is heard. This is called resonance. The open end always represents an antinode.
b. The first normal mode of vibration

Let l₁ be the wave length of standing have set up in the pipe corresponding to

The second normal mode of vibration (3rd harmonic, 1st overtone)

Let λ₂ be the wavelength of standing wave set up in the pipe corresponding to n = 2

Let λ₃ be the wave length of standing wave set up in the pipe corresponding to n = 3

The ratio of the first, second and third mode. V₁ : V₂ : V₃ = 1 : 3 : 5
c. All harmonics are present in open pipe, but in the closed pipe, only odd harmonics are present. So open pipe is preferred in a musical instrument.

Answer 21.

Let ‘mg’ be the weight of a vehicle moving with a speed ‘V around a banked road of radius ‘r’. Its normal reaction ‘ R’ can be resolved into 2 component R cos0 vertically upwards and R sinq towards the center of the curve. R sin0 gives necessary centripetal force while R cos0 balances the weight ‘mg’.

The direction of the frictional force Fs is such that the force resists the tendency of the car to skid to the outside of the curve. The horizontal component Fs cos0 is added to R sinq to provide a large centripetal force.

Substituting the value of R in equation (2)

divide the numerator and denominator by cosθ

Answer 22.

c. Satellite in a circular orbit of radius about 36,000 km around the earth in the equatorial plane with T = 24 hours is called geostationary satellites. They are mainly used for communication purpose, TV and Radio broadcasting and Weather forecasting.
Polar satellites are low altitude satellites that go around the poles of the earth in a north-south direction. Its time period is around 100 minutes and so it crosses any altitude many times a day. Its height above the earth is about 500800 km. In formation gathered from such satellites is extremely useful for remote sensing, meteorology as well as for environmental studies of the earth.

Answer 23.
a. Mercury barometer.
b. Pascal law. It states that an increase in pressure at one point of the enclosed liquid at rest is transmitted equally to every part of the liquid and to the wall of the container provided the effect of gravity is neglected.

In a hydraulic lift, two pistons are separated by the space filled with a liquid. A piston of small cross section A₁ is used to exert a force F₁ directly on the liquid. The pressure is P = \(\frac { { F }_{ 1 } }{ { A }_{ 1 } }\) is transmitted throughout the liquid to the larger cylinder attached with a larger piston of area A₂, which results in an upward force of P x A₂. Therefore, the piston is capable of supporting a large force (large weight of, say a car, or a truck, placed on the platform) F₂ = PA₂ = \(\frac { { F }_{ 1 }{ A }_{ 1 } }{ { A }_{ 1 } }\) By changing the force at A1, the platform can be moved up or down. Thus, the applied force has been increased by a factor of \(\frac { { A }_{ 2 } }{ { A }_{ 1 } }\) and this factor is the mechanical advantage of the device. The example below clarifies it.

c. Decreases, because of g decreases OR (g’ = g – a)

Answer 24.
a. Ideal gas or perfect gas

Carnot engine is an ideal heat engine. Main parts of Carnot engine are a source, working substance is an ideal gas which taken in a cylinder provided with a piston. The 3 sides of the cylinder are an insulator and the lower side is conducting, sink and an insulated stand. Adiabatic process in a car not cycle is performed in this insulated stand.
The four stages of the cycle are:

1. Isothermal expansion The cylinder containing the gas is placed in thermal contact with the source kept at high temperature (T₁,), It absorbs Q₁ amount of heat and expands, the expansion is isothermal. The initial pressure p₁ and volume V₁ of the gas change to p₂ and V₂. Thus the gas does a work W_AB

2. Adiabatic expansion (BC) The gas is placed on an insulating stand. Now no heat enters or leaves the system, the expansion is adiabatic. Pressure and volume change from p₂ and p₃ and V₂ to V₃. During the process, temperature falls to T₂. Work done by the gas is WBC.

3. Isothermal compression (CD) The cylinder is then placed on the sink at temperature T₂. Gas is compressed to reject some heat Q₂ to the sink. Since temperature T₂ remains constant, the compression is isothermal. Pressure and volume changes to p₄ and v₄ work done on the gas is WCD.

4. Adiabatic compression. The cylinder is again placed on the insulating stand for the completion of the compression process. Since no heat transfers or leaves the system, the compression is adiabatic. The gas attains the original pressure p₁ and volume v₁ at the end of this. Work done now is WDA.

Answer 25.
a.
i. Modulus of elasticity of gas is zero.
ii. Laplace corrected Newtons formula taking condensation and rare fraction as adiabatic process, v = \(\sqrt { \frac { VP }{ p } }\)

Plus One Physics Previous Year Question Papers and Answers

Kerala Plus One Physics Improvement Question Paper 2018

Time: 2 Hours
Cool off time: 15 Minutes
Maximum: 60 Scores

General Instructions to candidates

• There is a ‘cool off time’ of 15 minutes in addition to the writing time.
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read the instructions carefully.
• Read questions carefully before you answering.
• Calculations, figures, and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• Give equations wherever necessary.
• Electronic devices except non-programmable calculators are not allowed in the Examination Hall.

Answer any four questions from question numbers 1 to 5. Each carries one score.

Question 1.
State TRUE or FALSE. “Some conservation laws are true for one fundamental force, but not for the others”.

Question 2.
The angle between

a. 45°
b. 90°
c. 60°
d. 180°

Question 3.
Three objects with a mass of 40 kg each are placed in a straight line 50 cm apart. What is the net gravitational force at the center object due to the other two?

Question 4.
Which one of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?
a. a = 5x
b. a = -200 x²
c. a = -5x
d. a = 100 x³

Question 5.
The stress required to double the length of a wire of Youngs modulus Y is ………………


a. Y/2
b. 2Y
c. Y
d. 4Y

Answer any four questions from question numbers 6 to 10. Each carries two scores.

Question 6.
A car traveling at a speed 54 km/hr is brought to rest in the 90s. Find the distance traveled by car before coming to rest.

Question 7.
The parallelogram law is used to find the resultant of two vectors. Find the magnitude of the resultant of two vectors in terms of their magnitudes and angle between them.

Question 8.
Select the CORRECT alternative.
a. When a conservative force does positive
work on a body, the potential energy of the body ………………………

1. increases
2. decreases
3. remain unaltered

b. Work was done by a body against friction always results in a loss of its …………..

1. kinetic energy
2. potential energy

c. The rate of change of total momentum of a system of many-particle systems is proportional to the …………… on the system.

1. external force
2. a sum of the internal forces

d. The quantity which is conserved in an in an elastic collision of two bodies is ………….

1. total kinetic energy
2. total linear momentum

Question 9.
A steel wire of length 1.5 m and diameter 25 cm is loaded with a force of 98 N. The increase in the length of the wire is 1.5 × 10⁴ m. Calculate the tensile stress and the fractional change in length of the wire.

Question10.
According to the kinetic theory of gases, gas molecules are always in random motion.
a. State the law of equipartition of energy.
b. Write the average value of energy of a molecule for each vibrational mode.

Answer any four questions from question numbers 11 to 15. Each carries three scores.

Question 11.
Two parallel rail tracks run north-south. Train A moves north with a speed of 15 m/s and train B moves south with a speed of 25 m/s.
a. What is the velocity of B with respect to A?
b. What is the velocity of the ground with respect to B?
c. What is the velocity of a monkey running on the roof of the train A against its motion (with a velocity of 5 m/s with respect to the train A) as observed by a man standing on the ground?

Question 12.
An insect trapped in a circular groove of radius 12 cm moves along the groove steadily and completes 7 revolutions in 100s.
a. What is the linear speed of the motion?
b. Is the acceleration vector a constant vector? What is its magnitude?

Question 13.
A car arid a truck have the same kinetic energies at a certain instant while they are moving along two parallel roads.
a. Which one will have greater momentum?
b. If the mass of truck is 100 times greater than that of the car, find the ratio of loci of the truck to that of the car.

Question 14.
A girl rotates on a swivel chair as shown below.

a. What happens to her angular speed when she stretches her arms?
b. Name and state the conservation law applied for your justification.

Question 15.
A solid sphere of mass m and radius, R starts from rest and rolls down along an inclined plane of height h without slipping as shown below.

a. Calculate the kinetic energy of the sphere when it reaches the ground.
b. Find the velocity when it reaches the base.

Answer any four questions from question numbers 16 to 20. Each carries four scores.

Question 16.
A man jumping out of a slow moving bus falls forward.
a. This is due to
b. Which Newtons law gives the above concept? State the law.
c. What is the net force acting on a book at rest on the table?

Question 17.
To reduce friction and accident by skidding the roads are banked at curves.
a. What is meant by banking of roads?
b. Sketch the schematic diagram of a vehicle on a banked road with friction and mark the various forces.
c. Derive an expression for the maximum safe speed of a vehicle on a banked road with friction.

Question 18.
For a liquid-gas interface, the convex side has a high Pressure than the concave side.
a. Derive an expression for excess pressure inside a drop.
b. Which is better, washing of cloth in cool soap wafer or warm soapy water? Why?

Question 19.
Linear expansion is a change in length of an object with temperature.
a. Write the equation for the coefficient of j linear expansion.
b. Show that the coefficient of volume expansion is thrice its coefficient of linear ex! pension.
c. The absolute zero is ……………………………….
[ 273.15°C, 273.15K, 273.15°F, 0°C]

Question 20.
The simplest example of simple harmonic motion is the oscillations of a simple pendulum.
a. Derive an expression for the period of oscillation of a simple pendulum.
b. In a simple pendulum made of a metallic wire, what will happen to the period when the temperature increases? Give a reason.

Answer any four questions from question numbers 21 to 25. Each carries 5 scores.

Question 21.
a. The centripetal force depends on the mass of the body, velocity, and radius of a circular path. Find the expression for the centripetal force acting on the body using the principle of dimensional analysis. (Take constant k= 1)
b. When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72” of an arc. Calculate the diameter of a Jupiter.

Question 22.
Satellites are objects which revolve around the earth.
a. The direction of revolution of a geosynchronous satellite is from
i. east to west
ii. west to east
iii. north to south
iv. south to north

b. Derive an expression for a total energy of an orbiting satellite.
c. What is the magnitude of the angular velocity for a geosynchronous satellite?

Question 23.
The flow of an ideal fluid in a pipe of a varying cross-section is shown below.

a. Write Bernoulli’s equation.
b. Find the speed of efflux using Bernoulli’s principle.
c. State Torricelli’s law.

Question 24.
The basic features of a device are schematically represented in the figure below.

a. Which type of device is this, a heat engine or a refrigerator?
b. Draw the indicator diagram and label the four processes in the Carnot cycle.
c. A steam engine delivers 5.4 × 108J of work per minute and services 3.6 × 109 J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?

Question 25.
A transverse harmonic wave on a string is described by y (x, t) = 3.0 Sin (36t + 0.018x + p/4)where ‘x’ and ‘y is in cm and’ is ins. The positive direction of’ is from left to right.
a. Is this a traveling wave or a stationary wave? If it is traveling, what are the speed and direction of its propagation?
b. What are its amplitude and frequency?
c. What is the least distance between two successive crests in the wave?

Answers

Answer 1.
True

Answer 2.
90°

Answer 3.
Zero

Answer 4.
c. a = -5x

Answer 5.
Y

Answer 6.

Answer 7.

Answer 8.
a. decrease
b. Kinetic energy
c. externally forced
d. Total linear momentum

Answer 9.

Answer 10.
a. Law of equipartition energy:
It states that in any dynamical system in thermal equilibrium, the energy is equally distributed amongst its various degrees of freedom and the energy associated with each degree of freedom per molecule is 1/2k_B T, where kB is Boltzmann’s constant and T is the absolute temperature of the system.

Answer 11.

Answer 12.

Answer 13.

Answer 14.
a. When the girl stretches her arm, according to a law of conservation of angular momentum the distance from the axis of rotation increases and so a moment of inertia increases and thereby angular speed decreases.
b. When no external torque acts on a system of particles, the angular momentum of the system remains constant.

Answer 15.

Answer 16.
a. Inertia
b. Newton’s First Law of Motion. “Everybody continues in its state of rest or uniform motion in a straight line unless some external unbalanced force acts on it”.
c. Zero

Answer 17.
c. Refer QNo. 23, Page No. 61

Answer 18.
a. Refer QNo. 25 (b), Page No. 61
b. Using hot water usually makes whatever is being treated expand or loosen so the dirt can be released easier. It is because hot water has lower surface tension than cold water(Temperature increases surface tension decreases).
This hot water is able to penetrate easily into the pores and wet the surface. In words, As we move along a streamline, Pressure energy + Kinetic energy + Potential energy, per unit volume = Constant.

Answer 19.

Answer 20.

An ideal simple pendulum is made of a heavy point mass body suspended from rigid support by an inextensible, weightless and perfectly flexible string. The body is free to oscillate in a vertical plane. When an undisturbed pendulum is in the position SO. S is the point of suspension and θ is the center of gravity of the bob.

The position SO is the equilibrium position. If the bob is slightly pulled aside and released, the pendulum oscillates between Q and P. Q & P represents the

position of a center of gravity of the bob in the displaced position during the oscillation, then the force at P is shown in the figure.

1. Weight mg of the bob acting vertically downwards.
2. The tension along the string T. ResoMng mg we get mg sinθ and mg cosθ as shown in the figure. Here mg cosθ balances the tension and mg sinθ acts tangentially at P hence, it acts as the restoring force.

Let SO = SQ = SP = I, OP = x Restoring force, F = -mg sinθ (restoring force tends to reduce angular displacement θ hence the -ve sign) If the displacement ‘x’ is small compared to ‘f, θ ¡s small hence sinθ = e Restoring force, F = -mgθ

b. As temperature increases the length of pendulum increases due to linear expansion. So the period of pendulum increases.

Answer 21.
a. Let F ∝ m^av^br^c or F = K m^av^br^c ………(1 where K is a dimensionless constant. Writing the dimensions of various quantities ¡n equation (1), we get

Comparing the dimensions of similar quantities on both sides, we get

This is the required expression for the centripetal force.

