Questions to summarize your exams

Model Question Paper
Mathematics
Class XII


Time Allowed : 3 hours Max:
Marks: 100


General Instructions
(i) The question paper consists of three parts A, B and C. Each question of each
part is compulsory.
(ii) Part A
Question number 1 to 20 are of 1 mark each.
(iii) Part B
Question number 21 to 31 are of 4 marks each
(iv) Question number 32 to 37 are of 6 marks each


Part A


Choose the correct answer in each of the questions from 1 to 20. Each of these question
contain 4 options with just one correct option.


1. Let N be the set of natural numbers and R be the relation in N defined as
R = {(a, b) : a = b – 2, b > 6}. Then
(A) (2, 4) ∈ R (B) (3, 8) ∈ R
(C) (6, 8) ∈ R (D) (8, 7) ∈ R.


2. If sin–1 x = y, then
−π π
(A) 0 ≤ y ≤ π (B) ≤ y≤
2 2

−π π
(C) 0 < y < π (D) < y<
2 2



⎛π 1 ⎞
3. sin ⎜ − sin –1 ( )⎟ is equal to
⎝3 2 ⎠

1 1
(A) (B)
2 3

, 1
(C) (D) 1
4


4. The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is
(A) 27 (B) 18
(C) 81 (D) 512


5. Let A be a square matrix of order 3 × 3, then kA is equal to

(A) k A (B) k 2 A

(C) k 3 A (D) 3k A


⎧1 + x, when x ≤ 2
6. If f ( x) = ⎨5 – x, when x ≤ 3 , then
⎩
(A) f is continuous at x = 2 (B) f is discontinuous at x = 2
(C) f is continuous at x = 3 (D) f is continuous at x = 3 and discontinu-
ous at x=2


d
7. (log tan x) is equal to
dx
(A) 2 sec 2x (B) 2 cosec 2 x
(C) sec 2 x (D) cosec 2x


8. The rate of change of the area of a circle with respect to its radius r when r = 6 is
(A) 10 π (B) 12 π
(C) 8 π (D) 11 π


9. The interval in which y = x2 e–x is increasing is
(A) (– ∞, ∞) (B) (–2, 0)
(C) (2, ∞) (D) (0, 2)


∫ xsec
2
10. x dx is equal to

(A) tanx2 + C (B) tan2x + C
(C) x tanx – log sin x (D) x tanx + log cos x + C