Plus Two Maths Model Question Paper 5

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.

Plus Two Maths Previous Year Question Papers and Answers 2018 1

QUESTIONS

Question 1 to 7 carry 3 scores each. Answer any six questions only
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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.
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Question 2.
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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.
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Question 4.
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Question 5.
Find area of a circle with centre (0, 0) and radius “a” using integration.
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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.
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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
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a. Write the objective function.
b. Whether it is a maximisation case or a minimisation case Justify,
c. Write the contraints.
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Question 8 to 17 carry 4 scores each. Answer any eight questions only
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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?
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Question 9.
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Question 10.
a. Find th relation between ‘a’ and ‘b’ so that the function defined by
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b. “All continuous function are not differ-entiable”. Justify this statement with an example.
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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.
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Question 12.
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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.
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Question 14.
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Question 15.
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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.
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Question 17.
Solve graphically :
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Question 18 to 24 carry 6 scores each. Answer any 5 questions only
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Question 18.
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Question 19.
a. Without expanding prove that
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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.
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Question 20.
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Question 21.
Evaluate the following.
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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.
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Question 23.
a. Find the shortest distance between the lines whos vector equations are
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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).
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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.
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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?
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ANSWERS

Answer 1.
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Answer 2.
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Answer 3.
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Answer 4.
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Answer 5.
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Answer 6.
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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.
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Answer 10.
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Answer 11.
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Answer 12.
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Answer 13.
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Answer 14.
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Answer 17.
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Answer 18.
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Answer 20.
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Answer 21.
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Answer 24.
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Plus Two Maths Previous Year Question Papers and Answers