Sample Question Paper CLASS: XII Session: 2021-22 Mathematics (Code-041)

Time Allowed: 90 minutes

Sample Question Paper CLASS: XII

Session: 2021-22 Mathematics (Code-041)

Term - 1

Subject Code - 041 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 [ -sin-1 (- 1)] is equal to:

1

3

2

a) 1

2

b) 1

3

c) -1

d) 1

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

1

1- , 0

()

=

{

1

, = 0

2

is continuous at = 0 is:

a) ?1

b) -1

c) ? 1

d) 1

2

2

3.

If

A

=

[aij]

is

a

square

matrix

of

order

2

such

that

aij

=

{10, ,

=

,

then

1

A2 is:

a) [11 00]

b) |10 10|

c) |11 10|

d) [10 01]

4.

Value of , for which A = [4 28] is a singular matrix is:

1

a) 4 c) ?4

b) -4 d) 0

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

1

increasing:

a) (? , 2) (2, ) c) (-, 2)

b) (2, ) d) (? , 2] (2, )

6. Given that A is a square matrix of order 3 and | A | = - 4, then | adj A | is

1

equal to:

a) -4 c) -16

b) 4 d) 16

7. A relation R in set A = {1,2,3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}.

1

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

[25

+ -

4-+23] = [141

-243], then value of a + b ? c + 2d is:

1

a) 8 c) 4

b) 10 d) ?8

9. The point at which the normal to the curve y = + 1, x > 0 is perpendicular to

1

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:

1

a)

1-2

b)

1 1-2

c)

1 1+2

d)

1+2

11. Let the relation R in the set A = {x Z : 0 x 12}, given by R = {(a, b) : |a ?

1

b| is a multiple of 4}. Then [1], the equivalence class containing 1, is:

a) {1, 5, 9} c)

b) {0, 1, 2, 5} d) A

12.

If ex + ey = ex+y , then is:

1

a) e y - x c) ? e y - x

b) e x + y d) 2 e x - y

13. Given that matrices A and B are of order 3?n and m?5 respectively, then the

1

order of matrix C = 5A +3B is:

a) 3?5 and m = n c) 3?3

b) 3?5 d) 5?5

14.

If

y

=

5

cos

x

?

3

sin

x,

then

2 2

is

equal

to:

1

a) - y c) 25y

b) y d) 9y

15. For matrix A =[-211 57], () is equal to:

1

a) [-112 --57]

b) [171 52]

c) [-75 121]

d) [171 -25]

16. The points on the curve 2 + 2 = 1 at which the tangents are parallel to y-

1

9 16

axis are:

a) (0,?4)

b) (?4,0)

c) (?3,0)

d) (0, ?3)

17. Given that A = [] is a square matrix of order 3?3 and |A| = -7, then the

1

value of 3=1 22, where denotes the cofactor of element is:

a) 7

b) -7

c) 0

d) 49

18. If y = log(cos ), then is:

1

a) cos -1

b) - cos

c) sin

d) - tan

19. Based on the given shaded region as the feasible region in the graph, at

1

which point(s) is the objective function Z = 3x + 9y maximum?

a) Point B c) Point D

b) Point C d) every point on the line

segment CD

20. The least value of the function () = 2 + in the closed interval [0,]

1

2

is:

a) 2 c)

2

b)

6

+

3

d) The least value does not

exist.

SECTION ? B

In this section, attempt any 16 questions out of the Questions 21 - 40. Each Question is of 1 mark weightage.

21. The function : RR defined as () = 3 is:

1

a) One-on but not onto c) Neither one-one nor onto

b) Not one-one but onto d) One-one and onto

22.

If

x

=

a

sec

,

y

=

b

tan

,

then

2 2

at

=

6

is:

1

a)

-33 2

c) -33

b) -23

d)

- 332

23.

In the given graph, the feasible region for a LPP is

1

shaded.

The objective function Z = 2x ? 3y, will be minimum

at:

a) (4, 10)

b) (6, 8)

c) (0, 8)

d) (6, 5)

24. The derivative of sin-1 (21 - 2) w.r.t sin-1x, 1 < < 1, is:

1

2

a) 2 c)

2

b) - 2

2

d) -2

25.

1

1 -1 0

2 2 -4

If A = [2 3 4] and B = [-4 2 -4], then:

012

2 -1 5

a) A-1 = B c) B-1 = B

b) A-1 = 6B d) B-1 = 1A

6

26. The real function f(x) = 2x3 ? 3x2 ? 36x + 7 is:

1

a) Strictly increasing in (-, -2) and strictly decreasing in ( -2, )

b) Strictly decreasing in ( -2, 3) c) Strictly decreasing in (-, 3) and strictly increasing in (3, )

d) Strictly decreasing in (-, -2) (3, )

27. Simplest form of tan-1 (1++1-) , < < 3 is:

1

1+-1-

2

a) -

42

b) 3 -

22

c) -

2

d) -

2

28. Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value 1 of |2A| is:

a) 4 c) 64

b) 8 d) 16

29. The value of for which the function () = + + is strictly

1

decreasing over R is:

a) < 1

b) No value of b exists

c) 1

d) 1

30. Let R be the relation in the set N given by R = {(a, b) : a = b ? 2, b > 6}, then: 1

a) (2,4) R

b) (3,8) R

c) (6,8) R

d) (8,7) R

31.

, < 0

1

The point(s), at which the function f given by () ={ ||

-1, 0

is continuous, is/are:

a) R c) R ?{0}

b) = 0 d) = -1and 1

32. If A = [03 -24] and A = [20 324], then the values of , and respectively

1

are:

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