Plus Two

Kerala State Board New Syllabus Plus Two Chemistry Previous Year Question Papers and Answers.

Kerala Plus Two Chemistry Previous Year Question Paper March 2018 with Answers

Board	SCERT
Class	Plus Two
Subject	Chemistry
Category	Plus Two Previous Year Question Papers

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

General Instructions to candidates:

• There is a ‘cool off time’ of 15 minutes in addition to the writing time of 2 hrs.
• Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
• Read questions carefully before you answering.
• Read the instructions carefully.
• 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 one score each. Answer all questions. (Scores: 7 × 1 = 7)

Question 1.
What is the co-ordination number of particles present in FCC crystal structure?
Answer:
12

Question 2.
Identify the order of reaction if the unit of rate constant is mol L^-1s^-1.
Answer:
Zero order

Question 3.
What is the structure of chromate ion ((CrO₄)2-)?
Answer:
Tetrahedral
OR

Question 4.
Name the test used to identify primary amines using CHCl₃ and ethanolic KOH.
Answer:
Carbylamine test/reaction or Isocyanide test

Question 5.
Which among the given vitamins is water soluble?
a) A
b) B
c) D
d) E
Answer:
b) B

Question 6.
What is the crosslinked polymer obtained by the polymerisation of phenol and formaldehyde?
Answer:
Bakelite

Question 7.
……….. is an artificial sweetener which is unstable at cooking temperature.
Answer:
Aspartame

(Questions 8 to 20): Answer any ten. Each question carries two scores. (Scores: 10 × 2 = 20)

Question 8.
a) Based on the nature of intermolecular forces, classify the following solids:
i) SiO₂
ii) Ice
b) ZnO turns yellow on heating. Why?
Answer:
a) i) SiO₂ – Covalent/Network solid
ii) Ice – Molecular slod/Hydrogen bonded molecular solid.

b) This is due to metal excess defect caused by the presence of extra cations at interstitial sites. ZnO is white in colour at room temperature. On heating it loses oxygen as,

The excess Zn²⁺ ions move to interstitial sites and electrons to neighbouring interstitial sites which imparts yellow colour to the crystal.

Question 9.
A solution contains 15g urea (molar mass = 60 g mol^-1) per litre of solution in water has the same osmotic pressure as a solution of glucose (molar mass =180 g mol^-1) in water. Calculate the mass of glucose present in one litre of its solution.
Answer:
πV = nRT
or π = \(\frac{n R T}{V}\)
Let π₁ be the osmotic pressure of urea and π₂ that of glucose. Then,

Here the two solutions are isotonic i.e., have same osmotic pressure.
Therefore, π₁ = π₂

Question 10.
Define minimum boiling azeotropes with example.
Answer:
Azeotropes are binary mixtures having the same composition in liquid and vapour phase and boil at a constant temperature. The solutions which show large positive deviation from Raoult’s law form minimum boiling azeotrope at a specific composition.
e.g. a 95% (v/v) solution of ethanol in water.

Question 11.
Write the chemical equation of the following reactions:
a) Preparation of XeO₃ from XeF₆.
b) Mixing PtF₆ and Xe.
Answer:
a) XeF₆ + 3H₂O → XeO₃ + 6HF
b) Xe + PtF₆ → Xe + PtF₆^–

Question 12.
Explain how the complexes of nickel, [Ni(CN)₄]² and [Ni(CO)₄] have different structures, but do not differ in their magnetic behaviour. (Ni, Atomic No: 28)
Answer:
In [Ni(CN)₄]^2-, Ni (3d⁸ 4s²) is in +2 oxidation state (Ni²⁺ – 3d⁸) and it undergoes dsp² hybridisation. So the ion has square planar geometry. But in [Ni(CO)₄], Ni is in 0 oxidation state and it undergoes sp³ hybridisation. So it has tetrahedral geometry. Due to the absence of unpaired electrons both the complexes are diamagnetic.

Question 13.
Complete the reaction:

Answer:

Question 14.
During the β-elimination reaction of 2-bromopentane in an alcoholic solution of KOH results Pent-2-ene as major product and Pent-1-ene as minor product. State the rule to explain the reaction.
Answer:
Zaitsev rule/Saytzeff rule. The rule states that “in dehydrohalogenation reactions, if there is a possibility of formation of more than one alkene, the preferred product is that alkene which has the greater number of alkyl groups attached to the doubly bonded carbon atoms.”

Question 15.
Aromatic aldehydes undergo electrophilic substitution reactions. Write the nitration reaction of benzaldehyde with chemical equation.
Answer:
The -CHO group being a meta-directing group, benzaldehyde on nitration gives m-nitrobenzaldehyde.

Question 16.
Briefly describe Gatterman Koch reaction.
Answer:
Gatterman – Koch reaction: When benzene or its derivative is treated with carbon monoxide and hydrogen chloride in the presence of anhydrous aluminium chloride or cuprous chloride, it gives benzaldehyde or substituted benzaldehyde.

Question 17.
How can it convert methyl iodide to ethanamine?
Answer:
Methyl iodide when treated with KCN or NaCN gives methyl cyanide or ethane nitrile which on reduction with LiAlH₄ or H₂ in presence of Ni/Pt/Pd or by sodium amalgam and ethanol we get ethanamine.

Question 18.
State two differences between globular and fibrous proteins.
Answer:
Globular proteins:

1. Polypeptide chains coil around.
2. Spherical shape.
3. Soluble in water.

Fibrous proteins:

1. Polypeptide chains run parallel and held together by hydrogen and disulphide bonds.
2. Fibre-like structure.
3. Insoluble in water.

Question 19.
Match the following:

a)	Polyacrylonitrile	i)	Terylene
b)	1,3-Butadien-Acrylonitrile	ii)	Natural Rubber
c)	Ethylene glycol-Terephthalic acid	iii)	Buna-N
d)	Cis-1, 4-polyisoprene	iv)	Acrilan

Answer:

a) Polyacrilonitrile	iv) Acrilan
b) 1,3-butadiene-Acrylonitrile	iii) Buna-N
c) Ethylene glycol-Terephthalic acid	i) Terylene
d) cis-1, 4-polyisoprene	ii) Natural Rubber

Question 20.
a) What are drugs?
b) Write an example for a drug classified based on its chemical structure.
Answer:
a) Drugs are chemicals of low molecular mass (~ 100 – 500u) which interact with macro molecular targets and produce a biological response.
b) Sulphonamides or Sulpha drugs like arsphenamine/salvarsan, prontosil, sulphapyridine.

(Questions 21 to 29): Answer any seven. Each question carries three scores: (Scores: 7 × 3 = 21)

Question 21.
An element crystallises as FCC with density 2.8 gm³. Its unit cell having edge length 4 × 10^-8 cm. Calculate the molar mass of the element. (Given N_A = 6.022 × 10²³ mol^-1)
Answer:
d = 2.8 g cm^-3, a = 4 × 10^-8 cm, z = 4 (since unit cell is FCC), N_A = 6.022 × 10²³ mol^-1.
Density, d = \(\frac{\mathrm{zM}}{\mathrm{a}^{3} \mathrm{~N}_{\mathrm{A}}}\)
Molar mass of the element, M = \(\frac{\mathrm{da}^{3} \mathrm{~N}_{\mathrm{A}}}{\mathrm{z}}\)

Question 22.
Write the anode and cathode reactions occur in the operation of a lead storage battery. Mention the electrolyte used in the battery.
Answer:
Anode reaction: Pb(s) + SO₄^2- (aq) → PbSO₄(s) + 2e^–
Cathode reaction: PbO₂(s) + SO₄^2- (aq) + 4H⁺(aq) + 2e^– → PbSO₄(s) + 2H₂O(l)
Electrolyte: 38% solution of sulphuric acid.

Question 23.
For hydrolysis of methyl acetate in aqueous solution, the following results were observed.

t/s	0	30	60
CH3COOCH3 C/mol L-1	0.60	0.30	0.15

Show that it follows pseudo first order reaction as the concentration of water remains constant.
Answer:
As the concentration of water remains constant, practically the reaction should be pseudo first order with respect to methyl acetate.

The rate constant for a pseudo first order reaction,

From the above results it can be seen that k = k’ [H₂O] is a constant and hence, it is a pseudo first order reaction.

Question 24.
a) State Hardy-Schulze rule with the help of example.
b) Why lyophilic colloids are used as protective colloids?
Answer:
a) The Hardy-Schulze rule states that the greater the valence of the flocculating ion added, the greater is its power to cause precipitation.
For example, in the coagulation of a negative sol like AS₂S₃, the flocculating power is in the order: Al³⁺ > Ba²⁺ > Na⁺
Or, in the coagulation of a positive sol like Fe₂O₃.xH₂O, the flocculating power is in the order:
[Fe(CN)₆]^4- > PO₄^3- > SO₄^2- > Cl^–

b) Lyophilic colloids have a unique property of protecting lyophobic colloids. When a lyophilic sol is added to the lyophobic sol, the lyophilic particles form a layer around lyophobic particles and thus protect the lyophobic sols from electrolysis.

Question 25.
Gibbs energy of formation (Δ_fG) of MgO(s) and CO(g) at 1273 K and 2273 K are given below:
(Δ_fG) [MgO(s)]: -941 kJ mol^-1 at 1273 K

On the basis of the above data, predict the temperature at which carbon can be used as a reducing agent for MgO(s)
Answer:
As per the Ellingham diagram, for using carbon as a reducing agent for MgO(s), the value of Δ_rG for the coupled reaction, MgO(s) + C(s) → Mg(s) + CO(g) should be negative at the required temperature.
Given that, at 1273 K
i) Mg(s) + \(\frac{1}{2}\)O₂(g) → MgO(s); Δ_fG = -941 kJ mol^-1
ii) C(s) + \(\frac{1}{2}\)O₂(g) → CO(g); Δ_fG = -439 kJ mol^-1
On reversing equation (i) and adding with equation (ii), we get
MgO(s) + C(s) → Mg(s) + CO(g); Δ_rG = (941 + – 439) kJ mol^-1 = +502 kJ mol^-1
Since Δ_rG is positive, carbon cannot be used as a reducing agent for MgO(s) at 1273 K.
Given that, at 2273 K
iii) Mg(s) + \(\frac{1}{2}\)O₂(g) → MgO(s); Δ_fG = -314 kJ mol^-1
iv) C(s) + \(\frac{1}{2}\)O₂(g) → CO(g); Δ_fG = -628 kJ mol^-1
On reversing equation (iii) and adding with equation (iv), we get
MgO(s) + C(s) → Mg(s) + CO(g); Δ_rG = (314 + – 628) kJ mol^-1 = -314 kJ mol^-1
Since Δ_rG is negative, carbon can be used as a reducing agent for MgO(s) at 2273 K.

Question 26.
a) What is the formula of the phosphine?
b) How phosphine is prepared in laboratory?
Answer:
a) PH₃
b) In the laboratory, phosphine is prepared by heating white phosphorus with concentrated NaOH solution in an inert atmosphere of CO₂.
P4 + 3NaOH + 3H₂O → PH₃ + 3NaH₂PO₂
(Or, any other laboratory method of preparation of PH₃.)

Question 27.
Assign the possible reason for following:
a) Stability of +5 oxidation state decreases and that of +3 oxidation state increases down to 15^th group elements.
b) H₂O is less acidic than H₂S.
c) H₃PO₂ act as a good reducing agent while H₃PO₄ does not.
Answer:
a) It is due to inert pair effect. In the case of heavier elements the lowest oxidation states are more prodominent due to non-participation of the s-electrons in the formation of bonds.

b) In the case of the hydrides (H₂E) of group 16 elements, down the group the H-E bond dissociation enthalpy decreases and hence acidic character increases. Due to small size of O compared to that of S, the O-H bond dissociation enthalpy is greater than the S-H bond dissociation enthalpy. Hence, H₂O is less acidic than H₂S.

c) The reducing property of oxoacids of phosphorus depends on the P-H bond. The acids which contain P-H bond have strong reducing properties. Thus, H₃PO₂ is a good reducing agent as it contains two P-H bonds. H₃PO₄ has no P-H bonds and hence it has no reducing property.

Question 28.
Give reasons for the following:
a) Transition metals and many of their compounds act as catalyst.
b) Scandium (Z = 21) does not exhibit variable oxidation state and yet it is regarded as a transition element.
c) Write the step involved in the preparation of Na₂CrO₄ from chromite ore.
Answer:
a) Transition metals and their compounds are known for their catalytic activity. This is due to their ability to adopt multiple oxidation states and to form complexes. Thus they can form with lower activation energy for the reaction. Also because the transition metal ions can change their oxidation states, they become more effective as catalysts.

In some cases transition metals provide a suitable surface for the reaction to take place. The reactants are adsorbed on the surface of the catalyst where reaction occurs. This has the effect of increasing the concentration of the reactants at the catalyst surface and also weakening of the bonds in the reacting molecules.

b) Scandium is regarded as a transition element because it has incompletely filled 3d orbitals in the ground state of the atom (3d¹ 4s²).

c) The chromite ore is fused with sodium carbonate or potassium carbonate in free access of air.
4FeCr₂O₄ + 8Na₂CO₃ + 7O₂ → 8Na₂CrO₄ + Fe₂O₃ + 8CO₂

Question 29.
How would you account for the following:
a) Aldehydes are more reactive than ketones towards nucleophilic addition reaction.
b) Boiling point of aldehydes are lower than alcohols.
c) Addition reaction of sodium hydrogen sulphite is useful for separation and purification of aldehydes.
Answer:
a) This is due to steric and electronic reasons.
Sterically, the presence of two relatively large substituents in ketones hinders the approach of nucleophile to carbonyl carbon that in aldehydes having only one such substituent.

Electronically, the two alkyl groups reduce the electrophilicity of the carbonyl carbon more effectively in ketones than in aldehydes.

b) The boiling points of aldehydes are lower than those of alcohols of comparable molecular masses due to the absence of intermolecular hydrogen bonding in aldehydes where as alcohols can associate through intermolecular hydrogen bonding and have higher boiling points.

c) The hydrogen sulphite addition compound is water soluble and can be converted back to the original aldehyde by treating it with dilute mineral acid or alkali. Therefore, these are useful for separation and purification of aldehydes.

(Questions 30 to 33): Answer any three. Each question carries four scores: (Score: 3 × 4 = 12)

Question 30.
a) What are primary batteries?
b) The cell potential of a mercury cell is 1.35 V, and remain constant during its life. Give reason.
c) Write the equation of the reactions involved at each electrode in a H₂-O₂ fuel cell.
Answer:
a) Batteries in which the reaction occurs only once and after use over a period of time they become dead and cannot be reused again.
b) This is because the overall reaction does not involve any ion in solution whose concentration can change during its life time.
c) Anode reaction: 2H₂(g) + 4OH^– (aq) → 4H₂O(l) + 4e^–
Cathode reaction: O₂(g) + 2H₂O(l) + 4e^– → 4OH^– (aq)

Question 31.
a) Draw the structures of geometrical isomers of [Fe(NH₃)₂(CN)₄]^–
b) Write the formula of pentaammine carbonate cobalt (III) chloride.
c) Wife any two limitations of valance bond theory.
Answer:
a)

b) [Co(NH₃)₅(CO₃)]Cl

c) i) It involves a number of assumptions.
ii) It does not give quantitative interpretation of magnetic data.
iii) It does not explain the colour exhibited by coordination compounds.
iv) It does not give a quantitative interpretation of the thermodynamic or kinetic stabilities of coordination compounds.
v) It does not make exact predictions regarding the tetrahedral and square planar structures of 4-coordinate complexes
vi) It does not distinguish between weak and strong ligands.
(Any two limitations)

Question 32.
a) Grignard reagents are important class of organometallic compounds used to prepare alcohols. Identify the compounds A and B and write the formula.


b) Write the name of products formed when salicylic acid is treated with acetic anhydride in acid medium
Answer:
a) i) Compound A : Ethanol/Ethyl alcohol – CH₃CH₂OH
ii) Compound B : Ethanal/Acetaldehyde – CH₃CHO
b) Acetylsalicylic acid/Aspirin and Acetic acid/Ethanoic acid

Question 33.
Lucas test is used to identify primary, Secondary and tertiary alcohols.
a) Explain the process.
b) Name the reagents used in the test.
Answer:
a) Lucas test – When treated with Lucas reagent, tertiary alcohols give turbidity immediately, secondary alcohols give turbidity within 5 minutes while primary alcohols do not give turbidity at room temperature but only on heating. This test is based upon the relative reactivities of various alcohols towards Lucas reagent. The order of reactivity is, 3° alcohols > 2° alcohols > 1° alcohols. Alcohols are soluble in Lucas reagent and form a clear solution. On reaction, alkyl chlorides are formed which being insoluble result in the development of turbidity,

b) Lucas reagent is a mixture of conc. HCl and anhydrous ZnCl₂.