Answer 22.
a. West to east
b. The kinetic energy of the satellite in a circular orbit at height h from a surface of the earth with speedy is

The potential energy at distance (R+h) from the center of the earth is

c. A time period of geosynchronous satellite = 24hrs

Answer 23.

In words, As we move along a streamline, Pressure energy + Kinetic energy + Potential energy, per unit volume = Constant.

b.

If the top of the tank is also open to atmosphere, then P = P_a

The velocity V₂ is called velocity of efflux. This is same as the velocity of an object falling freely under gravity through a height h.

c. Torricelli’s theorem states that the speed at which fluid leaves the orifice at the bottom of a reservoir is the same as if an object is falling freely through the same height.

Answer 24.
a. Heat Engine

Answer 25.

Plus One Physics Previous Year Question Papers and Answers

Kerala Plus One Physics Previous Year Question Paper 2017

Time: 2 Hours
Cool off time: 15 Minutes
Maximum: 60 Scores

General Instructions to candidates

• There is a ‘cool off time’ of 15 minutes in addition to the writing time.
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read the instructions carefully.
• Read questions carefully before you answering.
• Calculations, figures, and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• Give equations wherever necessary.
• Electronic devices except non-programmable calculators are not allowed in the Examination Hall.

Question 1.
Pick the odd one out among the following forces:
a. Gravitational force
b. Weak nuclear force
c. Viscous force
d. Electromagnetic force

Question 2.
The demonstration of conservation of angular momentum is schematically shown in the figures.

Identify the figure which has more angular velocity.

Question 3.
“Two systems in thermal equilibrium with a third system, are in thermal equilibrium with each other”. Identify the law given by the above statement.

Question 4.
A steel rod has a radius of 10 mm and a length of 1.0 m. A 100 kN force stretches it along its length. Calculate the elongation of the steel rod. [Young’s modulus of steel is 2.0 × 10¹¹ N/m².]

OR

A metal cube of side 10 cm is subjected to a; shear stress 10⁴ N/m². Calculate the rigidity: modulus, if the top of the cube is displaced by 0.05 cm with respect to its bottom.

Question 5.
Draw the schematic diagram of a hydraulic lift. Give its working principle.

Question 6.
Estimate the average thermal energy of the helium atom at a temperature of 27°C. [Boltzmann constant is 1.38 × 10^-23J/K.]

Question 7.
The graph below exhibits the anomalous expansion of water.


Based on the graph, explain how lakes freeze from the top to bottom rather than from bottom to top.

Question 8.
Match the following in three columns.

Question 9.
a. The figure below shows the ‘parallax method’ to measure the distance ‘D’ of a planet ‘S’ from the earth.


Mark the parallax angle ‘0’ in the figure. Explain how the distance ‘D’ can be measured.

b. Check whether the equation mv² = mgh is dimensionally consistent. Based on the above equation, justify the following statement. “A dimensionally correct equation need not be actually an exact equation”.

Question 10.
a. Choose the correct statement/statements related to uniform circular motion.
i. The acceleration in uniform circular motion is tangential to the circle.
ii. The acceleration in uniform circular motion is directed radially inwards.
iii. The velocity in uniform circular motion has constant magnitude.
iv. The velocity in uniform circular motion is directed radially inwards.
b. A particle is projected up into the air from the point with a speed of 20 m/s at an angle of projection 30°. What is the maximum height reached by it?

Question 11.
a. The escape speed from the surface of the earth is given by …………………..

b. An artificial satellite circulating the earth is at a height 3400 km from the surface of the earth. If the radius of the earth is 6400 km and g = 9.8 m/s², calculate the orbital velocity of the satellite.

Question 12.
a. Among the following, which are examples of simple harmonic motion?
i. The rotation of the earth about its axis.
ii. Vertical oscillations of a loaded spring.
iii. Oscillations of a simple pendulum.
iv. Uniform circular motion.
b. The displacement in simple harmonic motion can be represented as x(t) = A Cos(ωt+ Φ), where ‘Φ’is the phase constant. Identify and define ‘A’ and ‘co’ in the equation.

Question 13.
a. A transverse harmonic wave is described j by y=3.0 Sin (0.018 × + 36t), where ‘x’ and ‘y’ are in cm. The amplitude of this; the wave is

b. The figure below shows the fundamental mode or first harmonic in a stretched j string when a standing wave is formed ‘ in the string.

Draw the figure that shows the second; harmonic in the string. If ‘L’ is the length of the string and Vis the speed of the: wave in the string, what are the equations of first and second harmonic frequent:

Question 14.
An object released near the surface of the I earth is said to be in free fall. (Neglect the air resistance)

a. Choose the correct alternative from the clues given at the end of the statement. “Free fall is an example of accelerated motion”.

b. The incomplete table shows the velocity (υ) of a freely falling object in a time interval of 1 s. (Take g = 10 m/s²)

Complete the table and draw the velocity time graph.

c. Area under velocitytime graph gives.

Question 15.
The schematic diagram of the circular motion of a car on a banked road is shown in the figure.


a. If the centripetal force is provided by the horizontal components of ‘N’ and ‘F’ arrive at an expression for maximum safe speed.

b. The optimum speed of a car on a banked road to avoid wear and tear on its tyres is given by …………….

Question 16.
Energy of a body is defined as its capacity of doing work”.
a. The energy possessed by a body by virtue of motion is known as ………….
b. A body of mass 5 kg initially at rest is subjected to a horizontal force of 20 N. What is the kinetic energy acquired by the body at the end of 10 s?
c. State whether the following statement is TRUE or FALSE. “The change in kinetic energy of a particle is equal to the work done on it by the net force”.

Question 17.
The angular momentum of a particle is the rotational analogue of its linear momentum.

a. The equation connecting angular momentum and linear momentum are ……………

b. Starting from the equation connecting angular momentum and linear momentum, deduce the relation between torque and angular momentum.

Moment of inertia in rotational motion is analogous to mass in linear motion.

a. The moment of inertia of a circular disc about an axis perpendicular to the plane, at the center is given by ………….

b. State perpendicular axis theorem and by using the theorem, deduce the moment of inertia of the circular disc about an axis passing through the diameter.

Question 18.
A region of streamline flow of an incompressible fluid is shown in the figure.

a. By considering mass conservation in the fluid flow, arrive at the ‘equation of continuity’.

b. The onset of turbulence in a fluid is determined by ‘Reynolds number’, given as …………….

Schematic diagram of capillary rise in a narrow tube is shown in the figure.

a. Arrive at an expression for capillary height ‘h’ in terms of the surface tension of the liquid.

b. On the surface of the moon, the liquid in a capillary tube will rise to the ……………..

i. same height as on earth,

ii. less height as on earth

iii. more height than that on earth

iv. infinite height.

Answers

Answer 1.
Viscous force (Not a fundamental force in nature)

Answer 2.
Figure 2. (Law of a moment of inertia) When the man stretched his arm, according to a law of conservation of angular momentum the distance from the axis of rotation increases and
so a moment of inertia increases and thereby angular speed decreases.

Answer 3.
Zeroth law of thermodynamics. 0 .05/10

Answer 4.

OR

Answer 5.
Pascal’s law is the working principle behind the hydraulic lift. Pascal’s law states that The pressure in a fluid at rest is same at all points if we ignore gravity.

If the pressure in a liquid is changed at a particular point, the change is transmitted to the entire liquid without being diminished in magnitude. The pressure exerted at any point on an enclosed liquid is transmitted equally in all directions.

Construction: It is a simple application of Pascal’s law. There are two cylinders C₁ and C₂ of cross-sectional areas A₁ and A₂ connected by a pipe. Pistons are fitted in both cylinders. The load to be lifted is kept on the platform of the piston with more area (A₂>A₁). The cylinders and pipe contain a liquid.

Working: A force is applied on the smaller piston. Then pressure exerted on the liquid is, \(P=\frac { { F }_{ 1 } }{ A }\) According to Pascal’s law, the same pressure ‘P’ is transmitted to the larger piston. Force on larger piston ¡s

Hence by making the ratio A₂/A₁ large, very heavy loads like cars can be lifted by using a small force.

Answer 6.

Answer 7.
When water is cooled from 4°C to 0°C, it expands. So ¡ce at 0°C ¡s less dense (more volume) than water at 4°C. When lake starts cooling water at the top reaches 4°C and sinks to the bottom due to high density. This continues till whole water reaches 4°C. Now when the temperature decreases to zero water on the top becomes ice which is less dense than the water below. So it does not sink.

Answer 8.

Answer 9.

To measure the distance D of a faraway planet S by the parallax method, we observe it from two different positions (observatories) A and B on the earth, separated by distance AB = b at the same time as in fig. We measure the angle between the two directions along which the planet is viewed at these two points. The ∠ASB represented by symbol 0 is called the parallax angle or parallactic angle.

As the planet is very far away, \(\frac { { b } }{ D } <<1\) and therefore, O is very small. Then we approxi mately take AB as an arc of length b or a circle with centre at S and the distance D as the radius AS = BS. So that AB = b = DO where O is in radians \(D=\frac { { b } }{ \theta }\)

b. mv² = mgh, takig dimension on both sides
[M] [LT^-1]² = [M] [LT^-1] [L]
[ML²T²] = [M¹L²T²]
The given equation is dimensionally cor rect. This is not the exact equation, which is mgh. Since the fraction ½ has no dimension, the complete consistency can’t be checked.

Answer 10.

Answer 11.

Answer 12.
a. (ii) and (iii)
b. A is the amplitude and w is the angular frequency.

Amplitude is the maximum displacement of the oscillating particle on either side of its mean position. Thus X_mxv = + A Angular frequency is equal to the product of the frequency of the body and 27t.

Answer 13.
a. 3 cm
b.Fundamental mode (or) First harmonic If the string is plucked in the middle and released, then it vibrates ¡n one segment with nodes at its ends and an antinode in the middle.

This is the lowest frequency with which string vibrates.

Second harmonic If the string is pressed in the middle and plucked at one-fourth of its length, then the string vibrates in two segments.

Answer 14.
Uniformly.

c. Displacement

Answer 15.
a. To avoid skidding and damage to tires of vehicles, the outer part of a road is slightly raised than the inner part. This is known as banking of roads.

1. The weight of the car vertically downwards.
2. Normal reaction R acting normal to the road.
3. Frictional force acting parallel to the road. Since there is no vertical acceleration,
R cosθ = mg + Fsinθ
or Rcosθ Fsinθ = mg …(1)
Now for maximum speed, F = μ, R
The centripetal force is provided by horizontal components of R and F as shown in the figure.

Answer 16.

Answer 17.

b. This theorem is good for flat bodies which means, thickness much less than length and breadth. The theorem states that “the moment of inertia of a planar body about an axis perpendicular to its plane is equal to the sum of moments of inertia about two mutually perpendicular axes passing through the same point, lying on the plane”. Moment of inertia about diameter can be found using perpendicular axis theorem.

Answer 18.
a. Consider a nonviscous (no internal friction) and incompressible (density constant during flow) liquid flowing steadily between the sections P and R of a pipe of varying cross-section. Let the area of a cross section at P be A, and that at R be A₂. Let the speed of fluid be v₁ at P and v₂ at R.

As, m = volume × density = area of cross-section × length × density Mass of fluid that flows through P in time Δt, m₁ = A₁v₁P₁ Δt
Mass of fluid that flows through R in time At, m2 = A₂V₂P₂ Δt
By conservation of mass, m1 = m₂
A₁v₁P₁ Δt = A₂v₂p₂ Δt and P₁ = p₂ (incompressible fluid)
A₁v₁= A₂v₂
The product of the area of crosssection and the speed remains the same at all points of a tube of flow. This is called the equation of continuity and expresses the law of conservation of mass in fluid dynamics.
b. iii \(\frac { p\upsilon d }{ n } =Re\)

OR

a. When a clean capillary tube is dipped in a liquid, which wets it, the liquid immediately rises in the tube. This is called capillary rise.

Consider a capillary tube of radius ripped vertically in a liquid of density p and surface tension a. The meniscus of the liquid inside the tube is concave. Thereby the liquid rises through the tube to some height. Let ‘ R’ be the radius of the meniscus, 0 be the angle of contact and h the height of the liquid column in the tube with respect to the level of a liquid outside.

Here the hydrostatic pressure exerted by the liquid column becomes equal to the excess pressure p. Therefore at equilibrium, we have p = hpg

b. iii. more height than that on earth

Plus One Physics Previous Year Question Papers and Answers

Kerala Plus One Physics Previous Year Question Paper 2018

Time: 2 Hours
Cool off time: 15 Minutes
Maximum: 60 Scores

General Instructions to candidates

• There is a ‘cool off time’ of 15 minutes in addition to the writing time.
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read the instructions carefully.
• Read questions carefully before you answering.
• Calculations, figures, and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• Give equations wherever necessary.
• Electronic devices except non-programmable calculators are not allowed in the Examination Hall.

Answer any four questions from question numbers 1 to 5. Each carries one score.

Question 1.
The branch of Physics, that was developed to understand and improve the working of heat engines is …………
a. Optics
b. Thermodynamics
c. Electronics
d. Electrodynamics

Question 2.
State the theorem of parallel axes on a moment of inertia.

Question 3.
Select a TRUE statement from the following:
a. A year and light year have the same dimensions.
b. The intensity of the gravitational field has the same dimensions as that of acceleration.
c. One angstrom is the mean distance between sun and earth.
d. Parsec is a unit of time.

Question 4.
If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its …………….. energy.

Question 5.
What is the time period of a second’s pendulum?

Answer any five questions from question numbers 6 to 11. Each carries two scores.

Question 6.
Using a suitable velocity-time graph, derive the relation x = v₀t+ ½ at².

Question 7.
A boy throws a ball of mass 200 g with a velocity 20 ms^-1 at an angle of 40° with the horizontal. What is the kinetic energy of the ball at the highest point of the trajectory?

