# Sample Question Paper

CLASS: XII

Session: 2021-22

Mathematics-041

Term – 1

### Time Allowed: 90 minutes Maximum Marks: 40

**General Instructions:**

1. This question paper contains three sections – A, B and C. Each part is compulsory.

2. Section – A has 20 MCQs, attempt any 16 out of 20.

3. Section – B has 20 MCQs, attempt any 16 out of 20

4. Section – C has 10 MCQs, attempt any 8 out of 10.

5. There is no negative marking.

6. All questions carry equal marks.

### SECTION – A

**In this section, attempt any 16 questions out of Questions 1 – 20.**

**Each Question is of 1 mark weightage.**

1.sin [ 𝜋3−sin-1 (−12)] is equal to:

a) 12

b) 13

c) -1

d) 1

2.The value of k (k < 0) for which the function 𝑓 defined as

𝑓(𝑥)={1−𝑐𝑜𝑠𝑘𝑥𝑥𝑠𝑖𝑛𝑥,𝑥≠012 ,𝑥=0

is continuous at 𝑥=0 is:

a) ±1

b) −1

c) ±12

d) 12

3.If A = [aij] is a square matrix of order 2 such that aij = {1,𝑤ℎ𝑒𝑛 𝑖 ≠𝑗0,𝑤ℎ𝑒𝑛 𝑖=𝑗 , then A2 is:

a) [1010]

b) |1100|

c) |1110|

d) [1001]

4.Value of 𝑘, for which A = [𝑘842𝑘] is a singular matrix is:

a) 4

b) -4

c) ±4

d) 0

5.Find the intervals in which the function f given by f (x) = x 2 – 4x + 6 is strictly increasing:

a) (– ∞, 2) ∪ (2, ∞)

b) (2, ∞)

c) (−∞,2)

d) (– ∞, 2]∪ (2, ∞)

6.Given that A is a square matrix of order 3 and | A | = – 4, then | adj A | is equal to:

a) -4

b) 4

c) -16

d) 16

7.A relation R in set A = {1,2,3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which of the following ordered pair in R shall be removed to make it an equivalence relation in A?

a) (1, 1)

b) (1, 2)

c) (2, 2)

d) (3, 3)

8.If [2𝑎+𝑏𝑎−2𝑏5𝑐−𝑑4𝑐+3𝑑]=[4−31124], then value of a + b – c + 2d is:

a) 8

b) 10

c) 4

d) –8

9.The point at which the normal to the curve y = 𝑥+1𝑥, x > 0 is perpendicular to the line 3x – 4y – 7 = 0 is:

a) (2, 5/2)

b) (±2, 5/2)

c) (- 1/2, 5/2)

d) (1/2, 5/2)

10.sin (tan-1x), where |x| < 1, is equal to:

a) 𝑥√1−𝑥2

b) 1√1−𝑥2

c) 1√1+𝑥2

d) 𝑥√1+𝑥2

11.Let the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by R = {(a, b) : |a – b| is a multiple of 4}. Then [1], the equivalence class containing 1, is:

a) {1, 5, 9}

b) {0, 1, 2, 5}

c) 𝜙

d) A

12.If ex + ey = ex+y , then 𝑑𝑦𝑑𝑥 is:

a) e y – x

b) e x + y

c) – e y – x

d) 2 e x – y

13.Given that matrices A and B are of order 3×n and m×5 respectively, then the order of matrix C = 5A +3B is:

a) 3×5 and m = n

b) 3×5

c) 3×3

d) 5×5

14.If y = 5 cos x – 3 sin x, then 𝑑2𝑦𝑑𝑥2 is equal to:

a) – y

b) y

c) 25y

d) 9y

15.For matrix A =[25−117], (𝑎𝑑𝑗𝐴)′ is equal to:

a) [−2−511−7]

b) [75112]

c) [711−52]

d) [7−5112]

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