Kerala Plus Two Physics Model Question Paper 5

Time: 2 Hours
Cool off time : 15 Minutes

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.

Speed of light, c = 3 x 10⁸m/s
Mass of proton, m_p = 1.6726 x 10^-27 kg
Mass of neutron, mn = 1.6749 x 10^-27 kg
Planck’s constant, h = 6.626 x 10^-34 Js
1eV=1.6 x 10^-19 J

Questions 1-7 carry 1 score each. Answer any six questions.

Question 1.
Write the expression for intensity of electric field near to the surface of a charged conductor with uniform charge density σ.

Question 2.
The unit of electrical resistivity is…………

Question 3.
E.m.f can be induced in a coil placed in an external magnetic field by:
a. Changing the intensity of magnetic field
b. Changing the area of coil
c. Changing the orientation of the coil
d. All of the above

Question 4.
Write the energy and momentum associated with a moving photon.

Question 5.
The value of relative permeability of a dia magnetic material is;

Question 6.
The electric field amplitude of an electromagnetic wave is 15V/m. Find the magnetic field amplitude of the wave.

Question 7.
A convex lens is placed in a medium having refractive index greater than that of the lens. The lens now behaves as;
a. Converging lens
b. Diverging lens
c. Plane glass plate
d. None of the above

Questions 8 to 15 carry 2 score each. Answer any 7 questions

Question 8.
a. ‘Electrostatic field is always normal to the surface of a charged conductor’. Justify the statement.
b. The value of electric potential at the surface of a charged conductor is 10 V. Find the value of intensity of electric field and potential at a point interior to it

Question 9.
A galvanometer with a coil of resistance 12 Ω shows a lull scale deflection for a current of 2.5 mA. How can it be converted into an ammeter of range 7.5 A?

Question 10.
The curves shown in figure are drawn for different magnetic materials. Among the three curves, name the curve that

a. Represent the material usually used for making permanent magnets.
b. Represent the material usually used for making electromagnets.

Question 11.
A capacitor C, a variable resistance R and a bulb B are connected in series to a.c mains in the circuit as shown. The bulb glows with some brightness. How the glow of the bulb change if.

a. A dielectric slab is introduced between the plates of the capacitor
b. The resistance R is increased keeping the same capacitance

Question 12.
James Clerk Maxwell modified Ampere’s circuital theorem by introducing the concept of displacement current.
a. What do you mean by displacement current?
b. Write down the equation for displacement current.

Question 13.
An object AB is kept in front of a concave mirror as shown in figure.


a. Complete the ray diagram showing the image formation of object
b. How will the position and intensity of image be affected if the lower half of the mirror’s reflecting surface is painted black?

Question 14.
Assuming that the two diodes D1 and D2 used in the electric circuit as shown in figure are ideal. Find out the value of current flowing through 2.5 Ω resistor.

Question 15.
a. Mention the function of the following used in the communication system
i. Transducer
ii. Transmitter
b. Figure shows the block diagram of a AM transmitter. Identify the boxes X and Y.

Questions 16 to 22 carry 3 scores each. Answer any 6 questions.

Question 16.
Three capacitors of capacitances 2µF, 3µF and 4µF are connected in series.
a. Find the equivalent capacitance of the combination.
b. The plates of a parallel plate capacitor have an area 20 cm² each are separated by a distance of 2.5 mm. The capacitor is charged by connecting it to a 400V supply. How much electrostatic energy is stored in the capacitor?

Question 17.
A circuit using potentiometer and a battery of. negligible internal resistance is set up as shown to develop a constant potential gradient along the wire PQ. Two cells of e.m.f s E1 and E2 are connected in series as in figure in combination 1 and 2. The balance points are obtained respectively at 400 cm and 240 cm from point P. Find

Question 18.
A conducting rod PQ of length ‘ l ’ connected to a resistance ‘R’ is moved at a uniform speed ‘ V’, normal to a uniform magnetic field ‘B’

a. Deduce the expression for e.m.f induced in the conductor
b. Find the magnitude and direction of current through the conductor

Question 19.
In tuner circuits, we use the phenomenon of resonance.
a. Write the condition of resonance in series LCR circuit
b. A series LCR circuit uses L = 0. 1 H,C = 10µF and R = 100Ω. Find the value of frequency at which the amplitude of current is maximum

Question 20.
The focal length of a lens has dependence on its radii of curvatures and refractive index. Derive Lens maker’s formula

Question 21.
a. Write the expression for the de Broglie wavelength associated with a charged particle having charge ‘q’ and mass ‘m’, when it is accelerated by a potential of ‘V’ volts.
b. A proton and an electron have same kinetic energy. Which one has greater value of de Broglie wavelength and why?

Question 22.
Find the binding energy per nucleon of ₂₀⁴⁰Ca nucleus. Given m ₂₀⁴⁰Ca = 39.962589u.
m_p = 1.00783u, m_n = 1.00867u
Take 1 amu = 931 MeV/c²

Questions from 23-26 carry 4 score. Answer any 3 questions.

Question 23.
Gauss’s theorem is useful for finding the intensity of electric field.
a. Write the Gauss’s law in its mathematical form
b. Using the law, prove that intensity of electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it

Question 24.
a. Express Ohm’s law in terms of current density, electrical resistivity and intensity of electric field
b. Explain the variation of resistance of a semiconductor with temperature. Also draw the graph showing the variation of resistivity of silicon with temperature

Question 25.
The relation between magnetic field and current is given by Biot-Savart’s law.
a. Write the expression for the magnetic field at point along the axis of a circular loop of radius ‘R’ carrying a current ‘I’.
b. From the above expression. Find the value of magnetic field at the centre of the loop
c. Sketch the magnetic field lines for current carrying circular loop

Question 26.

a. Identify the diode in the circuit and write the use of the resistance R_s
b. Explain how the diode helps as to stabilize the output voltage of the circuit
c. Name the type of biasing used in this diode

Questions 27 to 29 carry 5 scores. Answer any 27 – 29 carry 5 score. Answer any 2 questions

Question 27.
In the figure, PQ is the incident ray on the equilateral glass prism ABC.

a. Complete the ray diagram showing the passage of light and mark angle of deviation.
b. Derive an expression for the refractive index of the material of the prism

Question 28.
According to Christian Huygens wave theory, light emanating from a source as wave fronts.
a. What is the shape of wave front emerging form a linear source?
b. Derive the mathematical expression for the bandwidth of interference bands obtained in young’s double slit experiment with the help of suitable diagram

Question 29.
a. The radius of n^th stationary orbit of hydrogen atoms is :

Using Bohr postulates, obtain an expression for the energy of electron in the stationary states of H-atom

b. Draw the energy level diagram showing how the spectral lines corresponding to Balmer series occur due to transition between the energy levels

Answers

Answer 1.
\(E=\frac { \sigma }{ { \varepsilon }_{ 0 } } \)

Answer 2.
Ωm

Answer 3.
(d)All the above

Answer 4.
E = hυ = bc/λ
\(P=\frac { h }{ \lambda } =\frac { h\upsilon }{ c } \)

Answer 5.
µ_r < 1 or µ_r = 0

Answer 6.

Answer 7.
b. Diverging lens

Answer 8.
a. If E is not normal, there is a component a long the tangent to the surface. Then free charge on the surface experience force and will move. But E should have no tangential component in static situation.
OR
V is constant on the surface, therefore E should be normal.
b. E = 0, V = 10V

Answer 9.
G = 12V, Ig = 2.5×10^-3 A
I = 7.5 A

Putting the low resistance S in parallel with the galvanometer

Answer 10.
a. A
b. C

Answer 11.

a. E_r introduced, capacitance increases i.e,.\(\frac { 1 }{ c\omega } \) will decrease ∴ I₀ will be increase so the brightness will be increased
b. R ↑, I₀ ↓ brightness ↓
resistance cause decrease in I₀ ∴ bright ness will be decreased

Answer 12.
a. Displacement current is current due to time varying electric flax

Answer 13.

b.No change in position intensity halved/reduced

Answer 14.
D₂ on reverse biasing so it does not conduct
D₁ on forward biasing so it conduct
R = 3 + 2.5 = 5.5
V = 10V
I = \(\frac { V }{ R }\) = \(\frac { 10 }{ 5.5 }\) = l.82A

Answer 15.
a. i. Convert energy from one form to an other.
ii. Convert message signal to modulated signal for transmission.
b. X → modulater
Y → Power amplifier

Answer 16.

Answer 17.
E α l

Answer 18.
a. The magnetic flux linked with the rectangular loop PQRS is φ = BA = Blx
According to Faraday’s law, induced emf is

Answer 19.
a. V_L = V_C
X_L = X_C

Answer 20.

Answer 21.

Answer 22.
BE = E_b = ∆mc²
= (Zmp + (A-Z) Mn – M) c²
= (20 x 1.00783 + 20 x 1.00867 – 39.962589) x

Answer 23.

Answer 24.
a. I = ne A V_d……….(1)

Answer 25.

Answer 26.
a. Zener diode
Any change in input voltage results in change in voltage drop across Rs. without any change in voltage across zener diode.
b. When V_i increases, main current increases, I_z increases with no change in load current I_L. So that V₀ = V_z = I_L R_L. When V_i decreases, I_z decreases with no change in I_L.
c. Reverse biasing

Answer 27.

Answer 28.
a. Cylinder
b. S1 and S2 are two narrow slits separated by a distance “d”. They are illuminated by a monochromatic source of wavelength λ . A screen is placed at a distance of D from the slits as shown in the figure

Light waves from S1 and S2 reach the point P. The path difference between these two waves is S2N.

Answer 29.
a. For a hydrogen atom, gives the expression to determine the energies of different energy states. But then this equation requires the radius r of the electron orbit. To calculate r, Bohr’s second postulate about the angular momentum of the electron-the quantization condition is used. The angular momentum L is given by
L = mvr
Bohr’s second postulate of quantization says that the allowed values of angular momentum are integral multiples of h/2π

where n is an integer, r_n is the radius of nth possible orbit and u_n is the speed of moving electron in the nth orbit. The
allowed orbits are numbered 1,2,3………
according to the values of n, which is called the principal quantum number of the orbit.
From the relation between u_n and r_n is

Plus Two Physics Previous Year Question Papers and Answers

Kerala Plus Two Physics Model Question Paper 4

Time: 2 Hours
Cool off time : 15 Minutes

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.

Questions 1 and 2 carry 1 score each. Answer both.

Question 1.
Energy in a current carrying coil is stored in the form of

a. Electric field
b. magnetic field
c. dielectric strength
d. heat

Question 2.
Who indirectly determined the mass of the electron by measuring the charge of the electron ?

Answer any six questions from question number 3 to 10. Each question carries 2 scores.

Question 3.
Match the following

Question 4.
A student made a circuit as shown in the figure. S1 and S2 are switches and B is a bulb.

a. He argues that this circuit is equivalent to an AND gate. Do you agree with him? Justify your answer.

b. Write down its truth table.

Question 5.
Using the data given below, state as to which of the given lenses will you prefer to use as
i. an eye-piece and
ii. an objective to construct an astronomical telescope? Give reason for your answer.

Question 6.
Electromagnetic spectrum is an orderly arrangement of electromagnetic radiations in the j ascending or descending order of frequency/wavelength
a. Arrange the following electromagnetic radiations in the ascending order of frequency:
Visible rays, Infrared rays, X-rays, micro-waves.
b. Give one application of infrared and X-rays each.

Question 7.
A magnetic needle made of iron is suspended in a uniform external magnetic field. It experience a torque and the needle starts oscillating

a. Write down the frequency of oscillation of the magnetic needle.

b. If this magnetic needle is heated beyond curie temperature while it is oscillating, then its period.

i. increases
ii. decreases
iii. remains the same
iv. becomes infinity

Question 8.
a. An equilateral glass prism is placed on a horizontal surface. A ray PQ is incident I on it. For minimum deviation:

i. PQ is horizontal
ii. QR is horizontal
iii. RS is horizontal
iv. None of these
b. A thick lens gives coloured images due to

Question 9.
The truth table of a logic gate is given below.

a. Identify the gate.
b. Draw the logic symbol of the gate.

Question 10.
a. State Gauss’ law for magnetism.
b. How this differs from Gauss’ law for electrostatics ?

Answer any five question from question number 11 to 16. Each question carries 3 scores.

Question 11.
a. Which of the following symbol represents a universal gate ?

b. Shown below is an experimental set up with a semiconductor diode

i.identify the experiment
ii.draw the resulting graph.

c. With the help of neat circuit diagram obtain an expression for voltage gain of a transistor amplifier in C-E configuration.

Question 12.
a. The electrical analog of mass is
(i) diode
(ii) capacitance
(iii) inductance
(iv) resistance
b. A 2 m long solenoid having diameter 6 cm and 2000 turns has a secondary of 500 turns wound closely near its mid-point. Calculate the mutual inductance between the two coils.

Question 13.
What is de Broglie hypothesis ?
b. Write the formula for de Broglie wave length.
c. Calculate de Broglie wavelength associated with an electron accelerated by a potential difference of 100 volts. Given mass of the electron = 9.1×10^-31kg, h= 6.634×10^-34 JS,1 eV= 1.6×10^-19J

Question 14.
Albert Einstein, the great physist proposed a clear picture to explain photoelectric effect.
a. Explain Einstein’s photo electric equation.
b. Name the quanta of light.

Question 15.
a. To construct an electronic circuit, you want to select a 470 KΩ resistor with 5% tolerance.Draw a schematic diagram indicating the colour combinations that you will select.
b. As the temperature of a metallic resistor is increased; the product of its resistivity and conductivity ………….
i. Increases
ii. Decreases
iii. Remains constant
iv. May increase or decrease
c. Draw a graph showing the relation between resistivity and temperature of a super conductor.

Question 16.
Earth behaves as a magnet with magnetic poles approximately near the geographic poles.
a. The order of magnitude of earth’s magnetic field in tesla is ….
b. What do you understand by ‘dynamo effect’?
c. Classify the following materials into diamagnetic and paramagnetic.
i. Lead
ii. Magnesium
iii. Tungsten
iv. Copper

Answer any four question from question number 17 to 21. Each question carries 4 scores.

Question 17.
When the magnetic flux associated with a coil changes an emf is induced in the circuit.
a. State Faraday’s law of electromagnetic induction.
b. Mention the physical significance of Lenz’s law with an example.
c. When an electrical appliance is switched off, sparking occurs. Why?

Question 18.
a. Obtain an expression for the number of radioactive nuclei present at any instant in terms of the decay constant and initial number of nuclei.
b. The half life of radioactive radon is 3.8 days. Find the time during which 1/20 of radon sample will remain undecayed.

Question 19.
Electric field lines are a pictorial representation of the electric field around charges.
a. State Gauss’s Law in Electrostatics.
b. Using this law derive an expression for the electric field intensity due to a uniformly charged thin spherical shell at a point.
i. Outside the shell
ii. Inside the shell
c. Suppose that you are in a cave deep within the earth. Are you safe from thunder and lightning ? Why ?