Question 8.
Write the work done in each of the following cases as zero, positive or negative.
a. Work was done by centripetal force in circular motion.
b. Work was done by friction.
c. Work was done by the gravitational force on a freely falling object.
d. Work was done by the applied force in lifting an object.

Question 9.
Derive an It escapes velocity of an object from the surface of a planet.

Question 10.
A typical stress-strain graph of a metallic wire is shown below.


a. Write the name of the point B labeled in the graph.
b. For materials like copper, the points D and E are ………………. (close/far apart).

Question 11.
The terminal velocity of a copper ball of radius 2.0 mm falling through a tank of oil at 20°C is 6.5 cm s^-1. Calculate the viscosity of the oil at 20°C.
(Hints: Density of oil is 1.5 × 10³ kg m^-3, a density of copper is 8.9 × 10³ kg m^-3.)

Answer any live questions from question numbers 12 to 17. Each carries three scores.

Question 12.
A body falling under the effect of gravity is said to be in free fall.

a. Draw the velocity-time graph for a freely falling object.

b. Define uniform acceleration.

c. From the given figures, identify the figure which represents uniformly accelerated motion.

Question 13.
A gun moves backward when a shot is fired from it.
a. Choose the correct statement.
i. The momentum of the gun is greater than that of the shot.
ii. The momentum acquired by Jche gun and shot have the same magnitude.
iii. Gun and shot acquire the same amount of kinetic energy.
b. A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m/s, what is the recoil speed of the gun?

Question 14.
Acceleration due to gravity decreases with depth.
a. Prove the above statement by deriving the proper equation.
b. Using the equation, show that acceleration due to gravity is maximum at the surface and zero at the center of the earth.

Question 15.
A device used to lift automobiles is shown in the figure.


a. Write the name of the device

b. In the situation shown in the figure, a mass of the car is 3000 kg and area of the piston carrying it is 425cm2. What pressure is to be applied to the smaller piston?

Question 16.
Based on the kinetic theory of gases, derive an expression for the pressure exerted by an ideal gas.

Question 17.
When 0.15 kg of ice at 0°C is mixed with 0.30 kg of water at 50°C in a container, the resulting temperature is 6.7°C. Calculate the latent heat of fusion of ice. Given specific heat capacity of water 4186 J kg^-1K^-1.

Answer any four questions from question numbers 18 to 22. Each carries four scores.

Question 18.
The accuracy in measurement depends on the limit or the resolution of the measuring instrument.
a. State whether the above statement is TRUE or FALSE.
b. A physical quantity P is related to four observables a,b,c, and d as P= The percentage errors in measurements of a,b,c, and d are 1%, 3%, 2%, and 3% respectively. What is the percentage error in the measurement of P?

Question 19.
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed.
a. What is the angle between velocity and acceleration at any instant of motion?
b. If the stone makes 14 revolutions in 25 s,
what is the magnitude of the acceleration of the stone?

Question 20.
a. If \(\xrightarrow { A }\) is perpendicular to \(\xrightarrow { B }\), what is the
value of \(\xrightarrow { A }\).\(\xrightarrow { B }\)?
b. Find the angle between the force \(\xrightarrow { F }\) = (\(3\hat { i }\) + \(4\hat { j }\) –\(5\hat { k }\))N and displacement \(\xrightarrow { d }\) = (\(5\hat { i }\) + \(4\hat { j }\) + \(3\hat { k }\))m.

Question 21.
Schematic diagram of a device is shown below.

a. Write the equation for the efficiency of the device.

b. Write the name of the four processes in the working cycle of the device

c. If T₁ =100°C, T₂ = 0°C, and Q₁ = 4200 J find the value of Q₂

Question 22.
a. Which one of the following relationships between the acceleration (a) and the displacement (x) of a particle involves simple harmonic motion?

i. a = 0.7 x
ii. a = 200 x
iii. a = 10x
iv. a=100x
b. A simple harmonic motion is represented as x = A cost. Obtain the expression for velocity and acceleration of the object and hence prove that acceleration is directly proportional to the displacement.

Answer any three questions from question numbers 23 to 26. Each carries five scores.

Question 23.
a. What is the condition for the equilibrium of concurrent forces?

b. A mass of 6 kg is suspended by a rope of length 2m from the ceiling. A force of 50 N in the horizontal direction is applied at the midpoint P of the rope, as shown. What is the angle, the rope makes with the vertical in equilibrium? (Take g=10 ms 2). Neglect the mass of the rope.

c. What will be the angle made by the rope with the vertical if its length is doubled?

Question 24.
a. Write the equation connecting torque with force.

b. A meter stick is balanced at its cecenter50 cm). When two coins, each of mass 5 g, are put one on the top of the other at the 12 cm mark, it is found to be balanced at 45 cm. What is the mass of the stick?

c. Derive the relation connecting torque with angular momentum.

Question 25.
a. Water rises up in a narrow tube in spite of gravity. This phenomenon is called…
b. Derive an expression for the height of water in the tube in terms of the radius of the tube and surface tension of the liquid.
c. Water with detergent dissolved in it should have an angle of contact. (Small/large)

Question 26.
The fundamental mode of vibration of a stretched string is shown below.


a. Draw the second and third harmonics.
b. Prove that frequencies produced in the string are in the ratio of 1: 2: 3.
c. Let the fundamental frequency is 45 Hz and the length of the wire is 87.5 cm. If the linear density of the wire is 4.0 × 10² kg/m. Find the tension in the string

Answers

Answer 1.
Thermodynamics

Answer 2.
This theorem is good for any shape. The moment of inertia of the body about any axis is equal to the sum of a moment of inertia of a parallel axis passing through the center of mass and product of its mass of the body and square of the distance between the two parallel axes. I = I_g + Ma²

Answer 3.
b

Answer 4.
Kinetic energy

Answer 5.
T = 2sec

Answer 6.

The area under the velocity-time graph gives the displacement of the body. Displacement, x = area OABD x = area of triangle ABC+ area of rectal

Answer 7.
At the top V = 0, V_x = ucosθ

Answer 8.
a. Zero
b. Zero or negative ( 0 for static)
c. Positive
d. Positive

Answer 9.
The total work done to move a body of mass’m’ from the surface of the earth (r=R) to
infinity (r = ) is given by, \(W=\frac { GMm }{ R }\)
Let v be the velocity of the body, then K.E of the body, when projected, is K = 1/2 mv² The body can escape from the gravitational pull of earth only if the KE is greater than or equal to the work done in overcoming the gravity.

Answer 10.
a. Elastic limit or Yield point
b. Far apart (Copper is malleable)

Answer 11.

Answer 12.

b. Equal change in velocity in an equal time interval.
c. Fig(3)

Answer 13.

Answer 14.

Answer 15.
a. Hydraulic Lift

Answer 16.

Consider a gas contained in a cubical vessel of side 7 and volume V = B. Let there be ‘n’ molecules per unit volume of the gas, each of masses’. Hence the total mass of the gas in the vessel M = nm × v The molecules are having random velocities and since the motion is not under a force. Consider such a molecule moving with a velocity V along X-direction as shown in the figure. As it moves in the positive X-direction it undergoes elastic collision and is a bounce from the wall O’A’B’C’. The momentum of the molecule before collision = mv

Momentum after collision=mv (rebounding) Change in momentum= mv (mv) = 2mv Hence the change of momentum imparted to the wall = 2mv For this molecule to undergo the next collision with the same wall it has to travel a distance 2l. The time to travel this distance by the molecule is given by t = 2//v Number of collision per second with this wall =\(\frac { l }{ t }\) = \(\frac { l }{ 2l }\)

According to Newton’s second law change in momentum per second = force on the wall. i.e., the thrust by 1 molecule. Taking all the ‘n’ molecules in a unit volume of the vessel, each will be travelling in x, y, z direction on the average. Let V₁ V₂, V₃, ………… V_n be the velocities of n molecules. Then average value of velocity square is shown as below.

where \(\vec { V }\) is called the root mean square velocity (rms velocity of the molecule), rms velocity of a gas molecule is defined as the square root of the mean of the squares of the velocities of the gas molecules. It is given by

Answer 17.

Answer 18.

Answer 19.

Answer 20.

Answer 21.

b. Isothermal expansion Adiabatic expansion Isothermal compression Adiabatic compression

Answer 22.

Answer 23.
a. Vector sum of all the forces = 0

c. All the fores are independent of length (for massless string)

Answer 24.

Differentiating with respect to line

Answer 25.
a. Cappilarity/Capillary rise
b. When a clean capillary tube is dipped in a liquid, which wets it, the liquid immediately rises in the tube. This is called capillary rise.

Consider a capillary tube of radius rdip ped vertically in a liquid of density p and surface tension a. The meniscus of the liquid inside the tube is concave. Thereby the liquid rises through the tube to some heightLet ‘R’ be the radius of the meniscus, 0 be the angle of contact and h the height of the liquid column in the tube with respect to the level of liquid outside.

Here the hydrostatic pressure exerted by the liquid column becomes equal to the excess pressure p. Therefore at equilibrium, we have


c. Small

Answer 26.

In an open tube, both ends are open. At both ends, antinodes are formed. The mode of vibration of the open organ pipe are

Plus One Physics Previous Year Question Papers and Answers

Kerala Plus One Maths Model Question Paper 4

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

• There is a ‘cool off time’ of 15 minutes in addition to the writing time .
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read instructions carefully .
• Read questions carefully before you answering.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• .Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Questions 1 to 7 carry 3 scor each. Answer any 6.

Question 1.
Consider the Venn-diagram given below.

Question 2.
For any triangle ABC, prove that

Question 3.
Consider the complex number z = 3 + 4i
a. Write the conjugate of z.
b. Verify that z z =|z|²

Question 4.
a. Solve the inequality

b. Represent the solution in real line

Question 5.
4 cards are drawn from a wellshuffled pack of 52 cards.
a. In how many ways can this be done?
b. In how many ways can this be done if all 4 cards are of the same colour?

Question 6.
Consider the equation of the ellipse 9x²+ 4y² = 36. Find
a. Focii
b. Eccentricity
c. Length of latus rectum

Question 7.

Questions from 8 to 17 carry 4 scor each. Answer any 8.

Question 8.
Consider A = {x : x is an integer, 0 < x ≤ 3}
a. Write A in roster form.
b. Write the power set of A.
c. The number of proper subsets of A =
d. Write the number of possible relations from A to A.

Question 9.
Consider the statement

a. Show that P(1) is true.
b. Prove that P(n) is true for all n ∈ N using principle of mathematical induction.

Question 10.
Consider the complex number, z =
\(\frac { 1 + 3i }{ 1 + 2 i}\)
a. Write z in the form a + ib.
b. Write z in polar form

Question 11.
Solve the following inequalities graphically

Question 12.
a. How many 3 letter words with or without meaning can be formed using 26 letters in English alphabet, if no letter is repeated?
b. Find the number of permutations of letters of the word MATHEMATICS
c. How many of them begin with the letter C?

Question 13.
Consider the figure given below. A (3, 0) and B (0, 2) are two points on axes. The line OP is perpendicular to AB.

a. Find the slope of OP.
b. Find the co-ordinates of the point P.

Question 14.
Equation of the parabola given in the figures is y= 8x.

a. Find the focus and length of latus rectum of the parabola.
b. The latus rectum of the parabola is a chord to the circle centered at origin as shown in the figure. Find the equation of the circle.

Question 15.
Let L be the line x – 2y+3 = 0.
a. Find the equation of the line L₁ which is parallel to L and passing through (1, -2).
b. Find the distance between L and L₂.
c. Write the equation of another line L₂ which is parallel to L, such that the distance from origin to L and L₂ are the same.

Question 16.
Consider the points A (3, 2, 01).
a. Write the octant in which A belongs to
b. If B (1, 2, 3) is another point in space, find distance between A and B.
c. Find the coordinates of the point R which divides AB in the ratio 1 : 2 internally.

Question 17.
a. Write the contrapositive of the statement:
P : If a triangle is equilateral, then it is isosceles.
b. Prove by the method of contradiction ‘ √3 is irrational’

Questions from 18 to 24 carry 6 score each. Answer any 5.

Question 18.
a. If A = {a, b} write A x A x A
b. If R = {(x,x³) : x is a prime number, less than 10}. Write R in roster form.
c. Find the domain and range of the function f (x) = 2+ √x-1

Question 19.
a. The minute hand of a watch is 3 cm long. How far does its tip move in 40 minutes? (Use π = 3.14).
b. Solve the trigonometric equation sin 2x-sin 4x + sin 6x = 0.

Question 20.
a. Find the sum of all 3 digit numbers which are multiples of 5.
b. How many terms of the GP 3, 3², 3³, …. are needed to give the sum 120?
c. Find the sum of first n terms of the series whose n* term is n(n + 3).

Question 21.
a. Expand using binomial theorem,
b. Find (a+b)4 – (a-b)⁴
c. Hence find (√3 + √2)4 -(√3-√2)4

Question 22.
a. Find the derivative of the function y = 1/x from first principles.
b. Differentiate f(x) = ,\(\frac { cos x }{ 1 + sinx }\)
with respect to x.

Question 23.
Calculate the mean deviation about median for the following data.

Question 24.
Consider a bag containing 3 red balls R₁, R₂, R₃ and 2 black balls B₁, B₂, which are identical. 2 balls are drawn simultaneously at random from the bag.
a. Write the sample space of the random experiment.
b. Write the event
A : Both balls are red B : One is red and one is black
c. Show that A and B are mutually exclusive
d. Find P(A) and P(B)

Answers

Answer 1.
a. A’= {5, 6, 7, 8, 9}
B’= {1, 2, 7, 8, 9}
(A ∩ B)’ = {l,2,5,6, 7, 8, 9}
b. LHS = (A ∩ B)’ = {1,2, 5, 6, 7, 8,9}
RHS=A’∪B’= {1,2, 5, 6, 7, 8, 9}
∴(A∩B)’= A’∪B’

Answer 2.

