# CBSE Class 12 Previous Year Question Papers With Solutions Pdf Maths

Here we are providing CBSE Previous Year Question Papers Class 6 to 12 solved with soutions CBSE Class 12 Previous Year Question Papers With Solutions pdf Maths Maths sample paper class 12, Maths previous year question paper class 12, cbse class 12 Maths sample paper, cbse class 12 Maths sample paper 2020, Maths sample paper class 12 2020, cbse sample paper 2020 class 12 Maths, class 12 Maths sample paper 20 Practice of previous year question papers and sample papers protects each and every student to score bad marks in exams.If any student of CBSE Board continuously practices last year question paper student will easily score high marks in tests. Fortunately earlier year question papers can assist the understudies with scoring great in the tests. Unraveling previous year question paper class 12 Maths is significant for understudies who will show up for Class 12 Board tests.

## 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.

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

(C) symmetric, but neither reflexive nor transitive

Question 2: (Marks 1)

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

(D) 27

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

(C) continuous but not differentiable at x = 1

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

(B) 2

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)

(D) (0, 2)

Question 7: (Marks 1)

(A) [0, 12]

Question 8: (Marks 1)

(A) –2

Question 9: (Marks 1)

(A) 35 sq. units

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)

(C) (0, –3, 0)

Fill in the blanks in question numbers 11 to 15.

Question 11: (Marks 1)

Question 12: (Marks 1)

0

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 _____________ .

2

OR

x – 3z = 10

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 _____________.

π cm/s

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 ________

(5, 4)

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

Question 16: (Marks 1)

Question 17: (Marks 1)

L.H.L. is k + 5

getting k = –3

Question 18: (Marks 1)

Question 19: (Marks 1)

Given differential equation is ey dy = ex dx

Integrating to get ey = ex + C

Question 20: (Marks 1)

SECTION B

Question numbers 21 to 26 carry 2 marks each.

Question 21: (Marks 2)

Question 22: (Marks 2)

Question 23: (Marks 2)

Question 24: (Marks 2)

Question 25: (Marks 2)

Any point on line is (2 + 3λ, - 1 + 4λ ,2 + 2λ)

Putting in equation of plane to get λ = 0

Thus point of intersection is (2, –1, 2)

Question 26: (Marks 2)

A purse contains 3 silver and 6 copper coins and a second purse contains 4 silver and 3 copper coins. If a coin is drawn at random from one of the two purses, find the probability that it is a silver coin.

SECTION C

Question numbers 27 to 32 carry 4 marks each.

Question 27: (Marks 4)

Let a ∈ N clearly a divides a ∴ (a, a) ∈ R

∴ R is reflexive

For symmetric

(1, 2) ∈ R but (2, 1) ∉ R

∴ R is not symmetric

For transitive

Let (a, b) , (b, c) ∈ R

∴ a divides b and b divides c

⇒ a divides c ∴ (a, c) ∈ R

R is transitive

As R is not symmetric ∴ It is not an equivalence relation

OR

Question 28: (Marks 4)

Question 29: (Marks 4)

Question 30: (Marks 4)

Question 31: (Marks 4)

Question 32: (Marks 4)

SECTION-D

Question numbers 33 to 36 carry 6 marks each.

Question 33: (Marks 6)

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.

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).

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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