Question 20.
a. State Kirchhoff’s rules for the analysis of electrical circuits.

b. The circuit diagram of a potentiometer for the determination of internal resistance of a cell is shown below. Calculate the value of the internal resistance (r) of the cell.
Given R = 100 Ω, balancing length when key (K) open = 60 cm. Balancing length when key (K) closed = 58 cm.

Question 21.
We are familiar with the semiconductors Silicon and Germanium,
a. With a necessary schematic diagram, briefly explain the characteristics of an intrinsic semiconductor.
b. Draw the energy bands of a n-type semi-conductor.
c. The following figure represents a……..

Answer any three quest on from question number 22 to 25. Each question carries 5 scores.

Question 22.
Capacitor is an arrangement to increase the charge carrying capacity of a conductor
a. Each plate of a parallel plate capacitor has a charge q on it. The capacitor is now connected to a battery. Pick out the correct statement/statements.
i. The facing surfaces of the plates have equal and opposite charges.
ii. The battery supplies equal and opposite charges to the two plates.
iii. The two plates of the capacitor have equal and opposite charges.
b. The plates of a parallel plate capacitor each of area A is charged with charges +Q and -Q. Deduce the force acting between the plates of the capacitor.
c. Van de Graaff generator is a high voltage generator used to accelerate charged particles.
Draw a labelled schematic diagram of a Van De Graaff generator and state the principle behind its working.

Question 23.
Force acting on a charged particle when it moves in a combined electric and magnetic field is known as Lorentz force.
a. A charged particle is released from rest in a region of steady and uniform electric and magnetic fields; which are parallel to each other. What will be the nature of the path followed by the charged particle? Explain your answer.
b. A rectangular loop carrying a steady current is placed in a uniform magnetic field. Obtain the expression for the torque acting on the loop.

Question 24.
In the potentiometer circuit shown, the balance point is at X.

State with reason, where the balance point will be shifted, when
a. Resistance R is increased, keeping all parameters unchanged.
b. Resistance S is increased, keeping R constant.
c. Cell P is replaced by another cell whose e.m.f. is lower than that of cell Q.
d. You are asked to compare the emf of two cells using a potentiometer. Draw the circuit diagram for this and explain how you will determine the ratio of e.m.f.

Question 25.
In the figure PQ is a ray incident on a prism ABC.

a. Complete the ray diagram showing the passage of light. Mark angle of incidence i, angle of emergence e, angle of deviation δ and angle of refractions r1 and r2.
b. Using the diagram obtain the relation
δ = i + e – A.
c. The critical angle for diamond is 30°. What is its refractive index?

Answers

Answer 1.
b

Answer 2.
Thomson

Answer 3.

Answer 4.
a. No. It is an OR gate
b.

Answer 5.
i. For an eye piece we prefer convex lens of max power and min.aperture is lens L₄.
ii. Objective must have minimum power and maximum aperture, ie., lens L₁

Answer 6.
a. Microwaves, infrared, visible, x-rays
b. Infrared – Mobile phone (Bluetooth), TV, Video recorders.
X-ray – Detect the fracture of bones.

Answer 7.

b. increases

Answer 8.
a. QR is horizontal
b. disperson.

Answer 9.
a. NOR gate.

Answer 10.
a. Gauss’s law for magnetism states that the net magnetic flux through any closed surface is zero, i.e.,

b. Gauss’s law in electrostatics states that the total flux through a closed surface is 1/ε₀ times the net charge enclosed by the closed surface.

Answer 11.
a. (ii)

b. (i) For studying the V-I characteristics of a p-n junction diode.

Answer 12.
a. (iii) inductance

Answer 13.
a. He proposed that material particles in motion should display wave-like properties.

Answer 14.
a. Einstein explained photoelectric effect based on quantum theory. According to quantum theory, light contain photons having energy hυ, when a photon of energy hυ₀ incident on a metal surface, electrons are liberated. A small portion of the photon energy is used for work function (φ) and remaining energy is appeared as K.E of the electrons.
By law of conservation of energy, we can write hυ = hυ₀ + ½ mv²; hυ energy of incident wave ; hυ₀ -» work function ½mv² -» K.E of electron
b. Photon.

Answer 15.

Answer 16.
a. 10^-5 T or 0.38 x 10^-4 T
b. Earth magnetic field arises due to electrical currents produced by convective motion of metallic fluids in the outer core of the earth. This is called dynamo effect.
c. Lead, Copper – Dia magnetic
Magnesium, Tungsten – Para magnetic

Answer 17.
a. Faraday’s first law: According to first law an EMF is induced in a circuit.when the magnetic flux linked with it changes.
b. Lenz’s law verifies conservation of energy in the electromagnetic induction phenomenon.
When N-pole of a bar magnet is moved towards a coil, the direction of induced current in the coil will be such that the end 2 will behave as N-pole (to oppose the incoming N-pole). For this the current in the coil will be anticlockwise as seen from the right face of the coil (using right hand thumb rule).
c. Due to back emf.

Answer 18.

t = 3.8 x 4.33 = 16.45 days

Answer 19.
a. Gauss’s Law states that the total flux through a closed surface is 1/ε₀ times the net charge enclosed by the closed surface.
b. (i).Outside the sphere (r > R)

c. Yes. This is because the electric field inside the cave will be zero. This is called electrostatic shielding.

Answer 20.
a. First law: The total current entering the junction is equal to the total current leaving the junction.
Second law: Total emf in a closed circuit is equal to the sum of the voltage drops.

Answer 21.

A pure semiconductor which is free from any impurity is called intrinsic semiconductor. Its conductivity controlled by the number of valence electron present in valence band. At 0K no electron is available in the conduction band semiconductor act as insulator.

c. Diode.

Answer 22.
a. i. True ii. True iii. True

c. The high electric field at the pointed ends of comb C1, ionises the air near them. The +ve charges in air are repelled and got deposited on the belt through a corona discharge.

The charges are carried upto C2. A similar corona discharge takes place at C2 and the charges are finally transferred to the shell M. The charges spread over uniformly on the outer surface of M raising its potential to few million volts.

Answer 23.
a. The charged particle execute an accelerated straight line motion along the direction of electric field. Since the electric field and magnetic field are parallel the magnetic field will be in the direction of the motion of the charged particle and hence the force due to magnetic field will be zero.,
b. A rectangular loop carrying a steady current I and placed in a uniform magnetic field experiences a torque. It does not experience a net force.
Consider a rectangular coil ABCD, placed in a uniform magnetic field, B. Then,
τ = I ab B = NIAB sin θ or τ =M x B ,
where A is the area of the coil, N is the no of turns. Here M = I (NA) is called magnetic dipole moment. If θ = 0 or 180, τ = 0.

Answer 24.
a. Balance point will be shifted towards B.
b. No change.
c. Balance point not found on AB.

Potential difference between two points of a current carrying conductor is directly proportional to the length of the wire between the two points.
A battery (B1), Rheostat and key are connected in between A and B. This circuit is called primary circuit. Positive end of E1 and E2, are connected to A and other ends are connected to a two way key. Jockey is connected to a two key through galvanometer. This circuit is called secondary circuit.
Key in primary circuit is closed and then E1 is put into the circuit and balancing length I1 is found out.

Answer 25.

Plus Two Physics Previous Year Question Papers and Answers

Kerala Plus Two Physics Model Question Paper 3

Time: 2 Hours
Cool off time : 15 Minutes

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.

Questions 1 – 7 carry 1 score each. Answer any six questions.

Question 1.
Potentiometer measures potential more accurately because

a. It measures potential in the open circuit
b. It uses sensitive galvanometer for null deflection
c. It uses high resistance potentiometer wire
d. It measures potential in the closed circuit

Question 2.
Tesla is the unit of

Question 3.
Write the time constant of C-R circuit ?

Question 4.
Green-house effect is the heating up of earth atmosphere due to____
a. green plants
b.infra-red rays
c. x-rays
d. ultraviolet rays

Question 5.
Rainbow is formed due to a combination of

a. dispersion and total internal reflection
b. refraction and absorption
c. dispersion and focusing
d. refraction and scattering

Question 6.
Ratio of intensities of two waves are given by 4:1. Then find the ratio of the amplitudes of the two waves.

Question 7.
The spectrum obtained from a sodium vapor lamp is an example of

a. band spectrum
b. continuous spectrum
c. emission spectrum
d. absorption spectrum

Questions 8 to 15 carry 2 score each. Answer any 7 questions.

Question 8.
Copper is one of the suitable materials to make connecting wires due to its low resistivity.
a. What do you mean by resistivity?
b. A copper wire is in the form of a cylinder and has a resistance R. It is stretched till its thickness reduces by half of its initial size. Find its new resistance in terms of R.

Question 9.
It was james Clark Maxwell who modified Ampere’s circuital theorem by introducing the concept of displacement current.

a. What do you mean by displacement current?

Question 10.
Match the following

Question 11.
A body of mass m is charged negatively. State whether the following statements are true or false.
a. During charging, there is change in mass of the body.
b. The body can be charged to 2.5 e where e is the charge of an electron.
c. While charging the body by induction new charges are created in it.
d. The force between two charged object is less when there is a medium between them (than in vacuum).

Question 12.
a. A receiver in a communication system must have
i. pick-up antenna
ii. demodulator
iii. amplifier
iv. all of these
b. Which of the following statements is wrong?
i. The attenuation of surface waves in creases with increase in frequency.
ii. The phenomenon involved in sky wave propagation is similar to total internal reflection.
iii. Space wave mode of propagation is used in satellite communication.
iv. Sky wave propagation is useful only in the range of frequencies 30 MHz to 40 MHz.

Question 13.
a. The core of a transformer has the following properties :
i. core is laminated.
ii. hysterisis loop is narrow.
Explain the significance of each property.
b. What is meant by resonance in an LCR circuit ?

Question 14.
a. Permanent magnets should have
i. high retentivity and low coercivity.
ii. low retentivity and high coercivity.
iii. high retentivity and high coercivity.
iv. low retentivity and low coercivity.
b. Distinguish between Para, Ferro an Dia magnetism.

Question 15.

a. From the above figures which one corresponds to a typical semiconductor.
b. Dimension of temperature coefficient α is……..

Questions 16 to 22 carry 3 score each. Answer any 6 questions.

Question 16.
a. Work function of a metal is the
i. energy required by an electron to get absorbed in the metal surface.
ii. minimum energy required by an electron to escape from the metal surface.
iii. energy required by an electron to be retained in the metal surface.
iv. maximum energy required by an electron to escape from the metal surface.
b. Write Einstein’s Photo-Electric Equation and explain the terms in it.
c. All Photo electrons are not emitted with the same energy as the incident photons. Why?

Question 17.
Kirchhoff’s rules are very useful for analysis of electrical circuits.
a. State Kirchhoff s junction rule.
b. Find the effective resistance of the circuit given below :

Question 18.
A fascinating behaviour of the series RLC circuit is the phenomenon of resonance.
a. Explain Resonance in an LCR circuit.
b. Draw a graphical representation of variation of current amplitude in i_m with frequency to ω
c. What do you mean by sharpness of resonance? Explain it.

Question 19.
a. When a low flying aircraft passes over head, we sometimes notice a slight shaking of the picture on our TV screen. Identify the optical phenomenon behind it.
b. In electromagnetic spectra, the wave length and frequencies are inversely related. A radio can tune into any station in the 7.5 MHz to 12 MHz band. Determine the corresponding wavelength band

Question 20.
Various propagation modes are used in communication.
a. Mention two communication system that uses space wave propagation.
b. Why modulation is necessary in communication ?
c. If a signal of frequency cos is used to ω_s modulate a carrier wave of frequency ω_c
which are the frequencies contained in the modulated signal other than ω_c?

Question 21.
Match the following quantities using the analogy between mechanical and electrical quantities.

Question 22.
In a nuclear reactor the chain reaction is carried out under controlled conditions.
a. Name the material that is used as control rods in a nuclear reactor.
b. Average energy of a neutron produced in fission of ₉₂²³⁵U nucleus is…….
c. Write down the reactions involved in the conversion of to ₉₂²³⁸U to ₉₄²³⁹Pu in a nuclear reactor

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

Question 23.
To emit a free electron from a metal surface a minimum amount of energy must be supplied.
a. This energy is called….
b. State three methods to supply this energy to the free electron.
c. When light of frequency 7.21×10¹⁴ Hz is incident on a metal surface, the maximum speed of the ejected electrons is 6×105 m/s. Calculate the threshold frequency for the metal.

Question 24.
Seema constructed a series LCR circuit in the laboratory as shown in the diagram. She found that the voltages across the inductor and capacitor are equal when the circuit is connected to an ac source.


a. State the condition at which the voltages across L and C become equal.

b. Obtain an expression for the frequency at which this situation occurs in a series LCR circuit.

c. Find the voltmeter and ammeter readings in the circuit.

Question 25.
Brewster’s law gives a relationship between angle of polarisation and refractive index of the material.

a. State Brsewster’s law

b. A ray of light is allowed to incident on the surface of a glass plate and it is found that the reflected and refracted rays are mutually perpendicular as shown in the figure. The refracted ray is deviated from its initial path by an angle of 30°
Determine the refractive index of the glass plate.

Question 26.
a. A ray of light travels from a denser to a rarer medium then, the ray
i. doesn’t bend at all.
ii. bends towards the normal.
iii. bends away from the normal.
iv. goes along the normal.
b. Draw a diagram showing the path of a monochromatic light through a triangular prism.
c. Using this diagram obtain the relation

Questions from 27 – 29 carry 5 scores. Answer any 2 questions.

Question 27.
a. What do you mean by barrier potential of a diode ?
b. With the help of a diagram explain the working of a full wave rectifier.

Question 28.
Various phenomena exhibited by light can be explained using the wave theory of light.
a. Name the phenomenon which proves the transverse nature of light.
b. What are the differences between interference and diffraction?
c. A plane wave front is incident on a single slit. Discuss the diffraction pattern formed by the slit. Represent the variation of intensity graphically.

Question 29.
A moving charge can produce a magnetic field.
a. How does a current loop behaves like a magnetic dipole ?
b. Draw the magnetic field lines for a current loop to support your answer.
c. i. What is a cyclotron ?
ii. Write down the expression for cyclotron frequency.

Answers

Answer 1.
a

Answer 2.
magnetic field

Answer 3.
CR

Answer 4.
b

Answer 5.
a

Answer 6.

Answer 7.
c

Answer 8.
a. Resistivity of the material of a conductor is defined as the resistance of the conductor of unit length and of unit area of cross-section.

Answer 9.
a. Displacement current is that current which comes into existence, in addition to the conduction current whenever the electric flux changes with time.
b. Ampere

Answer 10.

Answer 11.
a. true
b. false
c. false
d. true

Answer 12.
a. (iv) all of these
b. (iv) Sky wave propagation is useful only in the range of frequencies 30 to 40MHz

Answer 13.
a. (i) For reducing eddy current. Eddy current heats the core and energy will be lost.
(ii) For reducing hysterisis loss.
b. In LCR, at a particular frequency X_L = X_C. This condition is called resonance. This frequency is called resonance frequency.

Answer 14.
a. iii. high retentivity and high coercivity.
b. Paramagnetism: Feebly magnetise along applied field.
Diamagnetism: Feebly magnetise opposite to magnetic field.
Ferromag netism: Strongly magnetise along magnetic field.

Answer 15.
a. Fig.(2)
b. α = coefficient of temp

Answer 16.
a. ii. minimum energy required by an electron to escape from the metal surface.

c. All the photoelectrons emitted from the metal do not have the same energy. Photoelectric current is zero when the stopping potential is sufficient to repel | even the most energetic photoelectrons, with the maximum kinetic energy (K_max),So that K_{max = eV0}

Answer 17.
a. In an electric circuit, the sum of currents | entering the junction is equal to the sum of currents leaving the junction.
b. Here 3Ω, 6Ω are parallel and 6Ω and 12Ω are parallel.