Answer 3.
a. conjugate of z = 3 + 4i = 3 – 4i
b. z z̄ = (3+4i) (3-4i) = 9 – 16i² = 9 – (-16) = 25
\({ \left| z \right| }^{ 2 }={ \left( \sqrt { { 3 }^{ 2 }+{ 4 }^{ 2 } } \right) }^{ 2 }={ \left( \sqrt { 25 } \right) }^{ 2 }=25\)
\(\Rightarrow z=\bar { z } ={ \left| z \right| }^{ 2 }\)

Answer 4.

Answer 5.
a. No. of ways = ⁵²C₄ = 270725
b. No. of ways of all cards of the same colour = ²⁶C₄+²⁶C₄ = 2 x ²⁶C₄ = 29900

Answer 6.
The standard form of the ellipse is \({ x }^{ 2 }+{ y }^{ 2 }\) = 1, is an ellipse whose major axis is on the y-axis.
a = 3, b = 2
c = \(\sqrt { { a }^{ 2 }-{ b }^{ 2 } } \) = \(\sqrt { 9-4 } \) = √5
a. Focii = (0, ± c) = (0, +√5)
b. Eccentricity = c/a = √5/3
c. Length of latus rectum = \(\frac { { 2b }^{ 2 } }{ a } =\frac { { 2\times 2 }^{ 2 } }{ 3 } =\frac { 8 }{ 3 } \)

Answer 7.

Answer 8.
a. A = {1, 2, 3}
b. Power set of A = P(A)={ 1,2,3}, {1,2}, {1,3}, {2,3}, {1}, {2}, {3}, φ}
c. No. of proper subject of A = 2ⁿ-1 = 2³-1 = 7
d. No. of relations from A to A = 2^mxm=2^3×3 = 512

Answer 9.

Answer 10.

Answer 11.

Answer 12.
a. No. of words = ²⁶P₃ = 15600
b. The word MATHEMATICS has

c. If the letter C is fixed first, the remaining 10 letters can be permuted as

Answer 13.
a. Slope of OP

b. Equation of OP is

Answer 14.
Equation of parabola is y² = 8x ⇒ a = 2
a. Focus = (a, 0) = (2, 0)
Length of latus rectum = 4a = 4 x 2 = 8
b. Coordinates of A is (a, -2a) = (2, -4) and that of B iss (1, 2a) = (2, 4)
∴ Radius of the circle

Answer 15.
a. Equation of L is x-2y + 3 = 0

its given that distance from origin to L and L₂ are same. We have,

Answer 16.

Answer 17.
a. Contrapositive statement: If a triangle is not isosceles, then it is not equilateral.
b. Let us assume that √3 be rational ∴√3 = a/b, where a and b are co-prime, i.e., a and b have no common factors othe than 1.
3b² = a² ⇒ 3 divides a.
∴ there exists an integer ‘k’ such that a = 3k
∴ a² = 9k² ⇒ 3b² = 9k² ⇒b² = 3k² ⇒3divides b.
i.e., 3 divides both a and b, which is contradiction to our assumption that a and b have no common factor.
∴ our supposition is wrong.

Answer 18.
a. Ax Ax A={(a, a, a), (a, a, b), (a, b, a),
(a, b, b), (b, a, a), (b, a, b), (b, b, a), (b, b, b)}
b. R = {(2, 8), (3, 27), (5, 125), (7, 343)}
c. Domain=[1, ∞ ),{x/x ≥ 1}
Range = [2,∞), {y/y ≥ 2}

Answer 19.
a. The required distance moved

Answer 20.

Answer 21.

Answer 22.

Answer 23.

Answer 24.

Plus One Maths Previous Year Question Papers and Answers

Kerala Plus One Maths Model Question Paper 3

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

• There is a ‘cool off time’ of 15 minutes in addition to the writing time .
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read instructions carefully .
• Read questions carefully before you answering.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• .Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Questions 1 to 7 carry 3 score each. Answer any 6.

Question 1.
a. Write set is the subset of all the given sets?
(a) {1,2,3,….}
(b) {1}
(c) {0}
(d) {}
b. Write down the power set of A = {1,2,3}

Question 2.
In any triangle ABC, prove that
a(SinB- sinC) + b(sinC- sinA) +c(sinA- sinB) = 0

Question 3.
a. Solve x² + 2 = 0
b. Find the multiplicative inverse of 2-3i
a. x² + 2 = 0

Question 4.
a. Solve

b. Find the graphical solution of the above inequality.

Question 5.
a. A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of atmost 3 girls,
b. Find n if ²ⁿC₃: ⁿC₃ = 12 : 1

Question 6.
a. The new coordinates of the points (2, 5) if the origin is shifted to the point (1, 1) by translation of axes.
A) (3, 1) B(1, 3) C (-1, 3) D (3, -1)
b. Find what the equation x² + xy – 3y²– y + 2 = 0 becomes when the origin is shifted to the point (1,1)?

Question 7.
Evaluate :

Questions from 8 to 17 carry 4 score each. Answer any 8.

Question 8.

Question 9.
Consider the statement 1.3 + 2.3² + 3.3³

a. Verify whether the statement is true for n =1.
b. Prove the result by using principle of mathematical induction.

Question 10.
a. Express (1 + i)³ + (1 – i)³ in a + ib form.
b. Find the polar form of the complex number – 1 – i.

Question 11.
solve the following linear inequalities graphically:

Question 12.
a. “P_r =

b. The letters of the word FATHER be permuted and arranged in a dictionary, find the rank of the word FATHER?

Question 13.
a. The distance of the point P(1,-3) from the line 2y – 3x = 4 is
A) 13
B)  \(\frac { 7 }{ 13 } \sqrt { 3 } \)
C) √13
D) None of these
b. Reduce the equation√3x + y + 8 = 0 in to normal form. Find the values of P and ω
imagee

Question 14.
a. A conic with e = 0 is known as
A) a parabola
B) an ellipse
C) a hyperbola
D) a circle
b. Consider the circle x² + y² + 8x + 10y – 8 = 0
i) Find the centre C and radius ‘r’.
ii) Find the equation of the circle with centre at C and passing through the point (1, 2)

Question 15.
a. What is the perpendicular distance from the point P(6,7,8) from XY plane.
A) 8
B) 7
C) 6
D) 9
b. Find the equation of the set of points P, the sum of whose distances from A(4,0,0) and B(-4,0,0) is equal to 10.

Question 16.
a. Convert 20°40‘ into radian measure.
b. If sin x = \(\frac { 12 }{ 13 } \) and x is an acute angle, find the value of cos 2x.
c. Prove that
\(\frac { sinx-sin\quad 3x }{ { sin }^{ 2 }x-{ cos }^{ 2 }x } \)
= 2 sin x.

Question 17.
a. Write the component statements of the following statement: All prime numbers are either even or odd
b. Verify by the method of contradiction, p = √7 is irrational

Questions from 18 to 24 carry 6 score each. Answer any 5.

Question 18.
a. Write the interval (6,12) in the set-builder form.
b. Draw the Venn diagram of the following sets :
i) A’ ∩ B’
ii)A – B
c. In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis? How many like tennis only and not cricket?

Question 19.
a. Write the number of terms in the expansion of (a – b)²ⁿ
b. Find the general term in the expansion of (x²– yx)¹², x ≠ 0
c. Find the coefficient of x⁶ y³ in the expansion of (x + 2y)⁹

Question 20.
a. The common ratio of the G.P is \(\frac { -4 }{ 5 } \) and the sum to infinity is \(\frac { -80 }{ 9 } \). Find the first term.
b. Evaluate:

c. Find the sum of first n terms of the series : 0.6+0.66+0.666+…….to n terms.

Question 21.
a. Find the derivative of xⁿ from first principles.

Question 22.
a. Find the point of intersection of the lines 2x + y = 5 and x + 3y + 8 = 0.
b. Find the equation of a line passing through the point of intersection of the above lines and parallel to the line 3x + 4y =7.
c. Find the distance between these two paralle lines.

Question 23.
a. Find the Mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from mean is ………

b. Calculate mean, variance and standard deviation of the following distribution:

Question 24.
a. In aleap year the probability of having 53 Sundays is ……..

b. Events E and F are such that P (not E or not F) = 0.25, state whether E and F are mutually exclusive.
c. How many points are there in a sample space, if a card is selected from a pack of 52 cards.

Answer

Answer 1.
a. d) { }
b. P(A)={{1,2,3}, {1,2}, {2,3}, {1,3}, {1}, {2}, {3}, ø}

Answer 2.
LHS = a (sinB-sinC) + 6(sinC-sinA) +c (sinA-sinB)
= 2R sin A(sinB-sinC) + 2R sin B (sinC-sinA)+2R sinC (sinA – sinB)
= 2R [sin A sin B – sinAsinC + sinB sinC – sinBsinA + sinCsinA – sin C sinB]
= 2R x 0 = 0 = RHS

Answer 3.

Answer 4.

Answer 5.

Answer 6.
a. B) (1, 3) since [2 – 1, 5 – 2]
b. Let the coordinates of a point P changes from (x,y) to (X,Y) when origin is shifted to (1,1)
∴ x = X + 1, y = Y + 1 Substituting in the given equation, we get
(X+1)² + (X + 1) (7 + 1) -3 (7 + 1)² -(7 + 1) + 2 = 0
⇒ X²+2X + 1 + XY + X+ Y+ 1-3 (P + 27 + 1) – (7+ 1) + 2 – 0
⇒ X² – 3Y² + XY + 3X- 6Y = 0
∴ Equation in new system is
X² – 3Y² + XY + 3X -6Y = 0

Answer 7.

Answer 8.

Answer 9.

Answer 10.

Answer 11.

Answer 12.
a. D
b. The alphabetical order of the word ‘ FATHER are A, E, F, H, R, T No. of words beginning with

Answer 13.

Answer 14.
a. D
b. Comparing x² + y¹ – 8x +10 y – 12 = 0 with

Answer 15.
a. A. 8 [ || perpendicular distance of a point from XY plane = z coordinate
b. Let P(x, y, z) be the point such that PA + PB = 10

Answer 16.

Answer 17.
a. p: All prime numbers are even. q: All prime numbers are odd
b. Let us assume that √7 is a rational number
∴ √7 = , where a and b are co-prime, i.e. a and b have no common factors, which implies that 7b² – a² ⇒ 7 divides a.
∴ there exists an integer ‘k’ such that a = 7k
a² = 49k² ⇒ 7b² = 49k²⇒b²= 7k² 7 divides b.
i.e., 7 divides both a and b, which is contradiction to our assumption that a and b have no common factor.
∴ our supposition √7 is wrong, is an irrational number.

Answer 18.
a. {x : x ∈ R, 6 < x ≤ 12}

Answer 19.
a. Number of terms in expansion can be given by 2n + 1
b. General term can be given by

Answer 20.

Answer 21.

Answer 22.
a.  2x + y =5 ……………. (1)
x + 3y = -8………………….. (2)
(1) x 3 – (2) ⇒
6x + 3y = 15 x + 3y = -8
(-) (-) (+)
————-
5x  = 7 7
∴ x = 7/5

b. Slope of the required line, m = \(-\frac { 3 }{ 4 } \)
|| slope of the parallel line Equation of the line is y – y = m (x – x₁)

Answer 23.
a. b


c. The parallel lines 15x + 20y – 57 = 0 and
3x + 4y – 7 = 0 ⇒15x + 20y – 35=0 x ing by 5
Parallel distance

Answer 24.
a. (b) 7/3
b. (not E or not F)
= P(E ‘∪ F’) = P(E ∩ F)’ = 1 = 1P(E ∩ F)
⇒ 0.25 = 1 -P(E n F) ⇒ p(E ∩ F) = 1 -0.25 = 0.75 ≠ 0
⇒ E and F are not mutually exclusive
c. 52

Plus One Maths Previous Year Question Papers and Answers

Kerala Plus One Maths Model Question Paper 2

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

• There is a ‘cool off time’ of 15 minutes in addition to the writing time .
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read instructions carefully .
• Read questions carefully before you answering.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• .Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Answer any six from question numbers 1 to 7. Each carries three scores.

Question 1.
Find 7+ 77 + 777 + 7777 +…. to n terms.

Question 2.

Question 3.
a. If A and B are two events in a random experiment, then
P(A) + P(B) – P(A ∩ B)
b. Given P(A) = 0.5, P(B) = 0.6 and P
(A ∩ B) = 0.3. Find P( A ∪ B) and P(A’).

Question 4.
Let A = {x:x is an integer, 1/2 < x < 7/2}
B = {2, 3, 4}
a. Write A in the roster form.
b. Find the power set of (A ∪ B)
c. Verify that (A – B )∪ (A ∩ B)=A

Question 5.
(i) Find the value of sin
\(\left( \frac { 3l\pi }{ 3 } \right) \)
(ii) Find the principal and general solutions of the equation cosx =
\(\frac { -\sqrt { 3 } }{ 2 } \)

Question 6.
A committee of 3 persons is to be constituted from a group of 2 men and 3 women.
a. In how many ways can this be done?
b. How many of these committees would consist of 1 man and 2 women.

Question 7.
a. Which one of the following points lies in the sixth octant?
i. (-4, 2, -5)
ii. (-4, -2, -5)
iii. (4, -2, -5)
iv. (4, 2, 5)
b. Find the ratio in which the YZ plane divides the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8).

Answer any six from question numbers 8 to 17. Each carries four scores.

Question 8.
Consider the following statement :

a. Prove that P(1) is true.
b. Hence by using the principle of mathematical induction, prove that P(n) is true for all natural numbers n.

Question 9.
a. Write the negation of the statement: “Every natural number is greater than zero”
b. Verify by the method of contradiction : “P : √13 is irrational”

Question 10.
a. The 8th term in the expansion of (√2+√3)
is
i. 27 √2
ii. 27 √3
iii. 72 √2
iv. 72 √3
b. Find the term independent of x in the expansion of

Question 11.
a. In a random experiment, 6 coins are tossed simultaneously. Write the number of sample points in the sample space.

b. Given that P(A’)=0.5. P(B) = 0.6, P
(A ∩ B) = 0.3. Find P(A’) , P(A ∪ B), P(A ∩ B)and P(A ∪ B).

