Page 1
Subject Code - 041
Sample Question Paper
CLASS: XII
Session: 2021-22
Mathematics (Code-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. All questions carry equal marks.
6. There is no negative marking.
SECTION – A
In this section, attempt any 16 questions out of Questions 1 – 20.
Each Question is of 1 mark weightage.
1.
sin [
?? 3
-sin
-1
(-
1
2
)] is equal to:
a)
1
2
b)
1
3
c) -1 d) 1
1
2. The value of k (k < 0) for which the function ?? defined as
?? (?? ) = {
1-?????????? ?????????? , ?? ? 0
1
2
, ?? = 0
is continuous at ?? = 0 is:
a) ±1 b) -1
c) ±
1
2
d)
1
2
1
3.
If A = [aij] is a square matrix of order 2 such that aij = {
1, ?? h???? ?? ? ?? 0, ?? h???? ?? = ?? , then
A
2
is:
a) [
1 0
1 0
] b) |
1 1
0 0
|
c) |
1 1
1 0
| d) [
1 0
0 1
]
1
4.
Value of ?? , for which A = [
?? 8
4 2?? ] is a singular matrix is:
a) 4 b) -4
c) ±4 d) 0
1
Page 2
Subject Code - 041
Sample Question Paper
CLASS: XII
Session: 2021-22
Mathematics (Code-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. All questions carry equal marks.
6. There is no negative marking.
SECTION – A
In this section, attempt any 16 questions out of Questions 1 – 20.
Each Question is of 1 mark weightage.
1.
sin [
?? 3
-sin
-1
(-
1
2
)] is equal to:
a)
1
2
b)
1
3
c) -1 d) 1
1
2. The value of k (k < 0) for which the function ?? defined as
?? (?? ) = {
1-?????????? ?????????? , ?? ? 0
1
2
, ?? = 0
is continuous at ?? = 0 is:
a) ±1 b) -1
c) ±
1
2
d)
1
2
1
3.
If A = [aij] is a square matrix of order 2 such that aij = {
1, ?? h???? ?? ? ?? 0, ?? h???? ?? = ?? , then
A
2
is:
a) [
1 0
1 0
] b) |
1 1
0 0
|
c) |
1 1
1 0
| d) [
1 0
0 1
]
1
4.
Value of ?? , for which A = [
?? 8
4 2?? ] is a singular matrix is:
a) 4 b) -4
c) ±4 d) 0
1
5. Find the intervals in which the function f given by f (x) = x
2
– 4x + 6 is strictly
increasing:
a) (– 8, 2) ? (2, 8) b) (2, 8)
c) (-8, 2) d) (– 8, 2]? (2, 8)
1
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
1
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)
1
8.
If [
2?? + ?? ?? - 2?? 5?? - ?? 4?? + 3?? ] = [
4 -3
11 24
], then value of a + b – c + 2d is:
a) 8 b) 10
c) 4 d) –8
1
9.
The point at which the normal to the curve y = ?? +
1
?? , 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)
1
10. sin (tan
-1
x), where |x| < 1, is equal to:
a)
?? v1-?? 2
b)
1
v1-?? 2
c)
1
v1+?? 2
d)
?? v1+?? 2
1
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) ?? d) A
1
12.
If e
x
+ e
y
= e
x+y
, then
????
????
is:
a) e
y - x
b) e
x + y
c) – e
y - x
d) 2 e
x - y
1
Page 3
Subject Code - 041
Sample Question Paper
CLASS: XII
Session: 2021-22
Mathematics (Code-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. All questions carry equal marks.
6. There is no negative marking.
SECTION – A
In this section, attempt any 16 questions out of Questions 1 – 20.
Each Question is of 1 mark weightage.
1.
sin [
?? 3
-sin
-1
(-
1
2
)] is equal to:
a)
1
2
b)
1
3
c) -1 d) 1
1
2. The value of k (k < 0) for which the function ?? defined as
?? (?? ) = {
1-?????????? ?????????? , ?? ? 0
1
2
, ?? = 0
is continuous at ?? = 0 is:
a) ±1 b) -1
c) ±
1
2
d)
1
2
1
3.
If A = [aij] is a square matrix of order 2 such that aij = {
1, ?? h???? ?? ? ?? 0, ?? h???? ?? = ?? , then
A
2
is:
a) [
1 0
1 0
] b) |
1 1
0 0
|
c) |
1 1
1 0
| d) [
1 0
0 1
]
1
4.
