CBSE Class 12 Previous Year Question Papers With Solutions Pdf Maths

Class 12 Subject Maths Paper Set 2 with Solutions

SECTION A

Question numbers 1 to 20 carry 1 mark each.

Question numbers 1 to 10 are multiple choice type questions. Select the correct option.

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Question 1: (Marks 1)

The relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1), (1, 1)} is

(A) symmetric and transitive, but not reflexive

(B) reflexive and symmetric, but not transitive

(C) symmetric, but neither reflexive nor transitive

(D) an equivalence relation

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Answer :

(C) symmetric, but neither reflexive nor transitive

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Question 2: (Marks 1)

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Answer :

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Question 3: (Marks 1)

If A is a non-singular square matrix of order 3 such that A2 = 3A, then value of |A| is

(A) – 3

(B) 3

(C) 9

(D) 27

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Answer :

(D) 27

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Question 4: (Marks 1)

The function f : R → R given by f(x) = – |x – 1| is

(A) continuous as well as differentiable at x = 1

(B) not continuous but differentiable at x = 1

(C) continuous but not differentiable at x = 1

(D) neither continuous nor differentiable at x = 1

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Answer :

(C) continuous but not differentiable at x = 1

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Question 5: (Marks 1)

Let A = {1, 3, 5}. Then the number of equivalence relations in A containing (1, 3) is

(A) 1

(B) 2

(C) 3

(D) 4

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Answer :

(B) 2

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Question 6: (Marks 1)

The interval in which the function f given by 2 x f(x) x e− = is strictly increasing, is

(A) (–∞, ∞)

(B) (–∞, 0)

(C) (2, ∞)

(D) (0, 2)

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Answer :

(D) (0, 2)

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Question 7: (Marks 1)

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Answer :

(A) [0, 12]

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Question 8: (Marks 1)

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Answer :

(A) –2

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Question 9: (Marks 1)

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Answer :

(A) 3√5 sq. units

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Question 10: (Marks 1)

The coordinates of the foot of the perpendicular drawn from the point (2, – 3, 4) on the y-axis is

(A) (2, 3, 4)

(B) (– 2, – 3, – 4)

(C) (0, – 3, 0)

(D) (2, 0, 4)

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Answer :

(C) (0, –3, 0)

Fill in the blanks in question numbers 11 to 15.

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Question 11: (Marks 1)

Answer :

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Question 12: (Marks 1)

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Answer :

0

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Question 13: (Marks 1)

The distance between parallel planes 2x + y – 2z – 6 = 0 and 4x + 2y – 4z = 0 is ___________ units.

OR

If P(1, 0, – 3) is the foot of the perpendicular from the origin to the plane, then the cartesian equation of the plane is _____________ .

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Answer :

2

OR

x – 3z = 10

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Question 14: (Marks 1)

If the radius of the circle is increasing at the rate of 0·5 cm/s, then the rate of increase of its circumference is _____________.

Answer :

π cm/s

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Question 15: (Marks 1)

The corner points of the feasible region of an LPP are (0,0), (0,8), (2,7), (5,4) and (6,0). The maximum profit P 3x 2y = + occurs at the point ________

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Answer :

(5, 4)

Question numbers 16 to 20 are very short answer type questions.

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Question 16: (Marks 1)

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Answer :

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Question 17: (Marks 1)

L.H.L. is k + 5

getting k = –3

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Question 18: (Marks 1)

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Answer :

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Question 19: (Marks 1)

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Answer :

Given differential equation is ey dy = ex dx

Integrating to get ey = ex + C

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Question 20: (Marks 1)

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Answer :

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SECTION B

Question numbers 21 to 26 carry 2 marks each.

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Question 21: (Marks 2)

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Answer :

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Question 22: (Marks 2)

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Question 23: (Marks 2)

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Answer :

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Question 29: (Marks 4)

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Answer :

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Question 30: (Marks 4)

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Answer :

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Question 31: (Marks 4)

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Answer :

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Question 32: (Marks 4)

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Answer :

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SECTION-D

Question numbers 33 to 36 carry 6 marks each.

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Question 33: (Marks 6)

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Answer :

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Question 34: (Marks 6)

Amongst all open (from the top) right circular cylindrical boxes of volume 125π cm3, find the dimensions of the box which has the least surface area.

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Answer :

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Question 35: (Marks 6)

Using integration, find the area lying above x-axis and included between the circle x2 + y2 = 8x and inside the parabola y2 = 4x.

OR

Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B(4, 5) and C(6, 3).

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Answer :

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Question 36: (Marks 6)

Find the probability distribution of the random variable X, which denotes the number of doublets in four throws of a pair of dice. Hence, find the mean of the number of doublets (X).

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Answer :

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