Question 12.
Let U={1,2, 3, 4, 5, 6, 7, 8, 9}, A= {1, 2, 4, 7} and B = {1, 3, 5, 7}
a. Find A ∪ B.
b. Find A’, B’ and hence show that (A ∪B)’ = (A’∩ B’)
c. The power set P(A ∪ B) has elements.

Question 13.
a. Let A= {7, 8} and B = {5, 4, 2} Find A x B.
b. Determine the domain and range of the
relation R defined by R = {(x, y): y = x + 1, x ∈ {0, 1,2, 3,4, 5}}

Question 14.
a. Find the distance between the points (2,-1, 3) and (-2, 1, 3)
b. Find the co-ordinates of the point which divides the line segment joining the points
(-2, 3, 5) and (1, -4,6) internally in the ratio of 2:3.

Question 15. A hyperbola whose transverse axis is X – axis, center (0,0) and the foci (±√10,0) passes through the point (3, 2)
a. Find the equation of the hyperbola.
b. Find its eccentricity.

Question 16.
a. Solve for the natural number n;
12. ⁽ⁿ⁺¹⁾ p₃ =5. ⁽ⁿ⁺¹⁾ p₃
b. In how many ways can 7 athletes be chosen out of 12?

Question 17.
Consider the statement: “n(n +1) (2n + 1) is divisible by 6”
a. Verify the statement for n = 2.
b. By assuming that P(k) is true for a natural number k, verify that P(k + 1) is true.

Answer any five from question numbers 18 to 24. Each carries six scores.

Question 18.
a. Match the following:

b. Find the derivatives of tan x using the first principles.

Question 19.
a. Find the equation of the line passing through the points (3, -2) and (-1,4).
b. Reduce the equation √3x + y – 8 = 0 into normal form.
c. If the angle between two lines is π/4 and slope of the line is 1/2, find the slope of the other line.

Question 20.
a. If x is the mean and c is the standard deviation of a distribution, then the coefficient of variation is……..

b. Find the standard deviation for the following data:
x_i : 3   8    13    18    23
f_i :  7   10  15    10    6

Question 21.
a. Which one of the following pair of a. Which one of the following pair of straight lines are parallel?
i. x – 2xy-4 = 0; 2x – 3y – 4 = 0
ii. x – 2y – 4 = 0; x – 2y – 5 = 0
iii. 2x – 3y – 8=0; 3x – 3y – 8 = 0
iv. 2x – 3y – 8 = 0; 3x – 2y – 8 = 0
b. Equation of a straight line is 3x – 4y + 10 = 0.Convert it into the intercept form and write the x-intercept and y-intercept.
c. Find the equation of the line perpen dicular to the line x – 7y + 5 = 0 and having x-intercept 3.

Question 22.
a. If (x+1, y-2) = (3,1), write the values of x and y.
b. Let A={ 1, 2, 3, 4, 5} and B={4, 6, 9} be two sets. Define a relation R from A to B by R={(x, y): x-y is a positive integer}. Find A X B and hence write R in the Roster form.
c. Define the modulus function. What is its domain? Draw a rough sketch.

Question 23.
a. Which among the following is the interval corresponding to the inequality -2 < x ≤ 3 ?
i. [-2, 3]
ii. [-2, 3)
iii. (-2, 3]
iv. (-2, 3)
b. Solve the following inequalities graphically
2x + y ≥ 4
x + y ≤ 3
2x – 3y ≤ 6

Question 24.
a. In how many ways can the letters of the word, PERMUTATIONS be arranged if:
i. the words start with P and end with S?
ii. there are always 4 letters between P and S?
b. In how many ways can 5 girls and 3 boys be seated in a row so that no two boys are together.
c. How many chords can be drawn through 21 points?

Answers

Answer 1.

Answer 2.

Answer 3.
a. P(A) + P(B) – P (A ∩ B) = P (A ∪ B)
b. P(A ∪ B) = P(A) + P(B) – P (A ∩ B)
= 0.5+ 0.6=0.3 = 1.1-0.3 = 0.8
P(A)’= 1- P (A) = 1-0.5 = 0.5

Answer 4.
a. Let A = {1, 2,3}
b. A ∪ B = {1, 2, 3,4}
P(A ∪ B)= {1}, {2}, {3}, {4},
{1, 2}, {1, 3}, {1, 4}, {2, 3},
{2, 4}, {3, 4}, {1, 2 ,3}, {1, 2, 4},
{2, 3,4}, {1,3,4}, {1,2, 3, 4},
{(j)} = 24 = 16 elements
c. A-B= {l}, A ∩ B = {2, 3}
(A – B) ∪ (A ∩ B) = {1, 2, 3} = A

Answer 5.

Answer 6.
a. Required number of ways = 5C₃ = 10
b. Number of committees =
2C₁ x 3C₂ = 2 x 3 = 6

Answer 7.
a. i. (-4, 2,-5)
b. Let YZ plane divides the line joining the points A (-2, 4, 7) and B (3, -5, 8) at R (x, y, z) in the ratio k: 1.
Then x coordinates of R = 0.

Answer 8.

Answer 9.
a. Let p : “Every natural number is greater than zero”. ~p: “ Every natural number is not greater than zero”.
b. Let us assume that √13 is a rational number.√13=a/b, where a and b are co-pnme, i.e., a and b have no common factors, which implies that 13b²= a² ⇒ 13 divides a. There exists an integer ‘k’ such that a= 13k a²= 169 k² ⇒ 13b²= 169k^{2 ⇒} 13k² ⇒ 13 divides b.
i.e., 13 dvides both a and b, which is contradiction to our assumption that a and b have no common factor. ∴ Our supposition is wrong. ∴ √13 is an irrational number.

Answer 10.

Answer 11.
a. 2⁶
b. P(A) = 0.5; P(B) = 0.6; P(A ∩ B) = 0.3
P(A’ ) = 1 – P(A) = 1 – 0.5 = 0.5
P(A ∪ B)=P(A)+P(B)-P(A ∩ B)
= 0.5 + 0.6 – 0.3 = 0.8
P( A ∩ B)=l-P P(A ∪ B)= 1-0.8 = 0.2
P(A ∪ B)=l-P(A ∩ B)= 1-0.3 =0.7

Answer 12.
U = {1,2, 3, 4, 5,7},
A = {1,2, 4, 7} and B = {1,3, 5, 7}
a. A ∪ B = {1,2, 3, 4, 5, 7}
b. A’ = {3, 5, 6, 8, 9}
B’ = {2, 4, 6, 8, 9}
A ∪ B = {1,2, 3, 4, 5, 7}
(A ∪ B)’ = {6, 8, 9}
A’∩ B’ = {6, 8, 9},
So (A ∪ B)’ = A’∩B’
c. The power set P(A ∪B) has 26 or 64 elements.

Answer 13.
a. A = {7, 8} and B = {5, 4, 2}
A x B = {(7, 5), (7, 4), (7,2), (8, 5), (8, 4), (8, 2)}
b. Domain = {0,1, 2, 3, 4, 5}
Range = {1,2, 3, 4, 5, 6}
R = {(0,1). (1, 2), (2, 3), (3, 4),(4, 5), (5, 6)}

Answer 14.

Answer 15.
Equation of hyperbola is

Answer 16.

Answer 17.
a. When n = 2,
2 (2+1) (2×2 + 1) = 2 x 3 x 5 = 30 is divisible by 6
b. P(k) = k(k + l)(2k + 1) is divisible by 6
P (k + 1) = (k + l)(k + 2) (2k + 1)
+ (k + 1) (k + 2)2 = (k + 1) (2k +1) k + (k + 1)
(2k + 1) x 2 + (k + 1) (k + 2)
= k (k + 1) (2k + 1) + 2 (k + 1)
[2k + 1 + k + 2]
= k (k + 1) (2k + 1) + 6(k + 1)²
is divisible by 6
∴ P(k + 1) is true

Answer 18.

Answer 19.

Answer 20.

Answer 21.
a. ii. x-2y-4 = 0; x-2y – 5 = 0
b. 3x – 4y + 10 = 0; 3x – 4y = -10

c. Slope of the given line is
\(\frac { -A }{ B } =-\frac { 1 }{ -7 } =\frac { 1 }{ 7 } \)
Slope of the required line is -7
Given x intercept of the required line is 3, the point is (3,0).
Hence equation of the required line is
y – 0= -7 (x – 3); y + 7x = 21 or 7x + y – 21 = 0

Answer 22.
a. (x+1, y-2) = (3, 1) x+l=3; x=2 y-2 = i; y=3
b. AxB = { (1,4),( 1,6),( 1,9), (2,4), (2,6), (2,9),(3,4),
(3,6), (3,9), (4,4), (4,6) ,(4,9), (5,4), (5,6), (5,9)}
R = {(5,4)}
c. A real function R is to be a modulus function, if f (x) = | x |, x ∈ R, is known as modulus function.

Answer 23.
a. ii (-2, 3)
b. 2x + y = 4

Solution region:
2x + y ≥ 4
⇒ 0 ≥ 4, which is false. || by putting x = 0, y = 0
Hence shade the half plane, which does not contain the origin. x + y < 3
⇒ 0 ≥ 3, which is true.
Hence shade the half plane, which contains the origin.
2x – 3y < 6
⇒ 0 ≤ 6, which is true.
Hence shade the half plane, which contains the origin. The common region shown in the figure ’ is the solution region.

Answer 24.
a. i. When word start with P and end with S, then there are 10 letters to be arranged of which T appears two times.

ii. When there are always 4 letters between P & S
P & S can be at
1st and 6^th place
2nd and 7^th place
3rd and 8^th place
4^th and 9^th place
5^th and 10^th place
6^th and 11^th place
7^th and 12^th place
So, P & S will placed in 7 ways & can be arranged in 7 x 2 ! = 14
The remaining 10 letters with 2T’s 10!
can be arranged in\(\frac { 10i }{ 2i } \)=1814400 ways
The required number of arrangements = 14 x 1814400 = 25401600
b. Can be done in 5 ! ways, such that xGxGxGxGxGx
where G represents the seats for girls and cross mark represents the seats for boys = Total number of ways

Plus One Maths Previous Year Question Papers and Answers

Kerala Plus One Maths Model Question Paper 1

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

• There is a ‘cool off time’ of 15 minutes in addition to the writing time .
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read instructions carefully .
• Read questions carefully before you answering.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• .Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Questions 1 to 7 carry 3 score each. Answer any 6.

Question 1.
Write the set \(\left\{ \frac { 1 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 3 }{ 4 } ,\frac { 4 }{ 5 } ,\frac { 5 }{ 6 } ,\frac { 6 }{ 7 } \right\} \) r in the set- builder form.
a. If A and B are two sets such that A ⊂ B , then what is A ∪ B
b. There are 200 individuals with a skin disorder, 120 had been exposed to the chemical C₁ 50 to the chemical C₂, and 30 to both the chemicals C₁ and C₂. Find the number of individuals exposed to Chemical C₁ but not chemical C₂.

Question 2.
A lamp post is situated at the middle point M of the side AC of a triangular plot ABC with BC=7m CA = 8m, AB = 9m. Lamp post subtends an angle 15° at the poiny B. Determine the height of the lamp post.

Question 3.
Find square root of the complex number 8- i6.

Question 4.
Arathi took 3 examinations in an year. The marks obtained by her in the second and third examinations are more than 5 and 10 respectively than in the first examination. If her average mark is at least 80 find the minimum mark that she should get in the first examination?

Question 5.
a. A die is thrown until a six comes up. Write down the sample space for this experiment.
b. What is the probability of getting a doublet in throws of a pair of dice.

Question 6.
(a) A hyperbola with a = b is known as…………..

A. rectangular hyperbola
B. isosceles hyperbola
C. equilateral hyperbola
D. None of these

(b) Find the equation of an ellipse whose length of major axis is 26 and foci (± 5, 6)

Question 7.

Questions from 8 to 17 carry 4 score each. Answer any 8.

Question 8.

Question 9.
Let P(n) be the statement : 1³ + 2³ + 3³ +………+n³
 \(={ \left[ \frac { n(n+1) }{ 2 } \right] }^{ 2 }\)
a.Verify whether the statement is true for n = 1
b. Prove the result by using mathematical induction

Question 10.
a. Express (5 – 3i)³ in the form a + ib
b. Solve the equation -x² + x – 2 = 0

Question 11.
Solve the folowing linear inequalities graphically:

Question 12.
a. How many 3 digit even number can be formed form the digits 1,2,3,4,5 and 6, if the digits can be repeated?
b. In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

Question 13.
a. The base of an equilateral triangle with side 2 a lies along they-axis such that the mid-point of the base is at the origin. Find vertices of the triangle….
b. Find the equation of the line passing through (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6)

Question 14.
a. find the centere and radius of the circle x²+ y² – 8x + 10y – 12 = 0
b. Find the equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.

Question 15.
a. If p is the length of perpendicular from the origin to the line whose intercepts on the exes are a and b, then show that

b. If the lines 2x + y-3=0, 5x + ky -3=0 and 3x – y-2=0 are concurrent, find the value of k.

Question 16.
a. Find the octant in which the points (-3,1,2) and (-3,1,-2) lie.
b. Find the coordinates of a point on y-axis which are a distance of 5√2 from the point P (3,-2,5)

Question 17.
a. Write the negation of the following statement: If you do all the exercises in this book, you get an A grade in the class,
b. Verify by the method of contradiction, p: √2 is irrational.

Questions from 18 to 24 carry 6 score each. Answer any 5.

Question 18.
a. Draw the graph of the function f: R→ R defined by f(x) = x³ x ∈ R
b. If set A has 2 elements and set B has 3 elements, then the number of function from A to B is
(i) 64
(ii) 6
(iii) 9
(iv) 8

Question 19.
a. If sec x = 13/5, x lies in fourth quadrant, find other t-functions.
b. Prove that show that tan 3x tan 2x tan x = tan 3x – tan 2x – tan x
c. Find the value of tan π/8

Question 20.
a. Find the sum of the sequence 7, 77, 777,  7777, ………….. to n terms.
b. Find the sum of first n terms of the series: 3 x 1² + 5 x 2² + 7 x 3²+…….