Value of ?? , for which A = [
?? 8
4 2?? ] is a singular matrix is:
a) 4 b) -4
c) ±4 d) 0
1
5. Find the intervals in which the function f given by f (x) = x
2
– 4x + 6 is strictly
increasing:
a) (– 8, 2) ? (2, 8) b) (2, 8)
c) (-8, 2) d) (– 8, 2]? (2, 8)
1
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
1
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)
1
8.
If [
2?? + ?? ?? - 2?? 5?? - ?? 4?? + 3?? ] = [
4 -3
11 24
], then value of a + b – c + 2d is:
a) 8 b) 10
c) 4 d) –8
1
9.
The point at which the normal to the curve y = ?? +
1
?? , 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)
1
10. sin (tan
-1
x), where |x| < 1, is equal to:
a)
?? v1-?? 2
b)
1
v1-?? 2
c)
1
v1+?? 2
d)
?? v1+?? 2
1
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) ?? d) A
1
12.
If e
x
+ e
y
= e
x+y
, then
????
????
is:
a) e
y - x
b) e
x + y
c) – e
y - x
d) 2 e
x - y
1
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 b) 5×3
c) 3×3 d) 5×5
1
14.
If y = 5 cos x – 3 sin x, then
?? 2
?? ?? ?? 2
is equal to:
a) - y b) y
c) 25y d) 9y
1
15.
For matrix A =[
2 5
-11 7
], (???????? )
'
is equal to:
a) [
-2 -5
11 -7
] b) [
7 5
11 2
]
c) [
7 11
-5 2
] d) [
7 -5
11 2
]
1
16.
The points on the curve
?? 2
9
+
?? 2
16
= 1 at which the tangents are parallel to y-
axis are:
a) (0,±4) b) (±4,0)
c) (±3,0) d) (0, ±3)
1
17. Given that A = [?? ????
] is a square matrix of order 3×3 and |A| = -7, then the
value of ? ?? ?? 2
?? ?? 2
3
?? =1
, where ?? ????
denotes the cofactor of element ?? ????
is:
a) 7 b) -7
c) 0 d) 49
1
18.
If y = log(cos ?? ?? ), then
????
????
is:
a) cos ?? ?? -1
b) ?? -?? cos ?? ??
c) ?? ?? sin ?? ?? d) - ?? ?? tan ?? ??
1
19. Based on the given shaded region as the feasible region in the graph, at
which point(s) is the objective function Z = 3x + 9y maximum?
a) Point B b) Point C
c) Point D d) every point on the line
segment CD
1
Page 4
Subject Code - 041
Sample Question Paper
CLASS: XII
Session: 2021-22
Mathematics (Code-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. All questions carry equal marks.
6. There is no negative marking.
SECTION – A
In this section, attempt any 16 questions out of Questions 1 – 20.
Each Question is of 1 mark weightage.
1.
sin [
?? 3
-sin
-1
(-
1
2
)] is equal to:
a)
1
2
b)
1
3
c) -1 d) 1
1
2. The value of k (k < 0) for which the function ?? defined as
?? (?? ) = {
1-?????????? ?????????? , ?? ? 0
1
2
, ?? = 0
is continuous at ?? = 0 is:
a) ±1 b) -1
c) ±
1
2
d)
1
2
1
3.
If A = [aij] is a square matrix of order 2 such that aij = {
1, ?? h???? ?? ? ?? 0, ?? h???? ?? = ?? , then
A
2
is:
a) [
1 0
1 0
] b) |
1 1
0 0
|
c) |
1 1
1 0
| d) [
1 0
0 1
]
1
4.
Value of ?? , for which A = [
?? 8
4 2?? ] is a singular matrix is:
a) 4 b) -4
c) ±4 d) 0
1
5. Find the intervals in which the function f given by f (x) = x
2
– 4x + 6 is strictly
increasing:
a) (– 8, 2) ? (2, 8) b) (2, 8)
c) (-8, 2) d) (– 8, 2]? (2, 8)
1
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
1
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)
1
8.
If [
2?? + ?? ?? - 2?? 5?? - ?? 4?? + 3?? ] = [
4 -3
11 24
], then value of a + b – c + 2d is:
a) 8 b) 10
c) 4 d) –8
1
9.
The point at which the normal to the curve y = ?? +
1
?? , 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)
1
10. sin (tan
-1
x), where |x| < 1, is equal to:
a)
?? v1-?? 2
b)
1
v1-?? 2
c)
1
v1+?? 2
d)
?? v1+?? 2
1
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) ?? d) A
1
12.
If e
x
+ e
y
= e
x+y
, then
????
????
is:
a) e
y - x
b) e
x + y
c) – e
y - x
d) 2 e
x - y
1
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 b) 5×3
c) 3×3 d) 5×5
1
14.