Answer 18.
a. In LCR, at a particular frequency X_L = X_C. This frequency is called resonance frequency.

c. Sharpness of resonance is depends of quality factor or Q factor.
Q factor is equal to the ratio inductive reactance or capacitative reactance to the impedence at resonance.

Answer 19.
a. Interference

Answer 20.
a. TV Broadcast, Satellite, FM, RADAR,
b. 1. Size of the antenna: We need an antenna having a size comparable to the wave length of the signal.
2. Effective power radiated by antenna,

Answer 21.

Answer 22.

Answer 23.
a. Work function.
b. Thermionic emission, field emission and photo electric emission.

Answer 24.
a. p.d across L and C are equal when inductive reactance = Capacitive reactance (X_L = X_C), i.e., at resonance.
b. At resonance, X_L = X_C

Answer 25.
a. Tangent of angle of polarization is equal to the reflective index.
b. i + r = 90°
θ + r = 90°
θ = 90° – r = 90 – 30 = 60°
n = tan 60° = √3 = 1.732

Answer 26.
a. iii bends away from the normal
b.

Answer 27.
a. During the formation of a p-n junction, holes diffuse from p to n side and electrons diffuse from n to p side. Thus there is excess of positively charged ions in n side and negatively charged ions in p side. This sets up a potential difference across the junction which is called barrier potential. It stops further diffusion.

• During +ve half cycle of a.c, the end A is positive and end B is negative with respect to the centre tap. Diode D1 gets forward biased and conducts current while D2 is reverse biased and does not conduct.
• During -ve half cycle, the end Abe comes negative and end B becomes positive with respect to the centre tap. The diode D gets reverse biased and does not conduct. The diode D2 gets forward biased and conducts current.
• The output current is unidirectional and pulsating which may be filtered by connecting a capacitor parallel to load R_L.

Answer 28.
a. polarization
b.

Answer 29.
a. One face north and other face south.
i.e.,


Cyclotron uses the fact that the frequency of revolution of the charged particle in a magnetic field is independent of its energy. The particles move most of the time inside two semicircular disc-like metal containers, D1 and D2, which are called dees.
The whole assembly is evacuated to minimise collisions between the ions and the air molecules. A high frequency alternating voltage is applied to the dees. Positive ions or positively charged particles (e.g., proton) are released at the centre P. They move a semi-circular path in one of the dees and arrive in the gap between the dees in a time interval T/2; where T, the period of revolution, is given T = 1/ u_c = 2πm/qB
u_c = qB / 2πm. This frequency is called the cyclotron frequency for obvious reasons and is denoted by u_c.

Plus Two Physics Previous Year Question Papers and Answers

Kerala Plus Two Physics Model Question Paper 2

Time: 2 Hours
Cool off time : 15 Minutes

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.

Questions 1 and 2 carry 1 score each. Answer both.

Question 1.
Electromagnets are made of soft iron because soft iron has

a. low retentivity and high coercive force
b. high retentivity and high coercive force
c. low retentivity and low coercive force
d. high retentivity and low coercive force

Question 2.
Draw the symbol of NOR gate

Answer any six questions from question number 3 to 10. Each question carries 2 scores.

Question 3.
a. The electric field of a plane electromagnetic wave traveling in the +ve Z-direction is described by
a. E_x = E₀ sin (kz + ωt)
b. E_x = E₀ sin (kz – ωt)
c. E_x = E₀ sin (2kz)
d. E_x = E₀ sin (kz)
b. We feel excessive sweating on a cloudy day. Why ?

Question 4.
For many purposes, it is necessary to change an alternating voltage from one value to another. This is done with a transformer.
a. The basic principle behind a transformer is…..
b. Give an expression for the voltage and current in a transformer.

Question 5.
a. Name the physical quantity which has its unit joule coulomb^-1. Is it a vector or a scalar?
b. Two plane sheets of charge densities +σ and -σ are kept in air as shown in figure. What are the electric field intensities at point A and B?

Question 6.
Name the electromagnetic waves used for the following applications.
a. Imaging of bones in human body.
b. Mobile phone communication.
c. Remote control of T.V.sets.
d. For sterilizing surgical instruments.

Question 7.
a. Range of an electronic communication system is the
i. distance to the nearest TV station.
ii. distance to the nearest radio station.
iii. largest distance the signal can travel.
iv. largest distance between a source and destination up to which the signal is received with sufficient strength.
b. If the height of TV transmitting antenna is increased its coverage increases. Why?

Question 8.
Match the following in 3 columns.

Question 9.
a. The resistance ‘R’ of a conductor depends on its length ‘I’, area of cross- section ‘A’ and the resistivity of the material ‘ρ’. The correct expression connecting R, I, A and ‘ρ’ is

b. The voltage – current graphs for two resistors of the same material and same radii with lengths L1 and L2 are shown in the figure. If L1 > L2 state with reason, which of these graphs represents voltage current charge for L1?

Question 10.
De Broglie proposed the wave nature of electrons suggesting matter waves.
Find the momentum, speed and de Broglie wavelength of an electron with kinetic energy of 120 eV.

Answer any five questions from question number 11 to 16. Each question carries 3 scores.

Question 11.
a. The work function of a metal is 6 eV. If two photons each having energy 4 eV strike with the metal surface
i. will the emission be possible ?
ii. why ?
b. The waves associated with matter is called matter waves. Let λ_e and λ_p be the de- Broglie wave lengths associated with electron and proton respectively. If they are accelerated by same potential, then

Question 12.
The region around a charge where its effect can be felt is called the electric field.
a. The electric field lines corresponding to an electric field is shown below.

b. Some equipotential surfaces are shown in the figure. What can you say about the magnitude and direction of the electric field ?

Question 13.
Given below is the graph between frequency (υ) of the incident light and maximum kinetic energy (E_k) of emitted photoelectrons.

a. Define the terms – work functions and threshold frequency.
b. Find the values of
i. threshold frequency and
ii.work function from the graph

Question 14.
Consider the logic circuit using NOR gates given below:

a. Write the truth table for the circuit.
b. Identify the logic operation which this circuit is performing.

Question 15.
The phenomenon in which electric current is generated by varying magnetic field is called electromagnetic induction.
a. Which law helps to detect the direction of induced current? State the law.
b. Explain what are eddy currents.
c. Write any two uses of eddy currents.

Question 16.
Biasing is provided for maintaining proper current flow across a p-n junction.

a. In a biased p-n junction the net flow of holes is from ‘n’ region to ‘p’ regional


b. For the device shown below draw the V-I characteristics when the potential is applied between the terminals A and B.

Answer any four questions from question number 17 to 21. Each question carries 4 scores.

Question 17.
a. Find the equivalent resistance of the circuit.

b. Determine the current through the 75Ω resistance.

Question 18.
a. A convex lens
i. is thicker at the edges than at the middle.
ii. is thicker at the middle than at the edges.
iii. diverges rays of light.
iv. is of uniform thickness everywhere.
b. With the help of a ray diagram sketch the image formation of a convex lens when the object is between C and F.
c. Derive the lens maker’s formula.

Question 19.
Remya makes the following circuit to measure the emf of a cell.

She says that the voltmeter reading will give the emf of the cell.

a. The Physics teacher says that it is not :possible to measure the emf of the cell in this way. Justify this statement.
b. Explain with a circuit diagram the method to measure the emf of a cell with a potentiometer if you are given another standard cell, (whose e.m.f. is known)

Question 20.
a. What do you mean by Q value of a nuclear reaction?
b. Write down the expression for Q value in the case of α decay.
c. Two nuclei have mass numbers in the ratio 1 : 64. What is the ratio of their nuclear radii ?

Question 21.
A capacitor is a device used for storing charge as well as energy. It is based on a property called capacitance.
a. Write the SI unit of capacitance and define it.
b. You are given two capacitors of 2µF and 3µF. What are the maximum and minimum values of capacitance that can be obtained by combining them?
c. Obtain an expression for the electrostatic energy stored in a capacitor.

Answer any three questions from question number 22 to 25. Each question carries 5 scores.

Question 22.
To emit a free electron from a metal surface a minimum amount of energy must be supplied.
a. This energy is called …….
b. State three methods to supply this energy to the free electron.
c. When light of frequency 7.21×10¹⁴ Hz is incident on a metal surface, the maximum speed of the ejected electrons is 6×10⁵ m/ s. Calculate the threshold frequency for the metal.

Question 23.
Figure shows a graph between angle of incidence and the respective deviation of light when it is passed through an optical element.

a. Name this optical element.
b. What will happen to the angle of minimum deviation D if it is completely immersed in water? Justify your answer.
c. Obtain an expression for the refractive index of the material of this optical element.

Question 24.
The idea of ‘Electric field lines ’ is useful in pictorially mapping the electric field around charges.
a. Give any two properties of electric lines of force.
b. State Gauss’s theorem in electrostatics.
c. Using the theorem, derive an expression for electric field due to a uniformly charged spherical shell.
i. at a point outside the shell
ii. at a point inside the shell
d.

A point charge of +10 μc is at a distance of 5cm directly above the centre of a square of side 10 cm as shown in the figure. What is the electric flux through the square?

Question 25.
Gauss’s law can be used to determine the electric field due to a charge distribution, a. Below are some statements about Gauss’s law. Say whether they are true or false.
i. Gauss’s law is valid only for symmetrical charge distributions.
ii. The electric field calculated by Gauss’s law is the field due to charges inside the Gaussian surface.
b. Apply Gauss’s law to find the electric field due to an infinitely long plane sheet of charge.
c. “There can be no net charge in a region in which the electric field is uniform at all points”. Do you agree with this statement? Justify your answer.

Answers

Answer 1.
d

Answer 2.

Answer 3.
a. b. E_x = E₀ sin (kz – ωt)
b. The clouds prevents IR radiation from passing through and thus keeps the earth’s surface warm.

Answer 4.
a. Mutual induction

Answer 5.
a. Electric potential. It is a scalar quantity.

Answer 6.
a. x-rays
b. Radio waves
c. Infrared rays
d. Ultraviolet rays

Answer 7.
a. iv. largest distance between a source and destination up to which the signal is received with sufficient strength.
b. We know range, d = √2hR ; Where h is the height of the antenna. Therefore increasing height increases the range ie., coverage.

Answer 8.

Answer 9.
a. \(R=\frac { pl }{ A }\)
b. B represents voltage change for L. Resistance of B is greater than that for A, since resistance increases with length.

Answer 10.
De Broglie wavelength of electrons

from V², we can calculate V so we get the value of P also.

Answer 11.
a. (i) No
(ii) Free electrons are bound to the metal with some force. The minimum energy j required to liberate an electron from the metal is called work function, here the energy of one photon is less than work function. So emission will not be possible.
b. (i) λ_e > λ_p

Answer 12.
a. E_A = E_C > E_B
b. The direction of electric field at any point on the equatorial line of the dipole will be opposite to the dipole moment. The magnitudes of electric fields are equal

Answer 13.
a. Work functions: It is the minimum amount of energy required by an electron to just escape from the metal surface of the metal.
Threshold frequency: The minimum value of the frequency of incident radiation which can emit photo electrons from a material.
b. i.Threshold frequency,v₀ = 10 x 10¹⁴ Hz
ii. Work function = hv₀
= 6.63 x 10^-34 x 10 x 10¹⁴
= 6.63 x 10^-19 J

Answer 14.
a. Truth Table

Answer 15.
a. Lenz’s law. This law states that the direction of the induced e.m.f or current is such as to oppose the cause that produced it
b. The currents induced in the body of a conductor, when the magnetic flux linked with the conductor changes are called eddy currents or Focault’s currents
c. i. Electric Brakes
ii. Speedometer

Answer 16.
a. Reverse

Answer 17.

Answer 18.
a. ii. is thicker at the middle than at the edges.

Answer 19.
a. The voltmeter reads terminal potential difference. Emf cannot be measured in this way since the cell is connected to a resistance. Emf is the potential different across the terminals of a cell in a open circuit.

Answer 20.
a. The disintegration energy or the Q- value of a nuclear reaction is the difference between the initial mass energy and the total mass energy of the decay products.
b. For α -decay

Answer 21.
a. SI unit of capacitance is farad. Capacity of a conductor is said to be one farad if one coulomb of charge on it raises its potential by one volt.
b. If the capacitors are in series,

Answer 22.
a. Work function.
b. Thermionic emission, field emission and photo electric emission.
c. u = 7.21 x 10¹⁴ Hz, V = 6 x 10⁵ m/s

Answer 23.
a. Prism
b. The angle of minimum deviation decreases.
Refractive index of glass with respect to water is 1.5. But refractive index of glass with respect to water is 1.33.

c.

Answer 24.
a. i. Electric lines of force will never intersect.
ii.The tangent to the line of force at any point gives the direction of electric field at that point.
b. The electric flux through any closed surface in free is equal to 1/ε₀ times the total charge enclosed by the surface.

Answer 25.
a. i. False
ii. False

c. Yes, there can be no net charge in a region in which the electric field is uniform at all points. Consider a region with uniform electric field and a cubical gaussian surface in it whose face is perpendicular to electric field. Now from one face electric field enters which is considered to be +ve from the possible face it gets out which is considered to be -ve. So net flux through the gaussian surface is zero.

Plus Two Physics Previous Year Question Papers and Answers

Kerala State Board New Syllabus Plus Two Physics Previous Year Question Papers and Answers.

Kerala Plus Two Physics Model Question Paper 1 with Answers

Board	SCERT
Class	Plus Two
Subject	Physics
Category	Plus Two Previous Year Question Papers

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

General Instructions to candidates:

• There is a ‘cool off-time’ of 15 minutes in addition to the writing time of 2 hrs.
• You 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 the 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.

Questions 1 – 7 Carry 1 Score each. Answer any six questions. (6 × 1 = 6)

Question 1.
Write the expression for intensity of electric field near to the surface of a charged conductor with uniform charge density σ.
Answer:
E = \(\frac{\sigma}{\varepsilon_{0}}\)

Question 2.
The unit of electrical resistivity is ……….
Answer:
Ωm (ohm meter)

Question 3.
E.m.f can be induced in a coil placed in an external magnetic field by:
a) Changing the intensity of the magnetic field
b) Changing the area of the coil
c) Changing the orientation of the coil
d) All of the above
Answer:
d) All of the above

Question 4.
Write the energy and momentum associated with a moving photon.
Answer:
E = hν, P = mc

Question 5.
The value of relative permeability of a diamagnetic material is;
a) μ_r > 1
b) μ_r = 1
c) μ_r < 1
d) μ_r = 1
Answer:
c) μ_r < 1

Question 6.
The electric field amplitude of an electromagnetic wave is 15V/m. Find the magnetic field amplitude of the wave.
Answer:
B = \(\frac{E}{C}=\frac{15}{3 \times 10^{8}}\) = 5 × 10^-8T

Question 7.
A convex lens is placed in a medium having a refractive index greater than that of the lens. The lens now behaves as;
a) Converging lens
b) Diverging lens
c) Plane glass plate
d) None of the above
Answer:
b) Diverging lens

Questions 8 to 15 carry 2 scores each. Answer any 7 questions. (7 × 2 = 14)

Question 8.
a) ‘Electrostatic field is always normal to the surface of a charged conductor’. Justify the statement.
b) The value of elelctric potential at the surface of a charged conductor is 10V. Find the value of the intensity of the electric field and potential at a point interior to it.
Answer:
a) The surface of the charged conductor is an equipotential surface. In equipotential surface, the potential is the same and hence the electric field is always normal to the surface of a charged conductor.
b) E = 0

Question 9.
A galvanometer with a coil of resistance 12Ω shows a full-scale deflection for a current of 2.5 mA. How can it be converted into an ammeter of range 7.5 A?
Answer:
G= 12Ω, I_g= 2.5 mA = 2.5 × 10^-3A, I = 7.5 A
S = \(\frac{I_{g} \times G}{I-I_{g}}=\frac{2.5 \times 10^{-3} \times 12}{7.5-2.5 \times 10^{-3}}=4 \times 10^{-3} \Omega\)

Question 10.
The curves shown in figure are drawn for different magnetic materials. Among the three curves, name the curve that,

a) Represent the material usually used for making permanent magnets.
b) Represent the material usually used for making electromagnets.
Answer:
a) A
b) C

Question 11.
A capacitor C, a variable resistance R, and a bulb B are connected in series to a.c. mains in the circuit as shown. The bulb glows with some brightness. How the glow of the bulb change if.

a) A dielectric slab is introduced between the plates of the capacitor.
b) The resistance R is increased keeping the same capacitance.
Answer:
a) The brightness of bulb increases.
(When dielectric slab is introduced, capacitance increases hence capacitive reactance decreases, then bulb glows with more brightness.)
b) The brightness of bulb decreases.