Question 21.
a. Find the middle term in the expansion of

b. Find the term independent in the expansion of

Question 22.
a. Find the derivative of x sin x form first principles.

Question 23.
a. Find mean deviation about median for the following data.

b. Calculate mean, variance and standard deviation of the following distribution:

Question 24.
Four cards are drawn from a well shuffled pack of 52 cards. Find the probability that it contains
a. all aces
b. atmost 2 aces
c. atleast two aces

Answers

Answer 1.

Answer 2.

Answer 3.
– 15 – 8i
Let \(\sqrt { 8-6i } \) = x + iy……….. (1)
Squaring we have,
8 – i6=(x + iy)² = x² + i²xy + i²y² = (x² – y²)  +i2xy
Equating the real and imaginary parts, we have
x² – y²= 8 ………….. (2)
2xy = – 6 ……………….. (3)
We know that (x² + y²)²
= (x² – y²)² + 4x² y²
= (8)²+(-6)²= 64+36 = 100
∴ x² + y² = 4m = √100 = 10 ………….. (4)
(2) + (4) we have,
x² -y²  = 8 x² + y² = 10 2x² = 18
x² = 9 ⇒ x = ± 3
In (4), we have, 3²+y²=10 ⇒ y²
=10 – 9 = 1 ⇒ y = ± 1
Since 2xy = -6,
When x = 3, y = -1 and when x = -3, y = 1
3-i and -3 + i are the square roots.

Answer 4.
Let the mark in the first exam = x
Mark in the second exam = x+5
Mark in the third exam = x + 10 x + x + 5 + x + 10.

x >75
Minimum mark Arathi should get in the first exam = 75.

Answer 5.
a. s = {6,(1,6),(1, 1, 6),….,(2, 6),(2, 1, 6),…. }
b. n (s) = 36
doublets are (1,1), (2,2), (3,3),
(4,4),(5,5) and (6,6)
∴ P (getting a doublet) =  \(\frac { 6 }{ 36 } \) = \(\frac { 1 }{ 6 } \)

Answer 6.
a. C.
b. 2a = 26 => a = 13
foci = (±5,0) => c = 5
But c² = a²– b² ⇒ b² =a² – c² = 13²-5² = 144

Answer 7.

Answer 8.

Answer 9.

Answer 10.
a. (5 – 3i)³ = 5³ – 3 x 5²(3i)+3 x 5(3i)²– (3i)³
= 125 – 225i+ 135i² – 21 i³
= 125 – 225i+ 135(-1)-27(-i)
= 125 – 225i – 135 + 27i
= -10 – 198i
b. -x² + x + 2 = 0
a = 1 ; b = 1 ; c = 2
D = b² – 4ac = (1)² – 4 (-1) (2)
= 1 – 8 = -7 < 0

Answer 11.

The shaded region is the solution region.

Answer 12.
a. Here unit place can filled in three ways (i.e. by 2, 4, 6), whereas tens and hundred place can be filled in 6 ways.
b. Out of available nine courses, two are compulsory, Hence the student is free select 3 courses out of 7 remaining courses. Then the number if ways of selecting courses out of 7 courses

Answer 13.
(a) Let ABC be the given equilateral triangle with side 2a. Assume that base BC lies along the y-axis such that the mid-point of BC is at the origin. i.e., BO = OC = a, where O is the origin Now, it is clear that the coordinates of point B are (-a, 0) and C are (a,0), while the coordinates of point. Using Pythagoras theorem to ΔAOC, we obtain
AC² = OA² + OC² (2a)²
= OA²+ a² 4a²– a² = OA²
⇒ OA² =3a² ⇒ OA = √3a

∴ co-ordinates of A are (±√3a ,0). Thus, the vertices of the given equilat­eral triangle are (0, a),(0,-a), and (√3a,0) or (0, a), (0, -a), and (-√3a ,0)
(b) Any line through (-3,5) is y-5 = m(x-(-3)) = m(x + 3) Slope of line joining (2, 5) and (-3, 6) =

∴  slope of a line⊥ to it = 5
∴reqd. line is y-5 = 5(x+3)
⇒ 5x – y + 20=0

Answer 14.
a. centre = (-g, -f) = (4, -5)

b. Equation is
(x₁ – x) (x – x₂)+(y₁ – y) (y – y₁)
(x – a)(x – 0)+(y – 0)(y – b) = 0
x²-ax + y² – by = 0
x² + y² – ax -by = 0

Answer 15.
a. The equaton of line making intercepts a and b on the axes is

(intercept from) ….(i)
Given p = perpendicular distance from

b. Three lines are said to be concurrent, if they pass through a common point, i.e., point of intersection of any two lines lies on the third line. Here given lines are
2x + y – 3 = 0 ……….. (1)
5x + ky – 3 = 0……….. (2)
3x – y – 2 = 0 …………. (3)
Solving (1) and (3) by cross – multipli­cation method, we get,

Therefore, the point of intersection of two lines is (1, 1). Since above three lines are concurrent, the point (1, 1) will satisfy equation (2) so that
5.1+k.1- 3 = 0 ⇒ k = -2.

Answer 16.
a. (-3,1,2) – 2^nd octant
(-3,1,-2) – 6^th octant
b. Let A (0,y,0) be a point on y-axis having distance 5 √2 from (3,-2,5)

⇒ y² + 4y – 12 = 0
⇒ (y + 6) (y-  2) =0
⇒ y = -6,2
∴ A(0,-6,0) and ,4(0,2,0) are the required points

Answer 17.
a. If you do not do all the exercises in this book, you will not get an a grade in the class.
b. Let us assume that be rational.
∴ √2 = a/b_, where a and b are co-prime,
i.e., a an b have no other common factors except 1.
Then 2b² = a² ⇒ 2 divides a.
∴ there exists an integer ^tk^> such that a – 2k
∴ 2b² = 4k² ⇒ 4k² = 2b² = 2k² = ⇒ b²=⇒ 2 divides b.
i.e., 2 devides both a and b, which is contradiction to our assumption that a and b have no common factor.
∴ our supposition is wrong.
∴  √2 is an irrational number.

Answer 18.
a.

b. (iii) n(b)^n(A) =3² = 9

Answer 19.



Answer 20.
a. This is not a G.P., however, we can relate it to a G.P by writing the terms as S_n =7 + 77 + 777 + 7777 + …….. to n terms

b. Let T_n denote the n^th term of the given series

Answer 21.
a. Here n = 10 is even
Middle term \(\frac { 10 }{ 2 }\) +1 = 6^th term

Since we have to find a term indepen­dent of x, i.e., term not having x, so

Answer 22.



Answer 23.
a. We have

b. We first make the data continuous by making classes as below :

Answer 24.

Plus One Maths Previous Year Question Papers and Answers

Kerala Plus One Maths Improvement Question Paper 2018

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

• There is a ‘cool off time’ of 15 minutes in addition to the writing time .
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read instructions carefully .
• Read questions carefully before you answering.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• .Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Answer any 6 questions from question numbers 1 to 7. Each carries 3 scores

Question 1.
a. If A= {2, 3, 4, 5} and B = {4, 5, 6, 7}, then write :
i. A ∪ B ii. A ∩ B
b. Which one of the following is equal to {x : x∈ R, ∂< x ≤ 4 }?
i. {2,3,4}
ii. {3,4}
iii. [2, 4]
iv.(2, 4]

Question 2.
Consider the set
A = {x : x is an integer, 0 ≤ x < 4}
a. Write A in Roser form
b. If B = {5, 6}, then write A x B
c. Write the number of possible relations from A to B

Question 3.
Prove that

Question 4.

Question 5.
Find the polar from of the complex number

Question 6.
How many terms of the GP, 3, 3/2, 3/4,…………………..are needed to give the sum
\(\frac { 3069 }{ 512 } \) ?

Question 7.
Consider the real valued function

a. Find the domain of f(x).

Question 8.
a. If U = {1, 2, 3,4, 5, 6, 7, 8, 9}
A = {2, 4, 6, 8}
B = {2, 3, 5, 7}
Verify (A ∪B) = A’ ∩ B’
b. If A and B are two disjoint sets with n(A) = 4 and n(B) = 2, then n (A-B) = …………

Question 9.
Consider the statement P(n) : 1-3 + 32 +……….. \({ 3 }^{ n-1 }=\frac { { 3 }^{ n-1 } }{ 2 } \)
a. Show that P(1) is TRUE
b. Prove by principle of Mathematical induction, that P(n) is TRUE for all n ∈ N

Question 10.
Solve the following inequalities graphically
2x + y ≥ 4
x + y ≤ 3 and
2x – 3y ≤ 6

Question 11.
Find the square roots of the complex number 3 – 4i.

Question 12.
a. Insert five numbers between 8 and 26 such that the resulting sequence is an AP. b. Find the sum to n terms of the series
1 x 2 + 2 x 3 + 3 x 4+…………..

Question 13.
a. Find the equation of the perpendicular bisector of the line joining the points (0, 0) and (-3, 4).
b. Find the coordinates of the point on the line y = 3x-2 that is equidistant from (0,0) and (-3 -4)

Question 14.
a. Reduce the equation x – y = 4 into normal form.
b. Write the distance of this line from origin

Question 15.
a. Find the derivative of f(x) = x Sin x with respect to x.
b. Find the derivative of the function y = √x with respect to x by using first principles.

Question 16.
Consider the points A (3, 8, 10) and B (6, 10, -8).
a. Find the ratio in which the line segment joining A and B is divided by the YZ coordinate plane.
b. Find the coordinates of the point of division.
c. Which coordinate plane divides the line segment AB internally? Justify your answer.

Question 17.
a. Write the contrapositive of the statement: “If the integer n is odd, then n2 is odd”,
b. Prove by the method of contradiction ‘ √7 is irrational’

Answer any 5 questions from question numbers 18 to 24. Each carries 6 scores

Question 18.

find the valueof x and y.
b. Consider the function f (x) = |x| = 3, draw the graph of f (x)
c. Write the domain and range of (x)

Question 19.
a. Find the value of Sin (75°)

b. In the given figure. ∠AOB = 30° and radius of the circle is d units. Find the length of are APB.
c. Find the length of chord AB

Question 20.
a. Find the number words with or without meaning, which can be made by using all the letters of the word GANGA.
b. If these words are written as in a dictionary, what will be the 26th word?
c. A group consists of 4 girls and 7 boys. In how many ways, can a team of 5 members be selected if the team should have at least 3 girls?

Question 21.
a. Write the expansion of (a + b)ⁿ.
b. Find the coefficient of x⁵ y⁷in the expansion of (x-2y)¹²
c. Show that 9^n-1 – 8n – 9 is divisible by 64.

Question 22.
Focii of the ellipse in the given figure are (± √12,0) and vertices are (± 4, 0).
a. Find the equation of the ellipse.
b. Write the equation of a circle with centre (0, k) and radius r.
c. The circle in the figure passes through the points A, B and C on ellipse. Find the equation of a circle.

Question 23.
Consider the following table

a. Find the arithmatic mean of marks given in the above data

b. Find the standard deviation of marks in the above data.

c. Find the coefficient of variation.

Question 24.
a. Consider the experiment in which a coin is tossed repeatedly until a head comes up. Write the sample space.
b. If A and B are two events of a sample space with P (A) = 0.54, (P(B) = 0.69 and P (A ∩ B) = 0.35. Find P (A’ ∩ B’).
c. 3 cards are drawn from a well shuffled pack of 52 cards. Find the prohibility that
i. all the 3 cards are diamond.
ii. at least one of the cards is non diamond
iii. one card is king and two are jacks.

Answers

Answer 1.
a. A ∪ B = {2, 3, 4, 5, 6, 7}
A∩B = {4, 5}
b. iv) (2, 4]

Answer 2.
a. A = {0, 1,2,3}
b. A x B = {(0, 5),(0, 6),(1, 5),(1, 6),(2, 5), (2, 6),(3, 5),(3, 6)}
c. No. of possible relations from A to B
= 2^mn = 2^{4 x 2} = 256

Answer 3.

Answer 4.

Answer 5.

Answer 6.

∴ n = 10

Answer 7.

Answer 8.
a. A ∪ B = {2, 3, 4, 5, 6, 7, 8}
(A ∩ B)’ = {1, 9}………….(1)
A’= {1, 3, 5, 7, 9}, B’={1, 4, 6, 8, 9} A’∩B’= {1, 9}…………….(2)
From (1) and (2), we have (A + B)’ = A’ ∩ B’
b. n (A – B) = n (A) = 4

Answer 9.

Answer 10.

Answer 11.

Answer 12.

Answer 13.
a. Let the required line l is perpendicular bisector of the line joining A(0,0) and B (-3, 4).

Since l is perpendicular bisector of AB, it passes through the midpoint of AB.

Answer 14.

Answer 15.

Answer 16.
a. Since the line joining A and Bis divided by the YZ plane, x = 0

∴ the points divides the YZ plane in the ratio 1 : 2 externally.
b. R divides AB in the ratio 1:2 externally,

Since m:n = – z₁ : z₂ = -10 : -8 = 5:4
XY plane divides the line segment internally.

Answer 17.
a. If n2 is not even, then the integer n is not even.
b. Let us assu,e that √7 is a rational number.
√7 =a/b, where a and b are co-prime, i.e., a and b have no common factors. Squaring we have,
7b² = a² ⇒ 7 divides a.
∴ Let a = lk
∴a²= 49k²  ⇒ 7b²= 49k² ⇒ b² = 7k² ⇒7  divides b.
i.e., 7 divides both a and b, which is contradition to our assumption that a and b have no common factor. our supposition is wrong.
∴ √7 is an irrational number.

Answer 18.

Answer 19.
a. sin 75 = sin (45 + 30) = sin 45 cos 30 + cos 45 sin 30

=1.05 units
The radius of the circle is not given
properly. Type mismatching happened,
c. OA = OB = 2 units.