If y = 5 cos x – 3 sin x, then
?? 2
?? ?? ?? 2
is equal to:
a) - y b) y
c) 25y d) 9y
1
15.
For matrix A =[
2 5
-11 7
], (???????? )
'
is equal to:
a) [
-2 -5
11 -7
] b) [
7 5
11 2
]
c) [
7 11
-5 2
] d) [
7 -5
11 2
]
1
16.
The points on the curve
?? 2
9
+
?? 2
16
= 1 at which the tangents are parallel to y-
axis are:
a) (0,±4) b) (±4,0)
c) (±3,0) d) (0, ±3)
1
17. Given that A = [?? ????
] is a square matrix of order 3×3 and |A| = -7, then the
value of ? ?? ?? 2
?? ?? 2
3
?? =1
, where ?? ????
denotes the cofactor of element ?? ????
is:
a) 7 b) -7
c) 0 d) 49
1
18.
If y = log(cos ?? ?? ), then
????
????
is:
a) cos ?? ?? -1
b) ?? -?? cos ?? ??
c) ?? ?? sin ?? ?? d) - ?? ?? tan ?? ??
1
19. Based on the given shaded region as the feasible region in the graph, at
which point(s) is the objective function Z = 3x + 9y maximum?
a) Point B b) Point C
c) Point D d) every point on the line
segment CD
1
20.
The least value of the function ?? (?? ) = 2???????? + ?? in the closed interval [0,
?? 2
]
is:
a) 2
b)
?? 6
+ v3
c)
?? 2
d) The least value does not
exist.
1
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 ?? : R?R defined as ?? (?? ) = ?? 3
is:
a) One-on but not onto b) Not one-one but onto
c) Neither one-one nor onto d) One-one and onto
1
22.
If x = a sec ?? , y = b tan ?? , then
?? 2
?? ?? ?? 2
at ?? =
?? 6
is:
a)
-3v 3?? ?? 2
b)
-2v 3?? ??
c)
-3v 3?? ??
d)
-?? 3v 3?? 2
1
23. In the given graph, the feasible region for a LPP is
shaded.
The objective function Z = 2x – 3y, will be minimum
at:
a) (4, 10) b) (6, 8)
c) (0, 8) d) (6, 5)
1
24.
The derivative of sin
-1
(2?? v1 - ?? 2
) w.r.t sin
-1
x, -
1
v 2
< ?? <
1
v 2
, is:
a) 2
b)
?? 2
- 2
c)
?? 2
d) -2
1
25.
If A = [
1 -1 0
2 3 4
0 1 2
] and B = [
2 2 -4
-4 2 -4
2 -1 5
], then:
a) A
-1
= B b) A
-1
= 6B
c) B
-1
= B
d) B
-1
=
1
6
A
1
Page 5
Subject Code - 041
Sample Question Paper
CLASS: XII
Session: 2021-22
Mathematics (Code-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. All questions carry equal marks.
6. There is no negative marking.
SECTION – A
In this section, attempt any 16 questions out of Questions 1 – 20.
Each Question is of 1 mark weightage.
1.
sin [
?? 3
-sin
-1
(-
1
2
)] is equal to:
a)
1
2
b)
1
3
c) -1 d) 1
1
2. The value of k (k < 0) for which the function ?? defined as
?? (?? ) = {
1-?????????? ?????????? , ?? ? 0
1
2
, ?? = 0
is continuous at ?? = 0 is:
a) ±1 b) -1
c) ±
1
2
d)
1
2
1
3.
If A = [aij] is a square matrix of order 2 such that aij = {
1, ?? h???? ?? ? ?? 0, ?? h???? ?? = ?? , then
A
2
is:
a) [
1 0
1 0
] b) |
1 1
0 0
|
c) |
1 1
1 0
| d) [
1 0
0 1
]
1
4.
Value of ?? , for which A = [
?? 8
4 2?? ] is a singular matrix is:
a) 4 b) -4
c) ±4 d) 0
1
5. Find the intervals in which the function f given by f (x) = x
2
– 4x + 6 is strictly
increasing:
a) (– 8, 2) ? (2, 8) b) (2, 8)
c) (-8, 2) d) (– 8, 2]? (2, 8)
1
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
1
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)
1
8.
If [
2?? + ?? ?? - 2?? 5?? - ?? 4?? + 3?? ] = [
4 -3
11 24
], then value of a + b – c + 2d is:
a) 8 b) 10
c) 4 d) –8
1
9.
The point at which the normal to the curve y = ?? +
1
?? , 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)
1
10. sin (tan
-1
x), where |x| < 1, is equal to:
a)
?? v1-?? 2
b)
1
v1-?? 2
c)
1
v1+?? 2
d)
?? v1+?? 2
1
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) ?? d) A
1
12.