Question 12.
James Clerk Maxwell modified Ampere’s circuital theorem by introducing the concept of displacement current.
a) What do you mean by displacement current?
b) Write down the equation for displacement current.
Answer:
a) The current due to time varying electric field is called displacement current.
b) i_d = \(\varepsilon_{0} \frac{\mathrm{d} \varphi}{\mathrm{dt}}\)

Question 13.
An object AB is kept in front of a concave mirror as shown in figure.

a) Complete the ray diagram showing the image formation of object.
b) How will the position and intensity of image be affected if the lower half of the mirror’s reflecting surface is painted black?
Answer:
a)

b) The position of image does not charge. But the intensity decreases.

Question 14.
Assuming that the two diodes D₁ and D₂ used in the electric circuit as shown in figure are ideal. Find out the value of current flowing through 2.5Ω resistor.

Answer:
Since D₂ is reverse biased, no current flows through 3Ω. We need to consider only the other two resistance 3Ω and 2.5Ω, which are connected in series. Total resistance, R = 3Ω + 2.5Ω = 5.5Ω
v = 10V
I = \(\frac{V}{R}=\frac{10}{5.5}\) = 1.81 A

Question 15.
a) Mention the function of the following used in the communication system
(i) Transducer
(ii) Transmitter
b) Figure shows the block diagram of an AM transmitter. Identify boxes X and Y.

Answer:
a) i) Transducer: The device that converts one form of energy into another is called transducer.
ii) Transmitter – Atransmittertransmits the information

b) x → Modulator
y → Power Amplifier

Questions 16 to 22 carry 3 scores each. Answer any 6 questions. (6 × 3 = 18)

Question 16.
Three capacitors of capacitances 2µF, 3µF and 4µF are connected in series.
a) Find the equivalent capacitance of the combination
b) The plates of a parallel plate capacitor have an area 20 cm² each are separated by a distance of 2.5 mm. The capacitor is charged by connecting it to a 400V supply. How much electrostatic energy is stored in the capacitor?
Answer:
a) C₁ = 2μF = 2 × 10^-6F
C₂ = 3μF = 3 × 10^-6F

b) A = 20cm² = 20 × 10^-4m²
d = 2.5 mm = 2.5 × 10^-3m
ε₀ = 8.85 × 10^-12C²/Nm²
v = 400v

Question 17.
A circuit using a potentiometer and a battery of negligible internal resistance is set up as shown to develop a constant potential gradient along the wire PQ. Two cells of e.m.fs E₁ and E₂ are connected in series as in figure in combination 1 and 2. The balance points are obtained respectively at 400 cm and 240 cm from point P. Find

a) The ratio between E₁ and E₂
b) Balancing length for the cell with emf E₁ only.
Answer:
a) From the connection (1), we get
E₁ + E₂ = k × 400 ………(1)
k = constant
From the connection (2), we get
E₂ – E₁ = 240 K ……….(2)
Adding (1) and (2), we get
2E₂ = 640 K
E₂ = 320 K
Subtituting for E₂ in equation (1)
E₁ + 320 K = 400 K
E₁ = 80 K
The ratio \(\frac{E_{1}}{E_{2}}=\frac{1}{4}\)
b) l₁ be the balancing length of E₁
E₁ = kl₁
80k ∝ kl₁
l₁ = 80 cm

Question 18.
A conducting rod PQ of length ‘l’ connected to a resistance ‘R’ is moved at a uniform speed ‘V’, normal to a uniform magnetic field ‘B’.

a) Deduce the expression for e.m.f induced in the conductor.
b) Find the magnitude and direction of current through the conductor.
Answer:
a) flux, Φ = BA
Here, Area A = ldx
dx is small displacement rod in time Δ T
Φ = B × l × dx

Question 19.
In tuner circuits, we use the phenomenon of resonance.
a) Write the condition of resonance in a series LCR circuit.
b) A series LCR circuit uses L = 0.1 H, C = 10μF and R = 100Ω. Find the value of frequency at which the amplitude of current is maximum.
Answer:
a) Lω = \(\frac{1}{\mathrm{C} \omega}\)
b) L = 0.1 H, C = 10μF = 10 × 10^-6F

Question 20.
The focal length of a lens has dependent on its radii of curvatures and refractive index. Derive lens maker’s formula.

Question 21.
a) Write the expression for the de Broglie wavelength associated with a charged particle having charge ‘q’ and mass ‘m’, when it is accelerated by a potential of ‘V’ volts.
b) A proton and an electron have the same kinetic energy. Which one has a greater value of de Broglie wavelength and why?
Answer:

For electron, λ_e = \(\frac{h}{\sqrt{2 m_{e} K E_{e}}}\)
But KE_p = KE_e and m_p > M_e, hence λ_e > λ_p
Electron has greater de Broglie wavelength.

Question 22.
Find the binding energy per nucleon of \({ }_{20}^{40} \mathrm{Ca}\) nucleus.
Given m\({ }_{20}^{40} \mathrm{Ca}\) = 39.962589u.
mp = 1.00783u, mn = 1.00867u.
Take 1 amu = 931 MeV/c²
Answer:
Mass detect, Δm = Zm_p + (A – Z) m_n – M
Δm = 20 m_p + 20 m_n – 39.962589
= 20 × 1.00783 + 20 × 1.00867 – 39.962589
= 0.367411 u
Binding energy = 0.367411 × 931 = 342.06 MeV

Questions from 23 – 26 carry 4 scores. Answer any 3 questions. (3 × 4 = 12)

Question 23.
Gauss’s theorem is useful for finding the intensity of elelctric field.
a) Write Gauss’s law in its mathematical form
b) Using the law, prove that the intensity of the electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it.
Answer:
\(\phi=\oint \overrightarrow{\mathrm{E}} \cdot \mathrm{d} \overrightarrow{\mathrm{s}}=\frac{\mathrm{q}}{\varepsilon_{0}}\)

Question 24.
a) Express Ohm’s law in terms of current density, electrical resistivity, and intensity of the electric field.
b) Explain the variation of resistance of a semiconductor with temperature. Also, draw the graph showing the variation of resistivity of silicon with temperature.
Answer:
a) J = σE
b) As temperature increases, the number density of electrons (η) of semiconductor increases.
ρ = \(\frac{m}{h e^{2} \tau}\)
Hence resistivity decreases with increase in temperature.

Question 25.
The relation between the magnetic field and current is given by Biot-Savart’s law.
a) Write the expression for the magnetic field at point along the axis of a circuit loop of radius ‘R’ carrying a current ‘I’.
b) From the above expression. Find the value of magnetic field at the centre of the loop.
c) Sketch the magnetic field lines for current carrying circular loop
Answer:
a) B = \(\frac{\mu_{0} \mathrm{NIR}^{2}}{2\left(\mathrm{x}^{2}+\mathrm{R}^{2}\right)^{3 / 2}}\)
I → Current
N → Number of turns
X → distance tot he point from the center of loop
b) B = \(\frac{\mu_{0} N I}{2 a}\)
c)

Question 26.

a) Identify the diode in the circuit and write the use of the resistance Rs.
b) Explain how the diode helps to stabilize the output voltage of the circuit.
c) Name the type of biasing used in this diode
Answer:
a) Zener diode, Voltage regulator
b) Solar Cell: Solar cell is a junction diode used to convert solar energy into electrical energy.

Circuit details:

Its p-region is thin and transparent and is called emitter. The n-region is thick and is called base. The output is taken across R_L.

Working: When light falls on this layer, electrons from the n-region cross to the p-region and holes in the p-region cross into the n-region. Thus a voltage is developed across R_L.
Solar cells are used to charge storage batteries during the daytime.
c) Reverse bias

Questions 27 to 29 carry 5 scores. Answer any 2 questions. (2 x 5 = 10)

Question 27.
In the figure, PQ is the incident ray on the equilateral glass prism ABC.

a) Complete the ray diagram showing the passage of light and mark the angle of deviation.
b) Derive an expression for the refractive index of the material of the prism.
Answer:

b)

ABC is a section of a prism. AB and AC are the refracting faces, BC is the base of the prism. ∠A is the angle of the prism.

A ray PQ incidents on the face AB at an angle i₁. QR is the refracted ray inside the prism, which makes two angles r₁ and r₂ (inside the prism). RS is the emergent ray at angle ‘i₂’

The angle between the emergent ray and incident ray is the deviation ‘d’.
In the quadrilateral AQMR,
∠Q + ∠R = 180°
[since N₁M and NM are normall
i.e. ∠A + ∠M = 18O° ………(1)
In the ΔQMR,
∴ r₁ + r₂ + ∠M = 180°……..(2)
Comparing eq (1) and eq (2)
r₁ + r₂ = ∠A ……….(3)
From the ΔQRT,
(i₁ – r₁) + (i₂ – r₂) = d
[since exterior angle equal sum of the opposite interior angles]
(i₁ + i₂) – (r₁ + r₂) = d
but, r₁ + r₂ = A
∴ (i₁ + i₂) – A = d
(i₁ + i₂) = d + A ……..(4)
It is found that for a particular angle of incidence, the deviation is found to be minimum value ‘D.
At the minimum deviation position,
i₁ = i₂ =i, r₁ = r₂ = r and d=D
Hence eq (3) can be written as,


It is found that when the angle of incidence increases deviation (d) decreases and reaches a minimum value and then increases. This minimum value of the angle of deviation is called the angle of minimum deviation.

Question 28.
According to Christian Huygens’s wave theory, light emanating from a source as wavefronts.
a) What is the shape of wavefront emerging from a linear source?
b) Derive the mathematical expression for the bandwidth of interference bands obtained in young’s double-slit experiment with the help of a suitable diagram.
Answer:
a) Cylinder
b)

S₁ and S₂ are two coherent sources having wavelength A. Let ‘d’ be the distance between two coherent sources. A screen is placed at a distance D from sources. ‘O’ is a point on the screen equidistant from S₁ and S₂.
Hence the path difference, S₁O – S₂O = 0
So at ‘O’ maximum brightness is obtained.
Let ‘P’ be the position of nm bright band at a distance x_n from O. Draw S₁A and S₂B as shown in the figure.
From the right angle ΔS₁AP



This is the width of the bright band. It is the same for the dark band also.

Question 29.
a) The radius of nth stationary orbit of hydrogen atom is:
r_n = \(\frac{\mathrm{n}^{2} \mathrm{~h}^{2} \varepsilon_{0}}{\pi \mathrm{me}^{2}}\)
Using Bohr postulates, obtain an expression for the energy of electron in the stationary states of H-atom.
b) Draw the energy level diagram showing how the spectral lines corresponding to Balmerseries occur due to the transition between the energy levels.
Answer:
a) Consider a hydrogen atom which has one electron revolving around the nucleus having one proton. The centripetal force for an electron is provided by the electrostatic force between electron and proton

b) Energy level diagram of the hydrogen atom

Note: An electron can have any total energy above E = 0 EV. In such situations electron is free. Thus there is a continuum of energy states above E = 0 EV.

Kerala State Board New Syllabus Plus Two Physics Previous Year Question Papers and Answers.

Kerala Plus Two Physics Previous Year Question Paper March 2017 with Answers

Board	SCERT
Class	Plus Two
Subject	Physics
Category	Plus Two Previous Year Question Papers

Time: 2½ Hours
Cool off time : 15 Minutes

General Instructions to Candidates

• There is a ‘cool off time’ of 15 minutes in addition to the writing time of 2½ hrs.
• You 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 the 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.
A concave lens always produces ………….. images
i. real
ii. virtual
iii. magnified
iv. None of these

Question 2.
A Zener diode is always operated in …….. bias.

Question 3.
Momentum of a photon with wavelength λ is……

Question 4.
Write down the truth table of a NOR gate.

Question 5.
a. How many electrons constitute an electric charge of -16 µC?
(i) 10¹³
(ii) 10¹⁴
(iii) 10¹⁵
(iv) 10¹²
b. An electric dipole is a pair of equal and opposite point charges +q and -q separated by a distance r. Write an expression for its dipole moment.
c. When an electric dipole is subjected to a uniform electric field, what will happen?

Question 6.
A message signal of frequency 10kHz and peak voltage 10V is used to modulate a carrier of frequency 1 MHz and peak voltage 20V. Find the modulation index.

Question 7.
a. Resistivity of a conductor depends upon
(i) its material
(ii) its cross-sectional area
(iii) its length
(iv) All of the above
b. Calculate the current flowing through the following circuit :

c. A potentiometer is a device to measure emf of a cell. Explain how the emfs of two cells can be compared using a potentiometer.

Question 8.
a. Choose the wrong option.
(i) Volt = Weber / second
(ii) Weber = Henry x Ampere
(iii) Joule = Henry x Ampere²
(iv) Volt = Weber x Second
b. The current in a coil of self-inductance 0.1 H varies from 2A to 5A in a time of 1ms. Find the induced emf across the coil.

Question 9.
a. Sound waves do not exhibit
i. interference
ii. diffraction
iii. polarization
iv. reflection
b. Describe Young’s double-slit experiment to determine the bandwidth of the interference pattern.
OR
a. The intensity of scattered light I in Rayleigh scattering is proportional to……
b. Explain the diffraction pattern obtained due to a single slit and represent graphically the variation of intensity with angle of diffraction.

Question 10.
a. Define half-life period of a radioactive nucleus. Write down the relation connecting half-life period and mean life.
b. Define 1 amu. Calculate its energy equivalent in MeV.

Question 11.
Photoelectric current does not depend on energy of the radiation, but on its intensity. Explain?

Question 12.
a. Speed of light in glass is 2 x 10⁸ m/s. The Refractive index of glass is……
b. For an equilateral prism made of a material of refractive index √2 . find the angle of minimum deviation for a ray of monochromatic light.
c. Draw the ray diagram of a simple microscope that uses a single convex lens. Derive an expression for its linear magnification.

Question 13.
a. A dielectric slab is placed between the plates of a parallel plate capacitor. Its capacitance
i. becomes zero
ii. remains the same
iii. decreases
iv. increases
b. Derive an expression for energy stored in a capacitor.

Question 14.
a. At resonance, in an LCR circuit, the emf and current are
(i) in phase
(ii) out of phase
(iii) having a phase difference of \(\frac { \pi }{ 2 } \)
(iv) having a phase difference of \(\frac { \pi }{ 6 } \)
b. In the following circuit, find the value of V

OR
a. In a circuit carrying an ideal coil with negligible resistance, the power dissipated is …….
b. In the following circuit, find the impedance.

Question 15.
Explain hysteresis and draw hysteresis curve for a ferromagnetic substance.

Question 16.
Choose the appropriate values for X-rays from the given table.

Question 17.
a. Unit of wavenumber is
i. Hz
ii. eV
iii. m
iv. m^-1
b.Energy of ground state of a hydrogen atom is -13.6 eV. What is its ionization potential?

Question 18.
The current amplification factor for CB configuration of a transistor is 0.9. Find out the current amplification ion factor for CE configuration.