Answer 20.
a. Number of words = \(\frac { 5! }{ 2!2! } \)
= 30
b. If A is fixed, the remaining 4 letters can 4!
be permuted in \(\frac { 4! }{ 2! } \) = 12 ways.
If G is fixed, the ramaining 4 letters
can be permuted in \(\frac { 4! }{ 2! } \) = 12 ways.
∴ the 25^th word is NAAGG.
∴ the 26^th word is NAGAG
c. No. of selections
= ⁴C₃ x ⁷C₂ + ⁴C₄ + ⁷C₄ = 4 x 21 + 1 x 7 = 84 + 7 = 91

Answer 21.

Answer 22.
a. (± c ,0) = (±√2 , 0) ; (± a, 0) = (± 4, 0)
c² = a² – b² ⇒ b² = a²– c² = 16 – 12 = 4
Equation of the ellipse is \(\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 4 } \) = 1
b.. (x – 0)²+(y – k)²= r² ⇒ x² + y² – 2ky + k² – r² = 0
c. The co-ordinates of the points are :
A(-4,0), B(4,0) and C(0, -2).
Equation of the circle is
x² + y² + 2gx + 2fy + c = 0 ………….. (1)
(1) passes through A(-4, 0)
: 16 + 0 – 8g + c = 0 …………… (2)
(1) passes through B (4, 0)
: 16 + 0 + 8g + c = 0…………. (3)
passes through C (0, -2)
: 4 + 0-4f + c = 0 ……………… (4)
(2) + (3) ⇒ 32+2c=0
⇒ 2c = -32
⇒ c = -16 when c= -16
⇒ 16 + 0-8g – 16 = 0
⇒- 8g=0 ⇒ g=0
when c=-16 ⇒ 4 + 0-4f – 16 = 0
⇒- 4f = 12 ⇒ f = -3
Equation of the circle is
x² + y² + 2 (0) x + 2(-3) y+ – 16 = 0
⇒ x² + y²-6y – 16 = 0

Answer 23.

24.
a. Sample space = {H, TH, TTH, TTTH, …………………… }
b. P(A’∩B’)= 1-P(A ∪ B)=1 -[P(A) + P(B)-P(A ∩ B)]
=1 – [0.54 + 0.69-0.35] =1-0.88=0.12
c. i. P(all cards are diamond)

Plus One Maths Previous Year Question Papers and Answers

Kerala Plus One Maths Previous Year Question Paper 2017

Time Allowed: 2 hours
Cool off time: 15 Minutes
Maximum Marks: 60

General Instructions to Candidates

• There is a ‘cool off time’ of 15 minutes in addition to the writing time of 2 hrs.
• Your are not allowed to write your answers nor to discuss anything with others during the ‘cool off time’.
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read questions carefully before you answering.
• All questions are compulsory and only internal choice is allowed.
• When you select a question, all the sub-questions must be answered from the same question itself.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Question 1.
Worker population ratio is……………
a. Population / Worker
b. Worker / Population
c. Population / Worker X 100
d. Worker/Population X 100

Question 2.
List any four effects which ‘the miracle seeds’ created in Indian agriculture.

Question 3.
For a classroom discussion, Ashna collected the following information about present In­dia.
a. Infant, mortality rate – 45
b. Life expectancy-66.4
c. Overall literacy level 74.04
d. Compare them with the British period and comments.

Question 4.
Demographic data on birth and death rates in India, a collected and published by………………
a. RG
b. NSSO
c. CSO
d. Labour Bureau

Question 5.
Distinguish between bar diagram and histo­gram. (Hint: Not to draw diagrams)

Question 6.
The various ranks secured by Merin and Kanchana in four medical entrance examinations are

Calculate the rank correlation and interpret the result.

Question 7.
Find the one which is NOT measured for im­proving agricultural market system.
a. Adoption of green revolution
b. Assurance of minimum support price
c. Maintenance of buffer stock
d. Public distribution system

Question 8.
a. Name the system of farming that restores, maintain and enhance Ecological balance,
b. Point out any three merits of it.

Question 9.
Prepare an essay on various policies and pro­grams towards poverty alleviation in India. Do you find any faults in the implementation of these programs? Substantiate.

Question 10.
A value of correlation coefficient (r) =+1.2 in­dicates
a. Perfect+ve correlation
b. High degree of +ve correlation
c. Low degree of +ve correlation
d. Error in calculation

Question 11.
Identify the names of the steps in a project to which you can include the following statisti­cal tools you have studied.


Question 12.
State the two senses in which the word ‘sta­tistics’ is used. Elucidate.

Question 13.
An import substitution policy.
a. Increase in the tax on imported goods
b. Fixing of quotas
c. Enlarge domestic production
d. All of these

Question 14.
a. Name the outcome of the two policy strat­egies of liberalization and privatization,
b. Do you think that Indian agriculture sec­tor was adversely affected by the reform process? Justify.

Question 15.
State to which country the following demo­graphic features belongs to.
(Hint: India, China or Pakistan)
a. Highest annual growth of population
b. Lowest population density.
c. Less urbanization
d. High fertility rate

Question 16.
Observe the graph. It is……..
a. Uni-modal data
b. Bi-model data
c. Multi-modal data
d. None of these

Question 17.
Calculate the Consumer Price Index (CPI)

Question 18.
“Most of the surveys conducted in India are sample surveys”.
Prepare any three reasons to support the above statement.”

Question 19.
Which is NOT a pair?
a. Tapas Majumdar Committee’ – Education
b. Brundtland Commission – Sustainable de­velopment
c. Karve Committee-Agriculture
d. VKRVRao-National income estimation

Question 20.
a. Name the relative measure of standard de­viation.
b. Define SD.
c. Calculate the standard deviation from the following data:

Question 21.
Do India faces challenges in the power sec­tor? Elucidate.

Question 22.
For conducting a survey among 200 house­holds, Anumitha has written the names of all 200 households on pieces of paper, mixed well and 20 names are selected one by one. It is
a. Census method
b. Random sampling
c. Nonrandom sampling
d. None of these

Question 23.
While preparing a frequency distribution from the raw data, name the questions we have to address. Briefly, explain in 1 % pages. (Hint: Four steps in the construction of a frequency distribution)

Question 24.
The heights (in cm) of 11 plants in a garden are

a. Choose the mode.
b.Calculate the mean and median height of the plants, by using the equations.

Question 25.
Which one of the following statements is NOT TRUE about the employment sector in India?
a. 93% workers are in the informal sector.
b. 50% of the workers are self- employed.
c. Disguised and seasonal unemployment exist in the Indian farm sector.
d. During 1972-2010 there was a movement of workers from casual wage to self-empl­oyment.

Question 26.
Define the term, ‘Sustainable development’. Suggest various strategies for attaining it in two pages.

Question 27.
Express your view in the following aspects with reference to the present human capital formation in India.
a. Education for all
b. Gender equity
c. Higher education

Question 28.
The current and base year prices of a group of commodities are Rs. 180 and Rs. 135 re­spectively. It shows
a. price is said to have risen by 38.33%
b. price is decreased by 33.33%
c. price is increased by 133.33%
d. none of these

Answers

Answer 1.
Worker /population X 100

Answer 2.

• Enable India to attain sufficiency in food grains.
• Increased market surplus
• Large-scale increase in production
• Price of food grains declined.
• Government procured surplus products for future use.

Answer 3.
a. 218/1000
b. 32 years
c. Less than 16 %

Answer 4.
RGI (also give merits for NSSO)

Answer 5.

Answer 6.

Answer 7.
a. Adoption of green revolution

Answer 8.
a. Organic farming
b. Substitute with locally produced and or­ganic inputs

• More nutritional value
• Pesticide-free
• Highly international demand
• Environment-friendly

Answer 9.
1. Rural Employment Generation Programme.
It is implemented through the Khadi and vil­lage Industries Commission (KVIC), To help eligible enterpreneurs to set up village indus­try units. Under this programme, enterpre­neurs can establish village industries by avail­ing of margin money assistance from KVIC and loans from public sector scheduled com­mercial banks, selected regional rural banks. Under REGP, bank appraises the projects as per the scheme and take credit decision.

2. Prime Minister’s Rozgar Yojana (PMRY): In this programme help to set up any kind of enterprise that generates employment to the educated unemployed from low income fami­lies in rural and urban areas.

3. Swarna Jayanthi Shahari Rozgar Yojana (SJSRY)
The urban self-employment Programme and the urban Wage Employment Programme are two special scheme of the SJSRY, initiated in December 1997.

4. National Food for Work Programme (NFWP)
This Programme was introduced February 2001 for five months and was further extend­ed. This programe aims at augmenting food security through wage employment in droug­ht affected rural areas.

5. Swarna Jay at hi Gram Swarozgar Yojana (SJGSY)

It was launched with effect from 1999. As a result of amalgamating certain erstwhile prog­rammes into a single self-employment pro­gramme. This programme aims at promoting micro-enterprises and helping the rural poor into Self Help Groups(SHG). This scheme cov­ers all aspect of self-employment.

6. Mid Day Meals Scheme: In this programme involves provision for free lunch on working days for children in primary and upper primary classes in government education centers. The primary objective of the scheme is to provide hot cooked meal to children of primary and upper primary.

7. National Social Assistance Programme (NSAP): It was introduced on 15 August 1995 as a 100% centrally sponsored scheme for social assistance to poor household affected by old age, death of primary bread earner and mater­nity.

8. Pradhan Mantri Gramodya Yojana (PMGY): It was started in 2001. It aims at improving the standard of living of the rural people by de­veloping five important area health primary education, drinking water, housing and roads.

9. Pradhan Mantri Gram Sadak Yojana (PMGSY): It was nationwide plan in india to provide good all-weather road connectivity to unconnected villages. The scheme has started to change the lifestyle of many villagers.

10.Sampoorna Gramin Rozgar Yojana (SGRY): It was introduced in 2001. Jawahar Gram Samridhi yojana and Employment Assurance Scheme were intergrated into a single yojana. The objective of this yojana is to provide em­ployment opportunity to the surplus Workers. Through the policy towards poverty alleviati­on has evolved in a progressive manner but over the last five and a half decades it has not undergone any radical transformation.

The three major area of concern which preve­nt the successful implementation of the progra­ms, they are:

• These program depend mainly on govern­ment and bank officials for their implementa­tion since such officials are ill motivated, the resources are inefficiently used and wasted.
• Unequal distribution of land and other as­sets due to the benefits have been availed by the non-poor.
• In comparison to the magnitude of poverty, the amount of resource allocated for these programmes is not sufficient.

Answer 10.
Error in calculation

Answer 11.
b. Analysis on interpretation
c. organisation or presentation of data

Answer 12.
In the plural sense:- statitics refers to the sys­tematic collection of numerical facts. It indic­ated information in terms of numbers or nume­rical data such as employment statistics and population statistics.
In the singular sense:- statistics refers to the science of studying statistical methods. It indic­ates the techniques or methods of collecting organising, presenting analysing and inter­preting data.

Answer 13.
d. All of these

Answer 14.
a. Globalisation
b. Yes, Reduction of public investment. There has been a drastic decrease in the volume of public investment. In the agricultural sector. There has been an acute outback from the Indian government to provide. Sufficient irri­gation facilities, electricity information sys­tem, market linkages and roads.

Removal at subsidies removal subsidies on fertilisers pushed up the cost of production of agriculture. This made forming more expen­sive, thereby, adversely affecting the poor and marginal farmers. Shift towards cash crops and lack of food grai­ns. The export-oriented production strategies led to the shift of agricultural production from food grains to the production of cash crops like cotton jute etc.

Liberalisation and reduction in impart duties on agricultural products. Due to adherence to the to commitment, Indian government re­duced impart duties on agricultural products that forced the poor and marginal farmers to complete with their foreign countries part in international markets.

Answer 15.
a. Pakistan
b. China
c. India
d. Pakistan

Answer 16.
b. Bi-modaldata

Answer 17.

Consumer price index = \(\cfrac { \Sigma WR }{ \Sigma W } =\cfrac { 14875 }{ 100 } =148.75\)

Answer 18.

• A sample can give recomable, reliable and accurate informations.
• Lower cost
• Shorter time
• More detailed information can be collected as sample is less than population.
• Need smaller loan of enumerators
• Easier to trains and supervise the enum­erators

Answer 19.
c. Karve Committee – Agriculture

Answer 20.
a. Coefficient of variables
b. Standard Deviation
Standard Deviation: is the positive square root of the mean of squared deviations from mean.
So if there are five values X₁, X₂, X_3,X₄and X5, first their mean is calculated. Then devia­tions of the values from mean are calculated. These deviation are then squared. The mean of these squared deviations is the variance. Positive square root of the variance is the standard deviation.
c.

Answer 21.
Yes.

1. Installed capacity to generate electricity is not sufficient to feed the annuval demand of7%
2. State electricity board are running is losses of Rs,’ 500 billion transmission and distri­bution loss, wrong price, inefficiency etc.
3. Challenge from the part of the private sector and foreign power generates.
4. General public interest due to high tariff and long power

Answer 22.
b. Random sampling

Answer 23.

• Find the range of data
• Decide the approximate number of classes
• Determine the approximate class interval size
• Decide the starting point
• Determine the remaining class limits
• Distribute the data into respective classes.

Answer 24.

Answer 25.
During 1972 -2010 there was a movement of workless from casual wage to self-empl­oyment.

Answer 26.
It refers to the development strategy to inte­rruption till the resource extraction was not above the rate of regeneration of the resource and the wastes generated were within the assimilating capacity of the environment But today, environment fails to perform its third and vital function of the substance resulting in an environmental crisis. The rising popula­tion of the developing countries and the af­fluent consumption and production stand­ards of the developed world have placed huge stress on the environment in terms of its first two functions.

Strategies for sustainable Development.

1. Use of a non-conventional source of energy: – India heavily, depends on the hydropower plants to meet its power needs. Both of the­se have adverse environmental impacts. Thermal power plants emit large quantities of carbon dioxide, which is a greenhouse gas. It is not used properly.