If e
x
+ e
y
= e
x+y
, then
????
????
is:
a) e
y - x
b) e
x + y
c) – e
y - x
d) 2 e
x - y
1
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 b) 5×3
c) 3×3 d) 5×5
1
14.
If y = 5 cos x – 3 sin x, then
?? 2
?? ?? ?? 2
is equal to:
a) - y b) y
c) 25y d) 9y
1
15.
For matrix A =[
2 5
-11 7
], (???????? )
'
is equal to:
a) [
-2 -5
11 -7
] b) [
7 5
11 2
]
c) [
7 11
-5 2
] d) [
7 -5
11 2
]
1
16.
The points on the curve
?? 2
9
+
?? 2
16
= 1 at which the tangents are parallel to y-
axis are:
a) (0,±4) b) (±4,0)
c) (±3,0) d) (0, ±3)
1
17. Given that A = [?? ????
] is a square matrix of order 3×3 and |A| = -7, then the
value of ? ?? ?? 2
?? ?? 2
3
?? =1
, where ?? ????
denotes the cofactor of element ?? ????
is:
a) 7 b) -7
c) 0 d) 49
1
18.
If y = log(cos ?? ?? ), then
????
????
is:
a) cos ?? ?? -1
b) ?? -?? cos ?? ??
c) ?? ?? sin ?? ?? d) - ?? ?? tan ?? ??
1
19. Based on the given shaded region as the feasible region in the graph, at
which point(s) is the objective function Z = 3x + 9y maximum?
a) Point B b) Point C
c) Point D d) every point on the line
segment CD
1
20.
The least value of the function ?? (?? ) = 2???????? + ?? in the closed interval [0,
?? 2
]
is:
a) 2
b)
?? 6
+ v3
c)
?? 2
d) The least value does not
exist.
1
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 ?? : R?R defined as ?? (?? ) = ?? 3
is:
a) One-on but not onto b) Not one-one but onto
c) Neither one-one nor onto d) One-one and onto
1
22.
If x = a sec ?? , y = b tan ?? , then
?? 2
?? ?? ?? 2
at ?? =
?? 6
is:
a)
-3v 3?? ?? 2
b)
-2v 3?? ??
c)
-3v 3?? ??
d)
-?? 3v 3?? 2
1
23. In the given graph, the feasible region for a LPP is
shaded.
The objective function Z = 2x – 3y, will be minimum
at:
a) (4, 10) b) (6, 8)
c) (0, 8) d) (6, 5)
1
24.
The derivative of sin
-1
(2?? v1 - ?? 2
) w.r.t sin
-1
x, -
1
v 2
< ?? <
1
v 2
, is:
a) 2
b)
?? 2
- 2
c)
?? 2
d) -2
1
25.
If A = [
1 -1 0
2 3 4
0 1 2
] and B = [
2 2 -4
-4 2 -4
2 -1 5
], then:
a) A
-1
= B b) A
-1
= 6B
c) B
-1
= B
d) B
-1
=
1
6
A
1
26. The real function f(x) = 2x
3
– 3x
2
– 36x + 7 is:
a) Strictly increasing in (-8, -2) and strictly decreasing in ( -2, 8)
b) Strictly decreasing in ( -2, 3)
c) Strictly decreasing in (-8, 3) and strictly increasing in (3, 8)
d) Strictly decreasing in (-8, -2) ? (3, 8)
1
27.
Simplest form of tan
-1
(
v 1+???????? +v 1-???????? v 1+???????? -v 1-???????? ) , ?? < ?? <
3?? 2
is:
a)
?? 4
-
?? 2
b)
3?? 2
-
?? 2
c) -
?? 2
d) ?? -
?? 2
1
28. Given that A is a non-singular matrix of order 3 such that A
2
= 2A, then value
of |2A| is:
a) 4 b) 8
c) 64 d) 16
1
29. The value of ?? for which the function ?? (?? ) = ?? + ???????? + ?? is strictly
decreasing over R is:
a) ?? < 1 b) No value of b exists
c) ?? = 1 d) ?? = 1
1
30. Let R be the relation in the set N given by 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
1
31.
The point(s), at which the function f given by ?? (?? ) ={
?? |?? |
, ?? < 0
-1, ?? = 0
is continuous, is/are:
a) ???? R b) ?? = 0
c) ???? R –{0} d) ?? = -1and 1
1
32.
If A = [
0 2
3 -4
] and ?? A = [
0 3?? 2?? 24
], then the values of ?? , ?? and ?? respectively
are:
1
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