Question 19.
a. An electric charge q is moving with a velocity v in the direction of a magnetic field B. The magnetic force acting on the charge is

b. starting from Biot – Savart law, obtain an expression for the magnetic field at an axial point of a circular coil carrying current.
OR
a. An ammeter is a current measuring device which is always connected in an electric circuit.
b. Describe a cyclotron and obtain an expression for cyclotron frequency.

Kerala State Board New Syllabus Plus Two Physics Previous Year Question Papers and Answers.

Kerala Plus Two Physics Previous Year Question Paper March 2018 with Answers

 

Board	SCERT
Class	Plus Two
Subject	Physics
Category	Plus Two Previous Year Question Papers

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 of 2 hrs.
• You 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 the 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.

The given value of constants can be used wherever necessary.

Velocity or light in vacuum, c = 3 × 10⁸ m/s
Plank’s constant, h = 6.64 × 10^-34 Js
Charge of electron, e = 1.6 × 10^-19C
Mass of the electron, m = 9.1 × 10^-31 kg
Avogadro number = 6.025 × 10²³ atom/mol
ε₀ = 8.854  × 10^-12 C² N^-1 m^-2
μ₀ = 4π × 10^-7 Tm/A

Questions 1 and 2 carry 1 Score each. Answer both. (2 × 1 = 2)

Question 1.
How will you represent a resistance of 3700 Ω ± 5% using colour code?
Answer:
Orange, Violet, Red and Gold.

Question 2.
Draw the symbol of NAND gate.
Answer:

Answer any six questions from question number 3 to 10. Each question carries 2 Scores. (Scores: 6 × 2 = 12)

Question 3.
Two equal and opposite charges placed in air as shown in figure:

a) Redraw the figure and show the direction of dipole moment (P), direction of resultant electric field (E) at P.
b) Write an equation to find out the electric field at P.
Answer:
a)

b) \(\overline{\mathrm{E}}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\overline{\mathrm{P}}}{\mathrm{r}^{3}}\)

Question 4.
Calculate the electrical capacitance of earth. The radius of earth is 6400 km.
Answer:
Capacitance of earth C = \(4 \pi \varepsilon_{0} \mathrm{R}\)
C = \(4 \pi \varepsilon_{0}\) × 6400 × 10³
= 710.8 µF

Question 5.
What do you mean by drift velocity? Write the relation between drift velocity and electric current.
Answer:
The average velocity acquired by an electron under the applied electric field is called drift velocity.
I = neAV_d

Question 6.
A galvanometer is connected as shown in the figure:

a) This combination can be used as ………..
(voltmeter/rheostat/ammeter)
b) Derive an expession to find the value of resistance S.
Answer:
a) Ammeter
b)

Let G be the resistance of the galvanometer, giving full deflection for a current I_g.
To convert it into an ammeter, a suitable shunt resistance ‘S’ is connected in parallel. In this arrangement Ig current flows through Galvanometer and remaining (I – Ig) current flows through shunt resistance.
Since G and S are parallel
P.d Across G = p.d across S
Ig × G = (I – Ig)s

Question 7.
An unpolarised light incident on a medium as shown in figure.

Show that the direction of reflected and refracted waves are mutually perpendicular.
Answer:
According to Brewster’s law
n = tan p = \(\frac{\sin p}{\cos p}\) ………(1)
According to Snell’s law
n = \(\frac{\sin p}{\sin x}\) …….(2)
Comparing (1) and (2), we get
\(\frac{\sin p}{\sin x}=\frac{\sin p}{\sin x}\)
sin x = cos p = sin(90 – p)
x = 90 – p, but p = r
x = 90 – r
x + r =90°
If x + r is 90°, angle between reflected and refracted ray will be 90°.

Question 8.
How many electrons, protons and neutrons are there in 16g of ₈O¹⁶?
Answer:
Number of atoms in 16g of ₈O¹⁶ = 6.023 × 10²³
Number of protons = 8 × 6.023 × 10²³
Numberof neutrons = 8 × 6.023 × 10²³

Question 9.
The given block diagram shows general form of a communication system.

a) Identify the blocks X and Y.
b) What is the difference between attenuation and amplification?
Answer:
a) X – transmitter
Y – Receiver
b) Attenuation: The loss of strength of a signal while propagating through a medium is known as attenuation.
Amplification: It is the process of increasing the amplitude of a signal.

Question 10.
What is the population covered by the transmission, if the average population density around the tower is 1200 km^-2? The antenna height is 160 m.
Answer:
Distance travelled by the wave d = \(\sqrt{2 R h}\)
Area = πd²
= π(\(\sqrt{2 R h}\))²
= π2Rh
= 3.14 × 2 × 6400 × 0.160 Km²
Population covered = Area × population density
= 3.14 × 2 × 6400 × 0.16 × 1200
= 7.72 × 10⁶

Answer any five questions from question number 11 to 16. Each question carries 3 Scores. (Scores: 5 × 3 = 15)

Question 11.
Two spheres encloses charges as shown in figure:

a) Derive and expression for electric field intensity at any point on the surface S2.
b) What is the ratio of electric flux through S₁ and S₂?
Answer:
a) According to Guess law

b) Flux a charge
for first sphere Φ₁ α Q
for second sphere Φ₂ α 3Q
∴ \(\frac{\phi_{1}}{\phi_{2}}=\frac{Q}{3 Q}=\frac{1}{3}\)
= 1 : 3

Question 12.
The electric field lines of a positive charge is as shown in figure:

a) Give the sign of potential difference Vp – Vq.
b) Give the sign of work done by the field in moving a small positive charge from ‘Q’ to ‘P’.
c) What is the shape of equipotential surface near the charge?
Answer:
a) positive.
b) negative.
c) spherical.

Question 13.
a) Name the part of electromagnetic spectrum:
i) used in radar systems.
ii) produced by bombarding a metal target by a high speed electrons.
b) Electromagnetic waves are produced by ………..
(charges at rest/charges in uniform motion/ charges in accelerated motion)
c) Why only microwaves are used in microwave ovens?
Answer:
a) i) Micro waves
ii) X – rays
b) Charges in accelerated motion.
c) The frequency of micro waves matches with the rotational frequency of water molecule.

Question 14.
Two thin convex lenses of focal length f₁ and f₂ are placed in contact:
a) If the object is at principal axis, draw ray diagram of the image formation by this combination of lenses.
b) Obtain a general expression for effective focal length of the combination in terms of f₁ and f₂.
Answer:
a)

b) Consider two thin convex lenses of focal lengths f₁ and f₂ kept in contact. Let O be an object kept at a distance ‘u’ from the first lens L₁, I₁ is the image formed by the first lens at a distance v₁.
Then from the lens formula, we can write,
\(\frac{1}{f_{1}}=\frac{1}{v_{1}}-\frac{1}{u}\) ……..(1)
This image will act as the virtual object for the second lens and the final image is formed at I (at a distance v). Then
\(\frac{1}{f_{2}}=\frac{1}{v}-\frac{1}{v_{1}}\) ……..(2)
Adding eq (1) and eq (2)

If the two lenses are replaced by a single lens of focal length ‘F’ the image is formed at ‘v’. Then we can write,
\(\frac{1}{F}=\frac{1}{v}-\frac{1}{u}\) …….(4)
from eq(3) and (4),
\(\frac{1}{F}=\frac{1}{f_{1}}+\frac{1}{f_{2}}\) …….(3)

Question 15.
A plane wave-front AB incident on a surface XY and undergoes refraction as shown in figure:

a) Prove Snell’s law of refraction by using this figure.
b) What is the change in speed of propagation and frequency of the refracted wave?
Answer:
a) AB is the incident wavefront and c₁ is the velocity of the wavefront in the first medium. CD is the refracted wavefront and c₂ is the velocity of the wavefront in the second medium. AC is a plane separating the two media.

The time taken for the ray to travel from P to R is

O is an arbitrary point. Hence AO is a variable.
But the time to travel a wavefront from AB to CD is constant. In order to satisfy this condition, the term containing AO in eq (2) should be zero.

where ¹n₂ is the refractive index of the second medium w.r.t. the first. This is the law of refraction.

b) Speed decreses
frequency remains same.

Question 16.
a) State radioactive decay law.
b) Prove the relation N(t) = N₀e^-λt.
Answer:
a) The number of nuclei undergoing decay per unit time is proportional to number of nuclei in the sample at that time.

b) According to Law of Radioactive decay,
\(\frac{\mathrm{d} \mathrm{N}}{\mathrm{d} \mathrm{t}}\) = -λN
\(\frac{\mathrm{d} \mathrm{N}}{\mathrm{d} \mathrm{t}}\) = -λdt
Integrating
In N = -λt + C …….. (1)
C is the constant of integration. To get value of C, let us assume that initially (t = 0) the number of nuclei be N₀.
∴ C = In N₀
Substituting for C in equation (1) we get,
In N – In N₀ = -λt
In \(\frac{\mathrm{N}}{\mathrm{N}_{0}}\) = -λt
\(\frac{\mathrm{N}}{\mathrm{N}_{0}}\) e-λt
N = N₀e^-λt

Answer any four questions from question number 17 to 21. Each question carries 4 Scores. (4 × 4 = 16)

Question 17.
Two charged partjeles q1 and q2 are moving through a uniform magnetic field (B) as shown in figure:

a) What is the shape of path of q₁ and q₂.
b) Derive an expression for cyclotron frequency with the help of a neat diagram.
Answer:
a) q₁ charges undergoes helical motion and q₂ moves in a circular path.

b)

Let ‘v’ be the velocity of ion, q the charge of the ion and B the magnetic flux density. If the ion moves along a semicircular path of radius ‘r’, then we can write

Question 18.
The B-H curve of a ferromagnetic material is as shown in figure:

a) What do you mean by ferromagnetic material? Write any two properties of it.
b) Identify the value of retentivity and coercivity from the figure.
c) A solenoid has a core of a material with relative permeability 400. The windings of the solenoid are insulated from the core and carry a current of 2A. If the number of turns is 1000 per metre, calculate magnetic intensity (H) and magnetic field (B).
Answer:
a) Ferromagnetic substances are those which gets strongly magnetized in an external magnetic field.
Properties: High susceptibility and permeability.
b) Ob represents retentivity and Oc coercivity.
c) H = nI
= 1000 × 2
= 2 × 10³ A/m
B = µ_sµ_rH
= µ₀ × 400 × 2 × 10³
B = IT

Question 19.
a) Derive an expression for self inductance of a solenoid.
b) What do you mean by eddy current? Write any two applications of it.
Answer:
a) Consider a solenoid (air core) of length/.number of turns N and area cross section A. let ‘n’ be the no. of turns per unit length (n = N/I)
The magnetic flux linked with the solenoid,
Φ = BAN
Φ = μ₀nIAN (since B = μ₀ ni)
but Φ = LI
∴ LI = μ₀nIAN
L = μ₀nAN
If solenoid contains a core of relative permeability
μr
Then L = μ₀μ_rnAN

b) when magnetic flux in a metal block changes, induced currents are produced. This current is called eddy current.
Applications:

• Magnetic beaking in trains
• Damping
• Induction furnace

Question 20.
The given graph shows the variation of KE with frequency of incident radiations for two surfaces A and B.

a) Which of the two metals has greater work function? For which of the metals will stopping potential be more for the same frequency of incident radiation?
b) The work function of caesium metal is 2.14 eV. When light of frequency 6 × 10¹⁴ Hz incident on the metal surface, what is the maximum KE of the photoelectrons and stopping potential?
Answer:
a) A
b) KE = hυ – Φ₀
= 6.6 × 10^-34 × 6 × 10¹⁴ – 2.14 × 1.6 × 10^-19
= 0.551 × 10^-19 J
= 0.345 eV
∴ Stopping potential = 0.345 V

Question 21.
a) Name different series of lines observed in hydrogen spectrum.
b) Draw energy level diagram of hydrogen atom.
Answer:
a) Laymen, Balmer, Paschen, Bracket, Pfund
b)

Answer any three questions from question number 22 to 25. Each question carries 5 Scores. (Scores: 3 × 5 = 15)

Question 22.
The circuit diagram of a potentiometer for determining the emf ‘E’ of a cell of negligible internal resistance is as shown in figure.

a) State the principle of working of a potentiometer.
b) How the balancing length AJ changes when the value of R₁ decreases?
c) Derive an expression to find out internal resistance of a cell.
Answer:
a) Potential difference between two points of current carrying conductor is directly proportional to the length of the wire between two points.
b) Balancing length decreases.
c)

The key (K₁) in the primary circuit is closed and the key is the secondary (K₂) is open. Jockey is moved to get zero deflection in galvanometer. The balancing length l₁ (from A) is found out.
Then we can write.
E₁ ∝ l₁ …….. (1)
Key K₂ is put in the circuit, corresponding balancing length (l₂) is found out. Let V be the applied voltage, then
V₁ ∝ l₁ ……..(2)
‘V’ is the voltage across resistance box.
Current through resistance box
i.e., voltage across resistance,

Question 23.
The phasor diagram of the alternating voltage across an unknown device X and current flowing through it are shown below.

a) Identify the device X.
b) Draw the graphical variation of current and voltage with ωt through this device.
c) Draw the phasor diagram which shows the relation among VR, VL, VC and I in a series LCR circuit.
Answer:
a) Resistor
b)

c)

Question 24.
A ray of light passing through a prism. If the refracted ray QR is parallel to the base BC, as shown in figure.

a) Derive an expression to find out deviation (d).
b) Draw a graph which shows the variation of ‘d’ with ‘i’.
c) Calculate the angle of minimum deviation if A = 60° and refractive index of the material of prism is 1.62.
Answer:
a)

The angle between the emergent ray and incident ray is the deviation ‘d’.
In the quadrilateral AQMR,
∠Q + ∠R = 180°
[since N1M and NM are normal]
i.e., ∠A + ∠M = 180° …….(1)
In the Δ QMR,
∴ r₁ + r₂ + ∠M = 180° …….(2)
Comparing eq (1) and eq (2)
r₁ + r₂ = ∠A …….(3)
From the Δ QRT,
(i₁ – r₁) + (i₂ – r₂) = d
(i₁ + i₂) – (r₁ + r₂) = d
but, r₁ + r₂ = A
∴ (i₁ + i₂) – A = d

Question 25.
The symbol of a diode is shown in the figure:

a) The diode is a ………… (rectifier diode/photo diode/Zener diode)
b) Draw the VI characteristics of above diode.
c) A zener diode with V_Z = 6.0 V is used for voltage regulation. The current through the load is to be 4.0 mA and that through the zener diode is 20 mA. If the unregulated input is 10.0 V, what is the value of series resistor R?
d) What is the fundamental frequency of the ripple in a full wave rectifier circuit operating from 50 Hz mains?
Answer:
a) Rectifier diode
b)

c) I = I_Z + I_L
= 20 × 10^-3 + 4 × 10^-3
I = 24 × 10^-3 A
Resistance R = \(\frac{V}{1}=\frac{10-6}{24 \times 10^{-3}}\)
R = 166.67 Ω
d) 100 Hz

Kerala Plus Two Maths Model Question Paper 5

Time : 2 1/2 Hours
Cool off time : 15 Minutes
Maximum : 80 Score

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 questions and to plan your answers.
• Read questions carefully before you answering.
• Read the instructions carefully.
• 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.

QUESTIONS

Question 1 to 7 carry 3 scores each. Answer any six questions only

Question 1.
a. Let R be a relation on the set {1,2,3} given by R= {(1,1), (2,2), (1,2), (2,1), (2,3)}. Which among the following element to be inclu¬ded to R so that R becomes Symmetric?
i. (3,3)
ii. (3,2)
iii. (1,3)
iv. (3,1)

b. If * is defined by a * b=a-b² and ⊕ is de-fined by a ⊕ is b=a²+b, where a and b are integers. Then find the value of (3⊕4)*5.

Question 2.

Question 3.
Find rate of change of area of a circle.
a. With respect to the radius, when r = 10cm
b. With respect to the time when the radius is increasing at the rate of 0.7cm/s. Given that r=5cm.

Question 4.

Question 5.
Find area of a circle with centre (0, 0) and radius “a” using integration.