2. Bio-Composting:-Inorder to increase pro­duction, we have started using chemical fertilisers which are adversely affecting the waterbodies, groundwater system, etc. But again farmers in large numbers have started using organic fertilisers for production.

3. Mini-Hydel Plants:- Mountainous region have streams everywhere, Most of such streams are perennial. Mini-hydel plants use the energy of such streams to move small turbines which generates electrici­ty. Such power plants are more or less envi­ronment friendly.

4. Traditional Knowledge and Practices:- Traditionally, Indian people have close to their environment. If we look back at our agriculture system, healthcare system, ho­using, transport, etc we find that all prac­tices have been environment-friendly.

5. Biopest Control:-With the advent of Gre­en Revolution, the country entered into the use of chemical pesticides to produce more which laid the adverse impacts on soil, wa­ter bodies, milk, meat, and fishes. To meet this challenge, better methods of pest control should be brought. One step is pesti­cides based on plants like neem. Even many animals also help in controlling pests like snakes, peacocks, etc.

6. CNG in Urban Areas:- In Delhi, the use of Compressed Natural Gas as fuel in the public transport system has significantly low­ered air pollution and the air has become cleaner in the last few years.

Answer 27.
a. It is still a dream
b. Better than before
c. A few takes

Answer 28.
d.None of these

Plus One Maths Previous Year Question Papers and Answers

Kerala Plus One Maths Previous Year Question Paper 2018

Time Allowed: 2 1/2 hours
Cool off time: 15 Minutes
Maximum Marks: 80

General Instructions to Candidates :

• There is a ‘cool off time’ of 15 minutes in addition to the writing time.
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read instructions carefully.
• Read questions carefully before you answering.
• Calculations, figures and graphs should be shown in the answer sheet itself.
• Malayalam version of the questions is also provided.
• .Give equations wherever necessary.
• Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Answer any six from question nunbers 1 to 7. Each carries three answers.

Question 1.
Find the sum to n terms of the sequence
4 + 44 + 444 +…………

Question 2.
Solve : Sin 2x – Sin 4x + Sin 6x = 0

Sin 2x – Sin 4x + Sin 6x = 0

Question 3.
If A and B are events such that P(A)= 1/4;
P(B) =1/2; P(A ∩ B) = 1\6 then find: 2 6
(a) P(A or B)
(b) P(not A and not B)

Question 4.
In a A ABC, prove that

Question 5.
(a) The maximum value of the function f(x) = Sin x is………
(i) 1
(ii) √3/2
(iii) 1/2
(iv) 2
(b) Prove that,
(Sin x + Cos x)2 = 1+Sin 2x.
(c) Find the maximum value of Sin x + Cos x.

Question 6.
\(\underset { x\rightarrow 2 }{ Lim } \) [x] = …….
i. 2
ii. 3
iii. 0
iv. does not exist
(b) Evaluate: \(\underset { x\rightarrow 2 }{ Lim } \) \(\frac { { x }^{ 3 }-\quad { 4x }^{ 2 }+\quad 4x }{ { x }^{ 2 }-4 } \)

Question 7.
Once card is drawn at random from a pack of 52 playing cards . Find the probability that,
(a) the card drawn is black.
(b) the card drawn is a face card.
(c) the card drawn is a black face card

Answer any eight from question numbers 8 to 17. Each carries four scores.

Question 8.
(a) If A={a, b, c}, then write Power Set P(A).
(b) If the numbed of subsets with two elements of a set P is 10, then find the total number of elements in set P.
(c) Find the number of elements in the power set of P.

Question 9.
Consider Venn diagram of the Universal Set
U = {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
U = {1, 2, 3,4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

(a) Write sets A, B in Roster form.
(b) Verify (A ∪ B)=A ∩ B
(c) Find n(A ∩ B).

Question 10.
Consider the following graphs :

(a) Which graph does not represent a function?
(b) Identify the function f(x)=1/x. from the above graphs.
(c) Draw the graph of the function f(x)=(x-1)² .

Question 11.
The figure shows the graph of a function f(x) which is a semi circle centred at origin.

(a) Write the domain and range of f(x).
(b) Define the function f(x).

Question 12.
a. If 3²ⁿ⁺² – 8n – 9 is divisible by ‘k’ for all n ∈ N is true, then which one of the following is a value of ‘k’ ?
i.8
ii. 6
iii. 3
iv. 12
b. Prove by using the principle of Math­ematical Induction
P(n) = 1+3+3²+…………….. +3^n-1 = \(\frac { { 3 }^{ n }-1 }{ 2 } \) is true for all n ∈ N.

Question 13.
(a) Solve the inequality

(b) Represent the solution on a number line.

Question 14.
(a) Find the n^th term of the sequence 3,5,7……………..
(b) Find the sum to n terms of the series. 3xl² + 5 x2² + 7×3²+ ……..

Question 15.
Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4x + y = 16.

Question 16.
Consider a point A(4, 8, 10) in space.
(a) Find the distance of the point A from XY – plane.
(b) Find the distance of the point A from X – axis.
(c) Find the ratio in which the line segm­entjoining the point A and B (6,10, -8) is divided by YZ -plane.

Question 17.
(a) Which one of the following sentences is a STATEMENT?
i. 275 is a perfect square.
ii. Mathematics is a difficult subject.
iii. Answer this question.
iv. Today is a rainy day.
(b) Verify by method of contradiction: ‘√2 is irrational’.

Answer any five from question numbers 18 to 24. Each carries six scores.

Question 18.
Consider the quadratic equation x² + x + 1 = 0
(a) Solve the quadratic equation.
(b) Write the polar form of one of the roots.
(c) If the two roots of the given quadratic are α and β . Show that α² = β .

Question 19.
The graphical solution of a system of linear inequalities is shown in the figure.


(a) Find the equation of the lines L₁, L₂, L₃
(b) Find the inequalities representing the solution region.

Question 20.
(a) Which one of the following has its middle term independent
i.\({ \left( x+\frac { 1 }{ x } \right) }^{ 10 }\)
ii. \({ \left( x+\frac { 1 }{ x } \right) }^{ 9 }\)
iii. \({ \left( { x }^{ 2 }+\frac { 1 }{ x } \right) }^{ 9 }\)
iv. \({ \left( { x }^{ 2 }+\frac { 1 }{ x } \right) }^{ 10 }\)
(b) Write the expansion of \({ \left( { x }^{ 2 }+\frac { 3 }{ x } \right) }^{ 4 }\)
(c) Determine whether the expansion of  \({ \left( { x }^{ 2 }+\frac { 2 }{ x } \right) }^{ 18 }\)  will contain a term containg x¹⁰.

Question 21.
The figure shows an ellipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 9 } \)= 1 and a line

(a) Find the eccentricity and focus of the ellipse.
(b) Find the equation of the line
(c) Find the equation of the line parallel to line L and passing through any one of the foci.

Question 22.
(a) Find the derivative of y = Sin x from the first principle.

Question 23.
Find n, if
(a) 12 x (n-1) p₃ =5 x (n+1) p₃
(b) If ⁿp_r = 840; ⁿC_r = 35 find r.
(c) English alphabet has 5 vowels and 21 consonants. How many 4 letter words with two different vowels and two different consonants canbe formed without repetition of letters?

Question 24.
Consider the following data:


(a) Find the standard deviation of the distribution.
(b) Find the coefficient of variation of the distribution.

Answers

Answer 1.
S = 4 + 44 + 444 + 4444+ …. to n terms

Answer 2.
sin2x – sin4x + sin6x = 0
sin6x + sin2x – sin4x = 0

Answer 3.

Answer 4.

Answer 5.
(a) 1
(b)   (sin x + cosx)²
= sin²x + cos²x + 2sinx cosx
= 1 + sin2x
(c)   Maximum value of sin2x = 1
Maximum value of sinx + cosx
= \(\sqrt { 1+1 } =\sqrt { 2 } \)

Answer 6.

Answer 7.

Answer 8.

Answer 9.
(a) A= {3,4,6,10} B = {2,3,4,5,11}
(b) (A∪B)’ = { 1, 7, 8, 9, 12, 13}
A’ = { 1, 2, 5, 7, 8, 9, 11, 12, 13}
B’ = {1, 6, 7, 8, 9, 10, 12, 13 }
A’∩B’ = {1,7, 8, 9, 12, 13}
∴ (A∪B)’ =A’ ∩B’
(c) n(A∩B)’ = n(U)-n(A∩B)=13-2=11

Answer 10.
a. (b) or (c)
b. (a)

Answer 11.
(a) Domain = [-4,4]
Range = [0,4]
(b) x² + y²=16
y²= 16-x²
y= \(\sqrt { 16-{ x }^{ 2 } } \)
i.e.,f (x)= \(\sqrt { 16-{ x }^{ 2 } } \)

Answer 12.
(a) 8
(b) P(n):1 + 3 + 3² + ……..3^n-1 =\(\frac { { 3 }^{ n }-1 }{ 2 } \)
Let P(1): 1 =\(\frac { { 3 }^{ 1 }-1 }{ 2 } \)=2/2=1
Hence, P(1) is true.
P(k): 1 + 3 + 3² +…… + 3^k-1=\(\frac { { 3 }^{ k }-1 }{ 2 } \)
To prove that P(k+1) is true. P(k+1):
1 + 3 +3² + + 3^i_1 +3^k+1-1 =\(\frac { { 3 }^{ k+1 }-1 }{ 2 } \)
⇒ P(k)+3^k = \(\frac { { 3 }^{ k+1 }-1 }{ 2 } \)
⇒ \(\frac { { 3 }^{ k }-1 }{ 2 } \) + 3^k= \(\frac { { 3 }^{ k+1 }-1 }{ 2 } \)
= \(\frac { { 3 }^{ k }-1 }{ 2 } \) + 3^k= \(\frac { { { 3 }^{ k } }-1+2\times { 3 }^{ k } }{ 2 } \)
Now, LHS = \(\frac { { { 3\times 3 }^{ k } }-1 }{ 2 } \) =  \(\frac { { 3 }^{ k+1 }-1 }{ 2 } \) = RHS
Hence, P(k+1) is true.
Hence, P(n) is true for all n∈N

Answer 13.
\(\frac { 2x-1 }{ 3 } \ge \frac { 5(3x-3)-4(2-x) }{ 20 } \)
40x-20 ≥ (15x-10-8+4x)³
40x-20 ≥ -54
40x-57x ≥ -54 + 20
-17x ≥-34
x ≤ 2 ⇒ x∈(-∞, 2)

Answer 14.
(a) t_n= 3+(n-1)² = 2n+1
(b) Let T_n denotes the nth term of the given series.
T_n = (n^lh term of 3, 5, 7……….. )(n^th term of 1², 2², 3²…….. )
= [3+(n-1)²].n² = (2n+1)n² = 2n³ + n²

Answer 15.
Let the equation of the circle be
(x – h)² + (y – k)² = r²
Since the circle passes through (4, 1) and (6,5), we have
(4-h)² + (1 -k)² = r²……….. (1)
and (6 -h)² + (5 – k)² = r²………… (2)
Also since the centre lies on the line 4x + y = 16, we have
4h + k = 16…………. (3)
Solving the equations (1), (2) and (3), we get
h = 3 and k = 4
(4 – 3)² + (1 – 4)² = r²
r²=10
Hence, the equation of the required circle is
(x-3)²+1 (y-4)²= 10
x²-6x + 9 + y²-8y + 16-10 = 0
x² + y² – 6x –  8y + 15 = 0

Answer 16.
(a) 10 [Z coordinate of the point]
(b) Let P(4,0,0) be a line on the X-axis.
distance = \(\sqrt { { (4-4) }^{ 2 }+{ (8-0) }^{ 2 }+{ (10-0) }^{ 2 } } \)
= \(\sqrt { 64+100 } =\sqrt { 164 } =2\sqrt { 41 } \)
(c) Since the line segment divided the YZ plane, its x coordinate is zero.
So =\(\frac { { mx }_{ 1 }+{ nx }_{ 1 } }{ m+n } \)
⇒ mx₂ + nx₁=0
\(\frac { m }{ n } =\frac { { -x }_{ 1 } }{ { x }_{ 2 } } =\frac { -2 }{ 3 } \)
⇒m : n=-2 : 3

Answer 17.
(a) 275 is a perfect square,
(b) Let -√2 is rational.
\(\sqrt { 2 } =\frac { p }{ q } \) , p and q have no common factor.
p² = 2q²
i.e., 2 divides p² is 2 divides p
∴ p = 2k, p² = 4k²
2q² = 4k², q² = 2k²
2 divides q² is 2 divides q.
p and q have a commonfactor 2.

Answer 18.

Answer 19.

b. The inequalities are: x + y ≤ 4, y ≥ 1, y ≤ x

Answer 20.

Answer 21.

In (1),3x + 5y-12 = 0

Answer 22.
a. Let f[x) = sinx
f(x + h) = sin(x + h)
f (x + h) – f(x)= sin(x + h) – sinx

Answer 23.
(a) 12 x (n-1)P₃ = 5 x (n+1)P₃
12 x (n-1 )(n – 2)(n – 3) = 5 x (n+1 )n(n-1)
12n² – 6Qn + 72 – 5n² – 5n = 0
7n²-65n+72 = 0
\(\frac { 65+\sqrt { 4225-2016 } }{ 14 } =\frac { 67647 }{ 14 } \)
\(\frac { 112 }{ 14 } ,\frac { 18 }{ 14 } =8,\frac { 9 }{ 7 } \)
But n cannot be a fraction. n = 8
(b) ⁿP = r! x ⁿC_r   840=r! x 35
r! = 24 ⇒ r = 4
Two different vowels can be selected in ⁵C₂ ways .Two different consonents can be selected in ^2IC₂ Ways.
Total selection 4 letters = ⁵C₂ x ²¹C₂
Total words = 4! x ⁵C₂ x²¹C₂
= 10 x 210 x 24 = 50400

Answer 24.
a.

Plus One Maths Previous Year Question Papers and Answers