CBSE Previous Year Question Papers Class 12 Maths With Solutions

Class 12 Subject Maths Paper Set 3 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)

If f and g are two functions from R to R defined as f(x) = |x| + x and g(x) = |x| – x, then fog (x) for x < 0 is

(A) 4x

(B) 2x

(C) 0

(D) – 4x

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Answer :

(D) –4x

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Question 2: (Marks 1)

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Answer :

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Question 3: (Marks 1)

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Answer :

(A) 64

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Question 4: (Marks 1)

The maximum value of slope of the curve y = – x 3 + 3x2 + 12x – 5 is

(A) 15

(B) 12

(C) 9

(D) 0

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Answer :

(A) 15

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Question 5: (Marks 1)

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Answer :

(A) tan (xex) + c

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Question 6: (Marks 1)

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Answer :

(A) 1

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Question 7: (Marks 1)

Answer :

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Question 8: (Marks 1)

The coordinates of the foot of the perpendicular drawn from the point (– 2, 8, 7) on the XZ-plane is

(A) (– 2, – 8, 7)

(B) (2, 8, – 7)

(C) (– 2, 0, 7)

(D) (0, 8, 0)

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Answer :

(C) (–2, 0, 7)

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Question 9: (Marks 1)

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Answer :

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Question 10: (Marks 1)

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Answer :

(B) (0, 8)

Fill in the blanks in question numbers 11 to 15

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Question 11: (Marks 1)

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Answer :

0

OR

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Question 12: (Marks 1)

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Answer :

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Question 13: (Marks 1)

The equation of the tangent to the curve y = sec x at the point (0, 1) is __________ .

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Answer :

y =1

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Question 14: (Marks 1)

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Answer :

3

OR

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Question 15: (Marks 1)

A bag contains 3 black, 4 red and 2 green balls. If three balls are drawn simultaneously at random, then the probability that the balls are of different colours is __________ .

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Answer :

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

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Question 16: (Marks 1)

Construct a 2 × 2 matrix A = [aij] whose elements are given by aij = |(i)2 – j|.

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Answer :

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Question 17: (Marks 1)

Differentiate sin2 (√x) with respect to x.

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Answer :

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Question 18: (Marks 1)

Find the interval in which the function f given by f(x) = 7 – 4x – x 2 is strictly increasing.

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Answer :

f′ (x) 4 2x =− − 1/2

⇒ f(x) is increasing on (–∞, –2)

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Question 19: (Marks 1)

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Answer :

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Question 20: (Marks 1)

An unbiased coin is tossed 4 times. Find the probability of getting at least one head.

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Answer :

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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Answer :

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Question 23: (Marks 2)

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Answer :

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Question 24: (Marks 2)

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Answer :

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Question 25: (Marks 2)

Find the coordinates of the point where the line through (– 1, 1, – 8) and (5, – 2, 10) crosses the ZX-plane.

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Answer :

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Question 26: (Marks 2)

If A and B are two events such that P(A) = 0·4, P(B) = 0·3 and P(A ∪ B) = 0·6, then find P(B’ ∩ A)

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Answer :

P(A ∩ B) = P(A) + P(B) − P(A ∪ B) 0.1 1

P(B’ ∩ A) = P(A) − P(A ∩ B) = 0.3

SECTION C

Question numbers 27 to 32 carry 4 marks each.

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Question 27: (Marks 4)

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Answer :

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Question 28: (Marks 4)

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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)

Find the general solution of the differential equation x 2y dx – (x3 + y3) dy = 0.

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Answer :

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Question 31: (Marks 4)

Solve the following LPP graphically :

Minimise z = 5x + 7y

subject to the constraints

2x + y ≥ 8

x + 2y ≥ 10

x, y ≥ 0

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Answer :

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Question 32: (Marks 4)

A bag contains two coins, one biased and the other unbiased. When tossed, the biased coin has a 60% chance of showing heads. One of the coins is selected at random and on tossing it shows tails. What is the probability it was an unbiased coin ?

OR

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Answer :

SECTION D

Question numbers 33 to 36 carry 6 marks each.

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Question 33: (Marks 4)

Solve the following system of equations by matrix method :

x – y + 2z = 7

2x – y + 3z = 12

3x + 2y – z = 5

OR

Obtain the inverse of the following matrix using elementary operations :

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Answer :

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Question 34: (Marks 4)

Find the points on the curve 9y2 = x2, where the normal to the curve makes equal intercepts with both the axes. Also find the equation of the normals.

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Answer :

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Question 35: (Marks 4)

Find the area of the following region using integration: {(x, y) : y ≤ | x | + 2, y ≥ x2}.

OR

Using integration, find the area of a triangle whose vertices are (1,0), (2, 2) and (3,1).

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Answer :

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Question 36: (Marks 4)

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Answer :

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