Question 6.
Consider the differential equation \(\frac { dy }{ dx } \) = \(\frac { x+y }{ x } \)
a. Write the order of the differential equation.
b. Solve above given differential equation.

Question 7.
Following Table shows a brief description about manufacturing process of a company. Time required in hours per unit of the product and maximum availability of machines is also given in the table

a. Write the objective function.
b. Whether it is a maximisation case or a minimisation case Justify,
c. Write the contraints.

Question 8 to 17 carry 4 scores each. Answer any eight questions only

Question 8.
a. Afunctionf: A → B whereA= {1,2,3} and B= {4,5,6} defined by f (1) = 5, f (2) = 6, f (3) = 4, Check whether f is a bijection. If it is bijection, write f¹ as set of ordered pairs.2
b. The operation table for an operation * is given below. Given that I is the identify element, then which among the following is true regarding the elements in first column?

Question 9.

Question 10.
a. Find th relation between ‘a’ and ‘b’ so that the function defined by

b. “All continuous function are not differ-entiable”. Justify this statement with an example.

Question 11.
a. Find the equation of the tangent to the curve y = x² – 2x + 7 at (2,7)
b. Find the maximum value of the function.

Question 12.

Question 13.
Consider the differential equation \(\frac { xdy }{ dx } \) + y = \(\frac { 1 }{ { x }^{ 2 } } \)
a. Find the integrating factor
b. Solve the above differential equation.

Question 14.

Question 15.

Question 16.
a. Find the cartesian equation of a line passing through the origin and (5,-2,3)
b. The point P(x,y,z) lies in the First Octant and its distance from origin is 12 units. If the position vector of P makes angles 45°, 60° with x and y axes respectively, find co-ordinates of P.

Question 17.
Solve graphically :

Question 18 to 24 carry 6 scores each. Answer any 5 questions only

Question 18.

Question 19.
a. Without expanding prove that

b. Consider the following system of equations 2x – 3y + 5z = 11, 3x + 2y – 4z = -5, x + y-2z = -3
i. Express the system in the form Ax = B.
ii. Solve the system by matrix method a.

Question 20.

Question 21.
Evaluate the following.

Question 22.
Consider the parabolas y² = 4x and x² = 4y
a. Draw rough figure for the above parabolas.
b. Find the point of intersection of the two parabolas.
c. Find the area bounded by these two pa-rabolas.

Question 23.
a. Find the shortest distance between the lines whos vector equations are

b. If a plane meets positive x axis at a distance of 2 units from origin, positive y axis at a distance of 3 units from orign and positive z axiz at a distance of 4 units from origin. Find the equation of the plane.
c. Find the prependicular distance of (0,0,0) from the plane obtained in part (b).

Question 24.
a. A die is thrown twice let the event A be ‘odd number on First throw’ and B be ‘odd number on the second throw’ check whether A and B are independent.
b. Coloured balls are distributed in three boxes as shown in the following table.

A box is selected at random and a ball is taken out. If the ball taken is of red colour, What is the probabability that the other ball in the box is also of red colour?

ANSWERS

Answer 1.

Answer 2.

Answer 3.

Answer 4.

Answer 5.

Answer 6.

Answer 7.
Lex x = Machine G and y = Machine H
a. Objective function: Z= 20x + 30y
b. It is a maximization problem.
c. Constraints are:
3x + 4y < 10 ; 5x + 6y < 1 5 ; x > 0 ; y > 0

Answer 8.
a. A = {1,2,3}
B = {4,5,6}
f(1) = 5 ; f (2) = 6 ; f (3) = 4
Since it is one-one as well as onto, f is bijective.

∴ f = {(1,5), (2,6), (3,4)}
∴ f^-1 ={(5,1), (6,2), (4,3)}

b. (ii) 1,2,3
1 * 1 = 2,
2 * 1=2
Further 3 * 2 = 3
2 * 3 = 3
∴ * is commutative.

Answer 9.

Answer 10.

Answer 11.

Answer 12.

Answer 13.

Answer 14.

Answer 15.

Answer 16.

Answer 17.

Answer 18.

Answer 19.

Answer 20.

Answer 21.

Answer 22.

Answer 23.

Answer 24.

Plus Two Maths Previous Year Question Papers and Answers

Kerala Plus Two Maths Model Question Paper 4

Time : 2 1/2 Hours
Cool off time : 15 Minutes
Maximum : 80 Score

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 questions and to plan your answers.
• Read questions carefully before you answering.
• Read the instructions careully.
• 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.

QUESTIONS

Question 1 to 7 carry 3 scores each. Answer any six questions only

Question 1.
a. The slope of the tangent to the curve given by
x = 1- cos θ , y = θ – sin θ at θ = \(\frac { \pi }{ 2 }\) is
(i) 0
(ii) -1
(iii) 1
(iv) Not defined

b. Find the intervals in which the function f (x) = x² – 4x + 6 is strictly decreasing.

Question 2.

Question 3.

Question 4.
a. Write the Cartesian equation of the straight line through the point (1, 2, 3) and along the vector 3\(\widehat { i }\) + \(\widehat { j }\) + 2\(\widehat { k }\).
b. Write a general point on this straight line.
c. Find the distance from (1, 2, 3) to the plane 2x + 3y – z + 2 = 0.

Question 5.

Question 6.
Solve the system of linear equations :
x + 2y + z = 8
2x + y – z = 1
x – y + z = 2
x + 2y + z = 8
2x + y – z = 1

Question 7.

Question 8 to 17 carry 4 scores each. Answer any eight questions only

Question 8.

Question 9.

Question 10.
i. Find the equation of the plane through the points (3,-1,2), (5,2,4) and (-1,-1,6).
ii. Find the perpendicular distance from the point (6,5,9) to this plane.

Question 11.

a. Express the euqations of the lines into vector form.
b. Find the shortest distance between the lines.

Question 12.

Question 13.
a. Find the equation of a plane with intercepts 2, 3 and 4 on X, Y and Z axes respectively.
b. Find the distance of the point (-1,-2, 3) from the plane r.(2\(\widehat { i }\) – \(\widehat { j }\)) + 4 \(\widehat { k }\)  = 4.

Question 14.

Question 15.

Question 16.

Question 17.
a. For two independent events A and B, which of the following pair of events need not be independent?
i. A’, B’
ii. A, B’
iii. A’, B
iv. A-B, B-A

Question 18 to 24 carry 6 scores each. Answer any 5 questions only

Question 18.
Consider the following L.P.P.
Maximize Z = 3x+2y
Subject to the constraints
x+2y < 10
3x+y < 15
x, y > 0
a. Draw its feasible region.
b. Find the comer points of the feasible region.
c. Find the maximum value of Z.

Question 19.
a. y=a cos x+b sin x is the solution of the differential equation

Question 20.

Question 21.

Question 22.

Question 23.

Question 24.
a. If \(\overline { a } \),\(\overline { b } \),\(\overline { c } \),\(\overline { d } \) respectively are the position vectors representing the vertices A, B, C, D of a parallelogram, then write \(\overline { d } \) in terms of \(\overline { a } \), \(\overline { b } \) and \(\overline { c } \) .

b. Find the projection vector of \(\overline { b } \) = \(\widehat { i }\) + 2 \(\widehat { j }\) + \(\widehat { k }\) along the vector \(\overline { a } \) = 2i +j + 2k. Also write \(\overline { b } \) as the sum of a vector along \(\overline { a } \) and a vector perpendicular to \(\overline { a } \) .

c. Find the area of a parallelogram for which the vectors 2 \(\widehat { i }\) + \(\widehat { j }\) and 3 \(\widehat { i }\) + \(\widehat { j }\) + 4 \(\widehat { k }\) are adjacent sides.

ANSWERS

Answer 1.

The point x = 2 divides the real line into two disjoint intervals namly (-∞, 2) and (2,∞). In the interval(-∞,2), f'(x)=2x-4 < 0
∴ f is strictly decreasing in this interval.

Answer 2.

Answer 3.

Answer 4.

Answer 5.

Answer 6.

Answer 7.

Answer 8.

Answer 9.

Answer 10.

Answer 11.

Answer 12.

Answer 13.

Answer 14.

Answer 15.

Answer 16.

Answer 17.

Answer 18.

Answer 19.

Answer 20.

Answer 21.

Answer 22.

Answer 23.

Answer 24.

Plus Two Maths Previous Year Question Papers and Answers

Kerala Plus Two Maths Model Question Paper 3

Time : 2 1/2 Hours
Cool off time : 15 Minutes
Maximum : 80 Score

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 questions and to plan your answers.
• Read questions carefully before you answering.
• Read the instructions careully.
• 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.

QUESTIONS

Question 1 to 7 carry 3 scores each. Answer any six questions only

Question 1.
a. Let f : R → R be a function defined by f (x) = x³ + 5. Then f¹ (x) is
i. (x+5)^1/3
ii. (x-5)^1/3
iii. (5-x)^1/3
iv. 5-x

b. Let * be a binary operation defined on Q
a*b = a-b + ab. Check whether
i. It is commutative?
ii. Is * associative ?

Question 2.

Question 3.

Question 4.

Question 5.
Prove that the function f given by f (x)= log sin x is strictly increasing on ( 0,\(\frac { \pi }{ 2 } \))

Question 6.

Question 7.

Question 8 to 17 carry 4 scores each. Answer any eight questions only

Question 8.
a. Show that the relation R in set of real numbers defined as R = {(a,b): a < b²} is neither reflexive nor symmetric not transitive.
b. Show that the operation * on Q, defined by a*b = a+b-ab is commutative, and ex-its and identity elements find it.

Question 9.
a. The principal value of the expression cos-1 cos (680) is …………..

Question 10.

Question 11.

Question 12.

Question 13.

Question 14.

Question 15.
a. Find the distance between the planes x-y + z-5 = 0 and 2x-2y + 2z = 0.
b. Write the vector equation corresponding to Cartesian equation of a line

Question 16.
Find the shortest distance between the lines

Question 17.

Question 18 to 25 carry 6 scores each. Answer any 5 questions only

Question 18.

Question 19.
a. Use differential to approximate (0.999)^1/10
b. A window is in the form of rectangle sur-mounted by a semicircular opening. The total perimeter of the windows is 1 Om. Find the dimensions of the window to admit maximum light through the whole opening.

Question 20.
Find the area lying above x axis and included between the circle x² + y² = 8x and inside of the parabola y² = 4x. Also draw a neat diagram.

Question 21.
Evaluate:

Question 22.
Minimize and maximize Z = 5x + 10 y subject to x + 2y < 120, x + y > 60, x – 2y > 0, x, y > 0
a. Draw the feasible region
b. Find the comer points
c. Find the maximum and minimum profit.

Question 23.
a. Find the distance of the point (-1, -5, -10) from the point of intersection of the line

Question 24.
a. Two numbers are selected at random (with-out replacement) from the Pt six positive integers.

Let X denote the larger of the two numbers obtained. Find E(X) and Var(X)

b. A card from a pack of 52 cards is lost from the remaining X cards of the pack, two cards are drawn and are found to be both spades. Find the probability of the lost card being a spade.

ANSWERS

Answer 1.
a. ii
b. a * b = a – b + ab
b*a = b- a + ba = b – a + ab
∴ * is not commutative.
(a,b) * c = d * c = d- c + dc
= a- b + ab – c + ac – bc + abc
= a- b + ab – c + ac – bc + abc
= a – b – c + ab – bc + ca + abc
a * (b * c) = a * d = a- d + ad
= a – (b – c + be) + a (b – c + be)
= a- b + c – bc + ab – ac + abc
= a – b + c ab – be + ca + abc
∴ * is not associative.

Answer 2.

Answer 3.
We are giving that

Answer 4.

Answer 5.

Answer 6.

Answer 7.

Answer 8.
a. R = {(a,b): a < b²}
Relation R is defined in the set of real numbers.
i. Reflexive
Consider a ∈ R
If a ∈ R ⇒ a < a² which is false (a, a) ∈ R
R is not reflexive.

ii. Symmetric
Let a,b ∈ R and
(a,b) ∈ R ⇒ a < b² and b < a²,
which is false ⇒ (a,b) ∈ R, but (b,a) ∈ R
∴ R is not symmetric.

iii. Transitive
Let a, b, c ∈ R

Answer 9.

Answer 10.

Answer 11.

Answer 12.

Answer 13.

Answer 14.

Answer 15.

Answer 16.

Answer 17.

Answer 18.

Answer 19.

Answer 20.
The given equation of the circle x² + y² = 8x can be expressed as (x – 4)² + y² = 16. Thus, the centre of the circle is (4,0) and radius is 4. Its intersection with the parabola y² = 4x gives
x² + 4x = 8x
or
x² – 4x = 0
or
x(x-4) = 0
or
x = 0, x = 4
Thus, the point of intersection of these two curves are 0 (0,0) and P (4,4) above the x-axis.

From the above the required area of the region OPQCO included between these two curves above x-axis is
= (area of the region OCPO)
+ (area of the region PCQP)

Answer 21.

Answer 22.
a. The feasible region determine! by the constraints,
x + 2y < 120, x + y > 60, x – 2y > 0,
x > 0 and y > 0
is as follows.

b. The comer points of the feasible are region are A(60,0), C(60,30) and D (40,20).
The values of Z at these comer points are as follows.

Corner point	Z=5x + 10y
A (60,0)	300	→ Minimum
B (120,0)	600	→ Maximum
C (60,30)	600	→ Maximum
D (40,20)	600

a. The minimum value of Z is 300 at (60,0) and the maximum value of Z is 600 at all the points on the line segment joining (120,0) and (60,30)

Answer 23.

Answer 24.
a. The two positive integers can be sele-cted from the fist six positive integers without replacement in 6 x 5 = 30 ways.

X represents the larger of the two numbers obtained. Therefore, X can take the value of 2,3,4,5 or 6.

For X=2, the possible observations are (1,1)and(2,1)
∴ P (x = 2) = \(\frac { 2 }{ 30 } \) = \(\frac { 1 }{ 15 } \)

For X = 3 the possible observations are (1,3), (2,3), (3,1) and (3,2).
∴ p (x = 3) = \(\frac { 4 }{ 30 } \) = \(\frac { 2 }{ 15 } \)

For x = 4 the possible observations are

(1,4), (2,4), (3,4), (4,3), (4,2) and (4,1).
∴ p (x = 4) = \(\frac { 6 }{ 30 } \) = \(\frac { 1 }{ 5 } \)

For X = 5, the possible observations are (1.5) , (2,5), (3,5), (4,5), (5,4), (5,3), (5,2) and (5,1).
∴ p (x = 5) = \(\frac { 8 }{ 30 } \) = \(\frac { 4 }{ 15 } \)

For X = 6, the possible observations are (1.6), (2,6), (3,6), (4,6), (5,6), (6,4), (6,3), (6,2) and (6,1)
∴ p (x = 6) = \(\frac { 10 }{ 30 } \) = \(\frac { 1 }{ 3 } \)

Therefore, the required probability distribution is as follows.

b. Let E and E, be the respective events of choosing a spade card and a card which is not spade. Out of 52 cards, 13 cards are spade and 39 cards are not spade.

Plus Two Maths Previous Year Question Papers and Answers

Kerala State Board New Syllabus Plus Two Maths Previous Year Question Papers and Answers.

Plus Two Maths Model Question Papers Paper 1 with Answers

Board	SCERT
Class	Plus Two
Subject	Maths
Category	Plus Two Previous Year Question Papers

Time : 2 1/2 Hours
Cool off time : 15 Minutes
Maximum : 80 Score

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 questions and to plan your answers.
• Read questions carefully before you answering.
• Read the instructions carefully.
• 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.

