Subject Code : 041
MATHEMATICS
Time allowed: 90 minutes Maximum marks : 40
General Instructions :
1. This question paper contains three sections A, Band 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 - Chas 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.
I. If / (x) =\;A. ~I,
then.l(Ax) - j(x) is equalto
(a) x(A.2 - 1) (b) 2A(x2- l) (c) x2(11.2 -l) (d) 11.(x2 - 1)
2. If cot (sin-I x)= cos (tan-I ✓3), then x =
2 2
(a) 0 (b) ✓3 (c) 2 (d) ✓5
3. 2x-3sinx
If f (x) =- - -, x =t O, 1s. continuous
. at x = 0, then f(O) =
3x +4tan x
(a) 3 (b) 2/7 (c) -1/7 (d) 2/ 3
4. Based on the given shaded region as the feasible region in the graph, at which point(s) is the objective
function Z = 2x + Sy maximum?
y
A(7, 0)
(a) (7, O) (b) (4, 5) (c) (6, 3) (d) (0, 6)
Mathematics 15
, I .
Tile (unction / : R -1 u, given by f(x) "' x - I IS
5 (b) an onto fonction
· (a) 0 one-one fun ction
(d a bijection (d) neither one-one nor onto
2x, x < 0 h
6• ((\")= . Ten
· . {2x+ I, x 2: 0
(a) f (x) is differentiable at x = 0 (b) .f (x) is continuous at x = O
(c) f (x) is discontinuous at x = 0 (d) none of these
7. Compute the product
[ -21 31 04] X l-~2 -~11·
(c) [--I6 3]4 (d) [-1-6 -43l
8. Derivative oflog 1o,X with respect to x2 is
(a) 2x2 lo&10 (b) log 10 e (c) loge 10
2x 2 2x 2
9. If A(adj A) = SI, where I is identity matrix of order 3, then ladj Al =
(a) 125 (b) 25 (c) 10 (d) 5
10. Which of the following is true about the function f(x) = x 4 - 4.x2 ?
(a) It has two local minima and one local maxima
(b) It has two local minima and zero local maxima
(c) It has one local minima and one local maxima
(d) It has two local minima and two local maxima
11. Let R be an equivalence relation defined on a set containing 6 elements. The minimum number of ordered
pairs that R must contain is
(a) 6 (b) 12 (c) 36 (d) 64
1'12. For the curve x2 + 4xy + 8y2 = 64 the tangents are parallel to the x-axis only at the points
(a) (o, 2✓2) and(o,-2✓2) (b) (8, - 4) and (- 8, 4)
(c) (8✓2,-2✓2)and(-8✓2, 2✓2) (d) (8, O) and (-8, O)
13. The existence of the unique solution of the system of equations x +y +z = ~. Sx - y +az = 10 and
2x + 3y - z = 6 depends on
(a) a only (b) ~ only
(c) a and~ both (d) neither~ nor a
14. The value of cos-1(cot(~))+ cos-I (sin( 237t)}s
(a) 21t (b) 2: 7t
(c) (d) 7t
3 3 2
15. If x = ct and y =~ . find dy att = 2.
t dx
(a) 4 (b) o (c) 4 (d)
4
16 ClasS 12
t(
MATHEMATICS
Time allowed: 90 minutes Maximum marks : 40
General Instructions :
1. This question paper contains three sections A, Band 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 - Chas 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.
I. If / (x) =\;A. ~I,
then.l(Ax) - j(x) is equalto
(a) x(A.2 - 1) (b) 2A(x2- l) (c) x2(11.2 -l) (d) 11.(x2 - 1)
2. If cot (sin-I x)= cos (tan-I ✓3), then x =
2 2
(a) 0 (b) ✓3 (c) 2 (d) ✓5
3. 2x-3sinx
If f (x) =- - -, x =t O, 1s. continuous
. at x = 0, then f(O) =
3x +4tan x
(a) 3 (b) 2/7 (c) -1/7 (d) 2/ 3
4. Based on the given shaded region as the feasible region in the graph, at which point(s) is the objective
function Z = 2x + Sy maximum?
y
A(7, 0)
(a) (7, O) (b) (4, 5) (c) (6, 3) (d) (0, 6)
Mathematics 15
, I .
Tile (unction / : R -1 u, given by f(x) "' x - I IS
5 (b) an onto fonction
· (a) 0 one-one fun ction
(d a bijection (d) neither one-one nor onto
2x, x < 0 h
6• ((\")= . Ten
· . {2x+ I, x 2: 0
(a) f (x) is differentiable at x = 0 (b) .f (x) is continuous at x = O
(c) f (x) is discontinuous at x = 0 (d) none of these
7. Compute the product
[ -21 31 04] X l-~2 -~11·
(c) [--I6 3]4 (d) [-1-6 -43l
8. Derivative oflog 1o,X with respect to x2 is
(a) 2x2 lo&10 (b) log 10 e (c) loge 10
2x 2 2x 2
9. If A(adj A) = SI, where I is identity matrix of order 3, then ladj Al =
(a) 125 (b) 25 (c) 10 (d) 5
10. Which of the following is true about the function f(x) = x 4 - 4.x2 ?
(a) It has two local minima and one local maxima
(b) It has two local minima and zero local maxima
(c) It has one local minima and one local maxima
(d) It has two local minima and two local maxima
11. Let R be an equivalence relation defined on a set containing 6 elements. The minimum number of ordered
pairs that R must contain is
(a) 6 (b) 12 (c) 36 (d) 64
1'12. For the curve x2 + 4xy + 8y2 = 64 the tangents are parallel to the x-axis only at the points
(a) (o, 2✓2) and(o,-2✓2) (b) (8, - 4) and (- 8, 4)
(c) (8✓2,-2✓2)and(-8✓2, 2✓2) (d) (8, O) and (-8, O)
13. The existence of the unique solution of the system of equations x +y +z = ~. Sx - y +az = 10 and
2x + 3y - z = 6 depends on
(a) a only (b) ~ only
(c) a and~ both (d) neither~ nor a
14. The value of cos-1(cot(~))+ cos-I (sin( 237t)}s
(a) 21t (b) 2: 7t
(c) (d) 7t
3 3 2
15. If x = ct and y =~ . find dy att = 2.
t dx
(a) 4 (b) o (c) 4 (d)
4
16 ClasS 12
t(
