#### 12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Three

12th Standard

Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

10 x 1 = 10
1. If $4{ cos }^{ -1 }x+{ sin }^{ -1 }x=\pi$ then x is

(a)

$\cfrac { 3 }{ 2 }$

(b)

$\cfrac { 1 }{ \sqrt { 2 } }$

(c)

$\cfrac { \sqrt { 3 } }{ 2 }$

(d)

$\cfrac { 2 }{ \sqrt { 3 } }$

2. The domain of cos-1(x2 - 4) is______

(a)

[3, 5]

(b)

[-1, 1]

(c)

$\left[ -\sqrt { 5 } ,-\sqrt { 3 } \right] \cup \left[ \sqrt { 3 } ,\sqrt { 5 } \right]$

(d)

[0, 1]

3. The auxiliary circle of the ellipse $\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 16 }$ = 1 is

(a)

x2 + y2 = 25

(b)

x2 + y2 = 16

(c)

x2 + y2 = 41

(d)

x2 + y2 = 5

4. The locus of the point of intersection of perpendicular tangents of the parabola y2 = 4ax is

(a)

latus rectum

(b)

directrix

(c)

tangent at the vertex

(d)

axis of the parabola

5. The angle between the vector $3\overset { \wedge }{ i } +4\overset { \wedge }{ j } +\overset { \wedge }{ 5k }$ and the z-axis is

(a)

30o

(b)

60o

(c)

45o

(d)

90o

6. The unit normal vector to the plane 2x + 3y + 4z = 5 is _______________

(a)

$\frac { 2 }{ \sqrt { 29 } } \overset { \wedge }{ i } +\frac { 3 }{ \sqrt { 29 } } \overset { \wedge }{ j } +\frac { 4 }{ \sqrt { 29 } } \overset { \wedge }{ k }$

(b)

$\frac { 2 }{ \sqrt { 29 } } \overset { \wedge }{ i } -\frac { 3 }{ \sqrt { 29 } } \overset { \wedge }{ j } +\frac { 4 }{ \sqrt { 29 } } \overset { \wedge }{ k }$

(c)

$\frac { 2 }{ \sqrt { 29 } } \overset { \wedge }{ i } -\frac { 3 }{ \sqrt { 29 } } \overset { \wedge }{ j } -\frac { 4 }{ \sqrt { 29 } } \overset { \wedge }{ k }$

(d)

$\frac { 2 }{ 5 } \overset { \wedge }{ i } +\frac { 3 }{ 5 } \overset { \wedge }{ j } +\frac { 4 }{ 5 } \overset { \wedge }{ k }$

7. For any value of n∈Z, $\int _{ 0 }^{ \pi }{ e{ cos }^{ 2x }{ cos }^{ 3 } } [(2n+1)x]$ is

(a)

$\frac{\pi}{2}$

(b)

$\pi$

(c)

0

(d)

2

8. Suppose that X takes on one of the values 0, 1, and 2. If for some constant k, P(X = i) = k P(X = i-I) i = 1, 2 and P(X = 0) =$\cfrac { 1 }{ 7 }$ then the value of k is

(a)

1

(b)

2

(c)

3

(d)

4

9. Subtraction is not a binary operation in

(a)

R

(b)

Z

(c)

N

(d)

Q

10. Which one of the following statements has truth value F?

(a)

Chennai is in India or $\sqrt 2$ is an integer

(b)

Chennai is in India or $\sqrt 2$ is an irrational number

(c)

Chennai is in China or $\sqrt 2$ is an integer

(d)

Chennai is in China or $\sqrt 2$ is an irrational number