Questions 1 to 7 carry 3 Scores each. Answer any six questions only. (6 × 3 = 18)

Question 1.
i) Let R be a relation on the set {1, 2, 3} given by R = {(1, 1), (2, 2), (1, 2), (2, 1), (2, 3)}. Which among the following element to be included to R so that R becomes Symmetric?
a) (3, 3)
b) (3, 2)
c) (1, 3)
d) (3, 1)
ii) If * is defined by a*b = a – b² and \(\oplus\) is defined by a \(\oplus\) b = a² + b , where a and b are integers. Then find the value of (3 \(\oplus\) 4) * 5
Answer:
i) b) (3, 2)
ii) (3 \(\oplus\) 4) * 5 = (32 + 4) * 5
= 13 * 5
= 13 – 5² = -12

Question 2.
If X + Y = \(\left[\begin{array}{ll}
5 & 2 \\
0 & 9
\end{array}\right]\) and X – Y = \(\left[\begin{array}{cc}
3 & 6 \\
0 & -1
\end{array}\right]\)find 2X – 3Y.
Answer:

Question 3.
Find rate of change of area of a circle.
a) with respect to the radius, when r = 10cm
b) with respect to the time when the radius is increasing at the rate of 0.7 cm/s. Given that r = 5cm
Answer:
i) Area of a circle A = πr²

Question 4.
i) Integrate \(\int \frac{(1+\log x)^{2}}{x} d x\)

Answer:

Question 5.
Find the area of a circle with centre (0, 0) and radius ‘a’ using integration.
Answer:
Equation of the circle is x² + y² = a²
y = \(\sqrt{a^{2}-x^{2}}\)
Area of the circle will 4 time the area under the curve from 0 to a.
Area = \(4 \int_{0}^{a} y d x=4 \int_{0}^{a} \sqrt{a^{2}-x^{2}} d x\)

Question 6.
Consider the differential equation \(\frac{d y}{d x}=\frac{x+y}{x}\)
i) Write the order of the differential equation.
ii) Solve the above given differential equation.
Answer:
i) Order = 1.

Question 7.
The following table shows a brief description of the manufacturing process of a company. The time required in hours per unit of the product and maximum availability of machine is also given in the table:

Product	The time required in hours/Unit on machine		Profit per Unit in Rupees
	Machine G	Machine H
A	3	5	20
B	4	6	30
	Maximum available time 10 hrs/day	Maximum available time 15 hrs/day

i) Write the objective function.
ii) Whether it is a maximization case or a minimization case. Justify.
iii) Write the constraints.
Answer:
Let x units = Machine G and y units = Machine H
i) Objective function: Z = 20x + 30y
ii) It is a maximization problem.
iii) Constraints are:
3x + 4y ≤ 10; 5x + 6y ≤ 15; x, y ≥ 0

Questions 8 to 17 carry 4 scores each. Answer any 8 questions. (8 × 4 = 32)

Question 8.
i) A function f : A → B, where A = {1, 2, 3} and B = {4, 5, 6} defined by f(1) = 5, f(2) = 6, f(3) = 4, Check whether f is a bijection. If it is a bijection, write f^-1 as set of ordered pairs.
ii) The operation table for an operation * is given below. Given that 1 is the identity element. Then which among the following is true regarding the element in the first column?

*	1	2	3
1		2	3
2		2	3
3		3	3

a) 3, 2, 2
b) 1, 2, 3
c) 1, 1, 2
d) 2, 2, 2
Check whether * is commutative.
Answer:
i) A = {1, 2, 3}; B = {4, 5, 6}
f(1) = 5, f(2) = 6, f(3) = 4
Hence f= {(1, 5),(2, 6),(3, 4)}
f^-1 = {(5, 1), (6, 2), (4, 3)}
ii) b) 1, 2, 3
Since; 1*2 = 2 and 2*1 =2
3 * 2 = 3 and 2*3 = 3
Therefore * is commutative

Question 9.
i) If Sin^-1 x = y, then
(a) 0 ≤ y ≤ π
b) \(-\frac{\pi}{2}\) ≤ y ≤ \(\frac{\pi}{2}\)
c) 0 < y < π
d) \(-\frac{\pi}{2}\) ≤ y ≤ \(\frac{\pi}{2}\)
ii) Find the principal value of sin^-1 (\(\frac{1}{2}\))
iii) sin^-1x = \(\frac{3}{4}\) find the value of cos^-1 x
Answer:
i) \(-\frac{\pi}{2}\) ≤ y ≤ \(\frac{\pi}{2}\)
ii) sin^-1 \(\frac{1}{2}\) = \(\frac{\pi}{6}\)
iii) sin^-1x + cos^-1x = \(\frac{\pi}{2}\)
\(\frac{3}{4}\) + cos^-1x = \(\frac{\pi}{2}\) ⇒ cos^-1x = \(\frac{\pi}{2}\) – \(\frac{3}{4}\)

Question 10.
i) Find the relation between ‘a’ and ‘b’ so that the function defined by
f(x) = \(\left\{\begin{array}{ll}
a x+1, & x \leq 3 \\
b x+3, & x>3
\end{array}\right.\) is continuous at x = 3
ii) “All continuous function are not differentiable.” Justify your answer with an example.
Answer:
i) Since f(x) is continuous at x = 3
\(\lim _{x \rightarrow 3^{-}}\) f(x) = \(\lim _{x \rightarrow 3^{+}}\) f(x) = f(3)
\(\lim _{x \rightarrow 3}\) (ax + 1) = \(\lim _{x \rightarrow 3}\) (bx + 3) = 3a +1
⇒ 3a + 1 = 3b + 3 = 3a +1
⇒ 3a + l = 3b + 3 ⇒ 3a – 3b – 2 = 0

ii) Consider the function f(x) = |x|.
Let us check the continuity and differentiability at x = 0.

Left derivative * Right derivative
Therefore not differentiable at x = 0.

Question 11.
i) Find the equation to the tangent to the curve y = x² – 2x + 7 at (2, 7)
ii) Find the maximum value of the function?
Answer:
f(x) = sin x + cos x, 0 < x < \(\frac{\pi}{2}\)
i) y = x² – 2x + 7 ⇒ \(\frac{d y}{d x}\) = 2x – 2
Slope at x = 2 is 2 × 2 – 2 – 2
Equation of the tangent is
(y – y₁) = m(x – x₁)
⇒ (y – 7) = 2(x- 2)
⇒ y – 7 = 2x – 4
⇒ 2x – y + 3 = 0

ii) c) f(x) = sin x + cos x
f'(x) = cos x – sin x
f”(x) = -sinx-cosx
For turning points;
f'(x) = cos x – sin x = 0 ⇒ tan x = 1

Question 12.
Integrate \(\int \frac{x+2}{2 x^{2}+6 x+5} d x\)
Answer:
Put x + 2 = A(4x + 6) + B
4A = 1 ⇒ A = \(\frac{1}{4}\)

Question 13.
Consider the differential equation
x \(\frac{d y}{d x}\) + y = \(\frac{1}{x^{2}}\)
i) Find the integrating factor.
ii) Solve the above differential equation.
Answer:

Question 14.
lf the vectors \(\overline{P Q}\) = -3i + 4j + 4k and \(\overline{P R}\) = -5i + 2j + 4k are the sides of a ΔPQR
i) Find the angle between \(\overline{P Q}\) and \(\overline{P R}\)
ii) Find the length of the median through the vertex P.
Answer:

ii)

With respect to the initial P the position vector of Q and R will be \(\overline{P Q}\) = -3i + 4j + 4k
and \(\overline{P R}\) = -5i + 2j + 4k respectively.
Since M is the midpoint of QR. The position vector of M will be

Question 15.
i) If \(\bar{a}\) = 5i – j – 3k and \(\bar{b}\) = i + 3j + 5k, then show that the vectors \(\bar{a}+\bar{b}, \bar{a}-\bar{b}\) are perpendicular.
ii) If \(\bar{a}\) = i – 2j + 3k, \(\bar{b}\) = 2i + 3j – 4k and
\(\bar{c}\) = i – 3j + 5k, then check whether \(\bar{a}\), \(\bar{b}\), \(\bar{c}\) are coplanar.
Answer:

Question 16.
i) Find the Cartesian equation of the line passing through origin and (5, -2, 3) ii) The point P(x, y, z) lies in the first octant and its distance from the origin is 12 units. If the position vector of P makes angles 45°, 60°with x and y axes respectively, find coordinates of P.
Answer:

Since P lies in the first octant, we take n = \(\frac{1}{2}\)
Therefore the coordinate of P is

Question 17.
Solve graphically Maximise Z = 5x + 3y Subject to the constraints 3x + 5y ≤ 15; 5x + 2y ≤ 10; x ≥ 0, y ≥ 0.
Answer:
In the figure the shaded region OABC is the fesible region. Here the region is bounded.
The corner points are
O(0, 0), A(2, 0), B(\(\frac{20}{19}, \frac{45}{19})\), C(0, 3)

Given Z = 5x + 3y

Corner points	Value of Z
O	Z = 0
A	Z = 5(2) + 3(0) = 10
B	Z = \(5\left(\frac{20}{19}\right)+3\left(\frac{45}{19}\right)=\frac{235}{19}\)
C	Z = 5(0) + 3(3) = 9

Since maximum value of Z occurs at B, the soluion is z = \(\frac{235}{19}\), (\(\frac{20}{19}\), \(\frac{45}{19}\))

Questions 18 to 24 carry 6 scores each. Answer any 5 questions. (5 × 6 = 30)

Question 18.
A = \(\left[\begin{array}{ccc}
3 & 3 & -1 \\
-2 & -2 & 1 \\
-4 & -5 & 2
\end{array}\right]\)
a) Find A^T
b) Express A as the sum of a symmetric and skew symmetric matrix.
ii) If A^T = \(\left[\begin{array}{cc}
\cos x & \sin x \\
-\sin x & \cos x
\end{array}\right]\), verift that A^T A = I
Answer:

Question 19.
i) Without expanding prove that
\(\left|\begin{array}{ccc}
x+y & y+z & z+x \\
z & x & y \\
1 & 1 & 1
\end{array}\right|\) = 0
ii) Consider the following system of equations
2x – 3y + 5z = 11; 3x + 2y – 4z = -5; x + y – 2z = -3
a) Express the system in Ax = B form.
b) Solve the system by matrix method.
Answer:

Question 20.
Find \(\frac{d y}{d x}\) of the following
i) x² + 2xy + 2y² = 1
ii) y^x = 2^x
iii) x = cos θ; y = sin θ at θ = \(\frac{\pi}{4}\)
Answer:
i) x² + 2xy + 2y² = 1
Differentiating w.r.to x;

ii) y^x = 2^x
Take log on both sides;
x log y = x log 2
Differentiating w.r.to x;

Question 21.
Evaluate the following

Answer:

Question 22.
Consider the parabolas y² = 4x, x² = 4y
i) Draw a rough figure for the above parabolas.
ii) Find the point of intersection of the two parabolas.
iii) Find the area bounded by these two parabolas.
Answer:

ii) solving the two conics we get the point of intersection as (0, 0) and (4, 4).
iii) Area of the enclosed region

Question 23.
i) Find the shortest distance between the lines whose vector equations are
\(\bar{r}\) = (i + 2j + 3k) + λ(i – 3j + 2k) and \(\bar{r}\) =(4i + 5j + 6k) + μ(i – 3j + 2k)
ii) If a plane meets positive x axis at a distance of 2 units from the origin, positive y axis at a distance of 3 units from the origin and positive z axis at a distance of 4 units from the origin. Find the equation of the plane.
iii) Find the perpendicular distance of (0, 0, 0) from the plane obtained in part (ii)
Answer:
i) \(\overline{a_{1}}\) = i + 2j + 3k; \(\bar{b}\) = i – 3j + 2k
\(\overline{a_{2}}\) = 4i + 5j + 6k Both lines are parallel.

Question 24.
i) A die is thrown twice let the event A be ‘odd number on first throw’ and B be ‘odd number on the second throw’ check whether A and B are independent.
ii) Coloured balls are distributed in three boxes as shown in the following table:

Box	Red	Black
1	2	0
II	0	2
III	1	1

A box is selected at random and a ball is taken out. If the ball taken is of red colour, What is the probability that the other ball in the box is also of red colour?
Answer:
i) n(S) = 36
A = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)}
B = {(1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (1, 3), (2, 3), (3, 3), (4, 3), (5, 3), (6, 3), (1, 5), (2, 5), (3,5), (4, 5), (5, 5), (6, 5)}
(A ∩ B) = {(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)}

Therefore A and B are independent.

ii) Let B₁, B₂, B₃ are the event of getting the boxes.
P(B₁) = P(B₂) = P(B₃) = \(\frac{1}{3}\)
Let E be the event of getting a red ball.

Kerala State Board New Syllabus Plus Two Maths Previous Year Question Papers and Answers.

Kerala Plus Two Maths Previous Year Question Paper March 2017 with Answers

Board	SCERT
Class	Plus Two
Subject	Maths
Category	Plus Two Previous Year Question Papers

Time: 2½ Hours
Cool off time : 15 Minutes

General Instructions to Candidates

• There is a ‘cool off time’ of 15 minutes in addition to the writing time of 2½ hrs.
• You 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 the 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.
a. Let R be a relation defined on A = {1,2, 3} by R = {(1,3), (3, 1), (2, 2)}.R is
a. Reflexive
b. Symmetric
c. Transitive
d. Reflexive but not transitive

b. Find fog and gof if f(x) = |x + 1| and g(x) = 2x – 1.

c. Let * be a binary operation defined on N x N by (a, b) * (c, d) = (a + c, b + d). Find the identity element for * if it exists.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.
Slope of the normal to the curve y² = 4x at (1, 2) is
a. 1
b. \(\frac { 1 }{ 2 } \)
c. 2
d.-1

b. Find the interval in which 2x³ + 9x² + 12x – 1 is strictly increasing.
OR
a. The rate of change of volume of a sphere with respect to its radius when the radius is 1 unit
a. 4π
b. 2π
c. π
d. \(\frac { \pi }{ 2 } \)

b. Find two positive numbers whose sum is 16 and the sum of whose cubes are minimum.

Question 7.

Question 8.

Question 9.

Question 10.

Question 11.

Question 12.
a. The angle between the vectors \(\widehat { i } \) + \(\widehat { j } \) and \(\widehat { j } \) + \(\widehat { k } \) is
(i) 60°
(ii) 30°
(iii) 45°
(iv) 90°

Question 13.
a. The line x – 1 = y = z is perpendicular to the line

b. Find the shortest distance between the lines

Question 14.

Question 15.
Consider the linear programming problem :
Maximize Z = 50x + 40y
Subject to the constraints
x + 2y > 10
3x + 4y < 24
x > 0, y > 0
a. Find the feasible region.
b. Find the comer points of the feasible region.
c. Find the maximum value of Z.
Maximize Z = 50x + 40y
Subject to the constraints
x + 2y > 10
3x + 4y < 24
x > 0, y > 0

Question 16.
If A and B are two events such that A ⊂ B and P(A) ≠ then P (A/B) is
a. \(\frac { P(A) }{ P(B) } \)
b. \(\frac { P(B) }{ P(A) } \)
c. \(\frac { 1 }{ P(A) } \)
d. \(\frac { 1 }{ P(B) } \)

b. There are two identical bags. Bag I contains 3 red and 4 black balls while Bag II contains 5 red and 4 black balls. One ball is drawn at random from one of the bags.
i. Find the probability that the ball is drawn is red.
ii. If the ball drawn is red what is the probability that it was drawn from the bag I?
OR
Consider the following probability distribution of a random variable X.

HSE Kerala Board Syllabus Plus Two Previous Year Model Question Papers and Answers Pdf HSSLive Free Download in both English medium and Malayalam medium are part of Plus Two Kerala SCERT. Here HSSlive.Guru have given Higher Secondary Kerala Plus Two Previous Year Sample Question Papers with Answers based on CBSE NCERT syllabus.

Board	SCERT, Kerala Board
Textbook	NCERT Based
Class	Plus Two
Subject	All Subjects
Papers	Previous Papers, Model Papers, Sample Papers
Category	Kerala Plus Two

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