Class 12 Mathematics (Maths) Official Sample Question Paper (2021-22- Term I) | Mathematics (Maths) Class 12 - JEE PDF Download

 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