Maths Sample Paper For Class 12 With Solution NCERT CBSE Board 2020

Class 12 Subject Maths Paper Set 4 with Solutions

Section – A

Question numbers 1 to 10 are multiple choice questions of 1 mark each. Select the correct option :

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Question 1: (Marks 1)

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Answer :

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Question 2: (Marks 1)

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Answer :

(a) [28]

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Question 3: (Marks 1)

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Answer :

(c) -1

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Question 4: (Marks 1)

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Answer :

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Question 5: (Marks 1)

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Answer :

(c) 60°

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Question 6: (Marks 1)

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Answer :

(d) aa’ + cc’ = –1

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Question 7: (Marks 1)

The two planes x – 2y + 4z = 10 and 18x + 17y + kz = 50 are perpendicular, if k is equal to

(a) –4

(b) 4

(c) 2

(d) –2

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Answer :

(b) 4

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Question 8: (Marks 1)

In an LPP, if the objective function z = ax + by has the same maximum value on two corner points of the feasible region, then the number of points at which zmax occurs is

(a) 0

(b) 2

(c) finite

(d) infinite

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Answer :

(d) infinite

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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 :

In Q. Nos. 11 to 15, fill in the blanks with correct word / sentence :

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Question 11: (Marks 1)

If f : R → R be given by f(x) = (3 – x 3 ) 1/3, then fof (x) = ________

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Answer :

x

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Question 12: (Marks 1)

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Answer :

- 3

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Question 13: (Marks 1)

The number of points of discontinuity of f defined by f(x) = |x| – |x + 1| is ____________.

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Answer :

Zero

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Question 14: (Marks 1)

The slope of the tangent to the curve y = x 3 – x at the point (2, 6) is _______.

OR

The rate of change of the area of a circle with respect to its radius r, when r = 3 cm, is _________.

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Answer :

11

OR

6π cm2 /cm

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Question 15: (Marks 1)

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Answer :

Q. 16 to 20 are very short answer questions.

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Question 16: (Marks 1)

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Answer :

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Question 17: (Marks 1)

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Answer :

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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 :

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Question 20: (Marks 1)

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Answer :

Section – B

Q. Nos. 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)

Show that the function f defined by f(x) = (x – 1) ex + 1 is an increasing function for all x > 0.

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Answer :

ff (x) = xex

Now x > 0 and ex > 0 for all x

∴ ff (x) > 0 ⇒ f is increasing function.

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Question 24: (Marks 2)

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Answer :

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Question 25: (Marks 2)

Find the equation of the plane with intercept 3 on the y-axis and parallel to xz – plane.

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Answer :

Let required plane parallel to xz -plane is y = k

Given y -intercept is 3 ⇒ k = 3

⇒Equation of required plane is y = 3

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Question 26: (Marks 2)

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Answer :

Section – C

Q. Nos. 27 to 32 carry 4 marks each.

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Question 27: (Marks 4)

Prove that the relation R on Z, defined by R {(x, y) : (x – y) is divisible by 5} is an equivalence relation.

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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)

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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)

A coin is biased so that the head is three times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails. Hence find the mean of the number of tails.

OR

Suppose that 5 men out of 100 and 25 women out of 1000 are good orators. Assuming that there are equal number of men and women, find the probability of choosing a good orator.

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Answer :

Section – D

Q. Nos. 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)

Find the intervals on which the function f(x) = (x – 1)3 (x – 2)2 is (a) strictly increasing (b) strictly decreasing.

OR

Find the dimensions of the rectangle of perimeter 36 cm which will sweep out a volume as large as possible, when revolved about one of its side. Also, find the maximum volume.

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Answer :

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Question 35: (Marks 6)

Find the area of the region lying in the first quadrant and enclosed by the x – axis, the line y = x and the circle x 2 + y2 = 32.

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Answer :

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Question 36: (Marks 6)

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Answer :

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Ncert Solution for class 6 to 12 download in pdf