#### 12th Standard Maths Inverse Trigonometric Functions English Medium Free Online Test One Mark Questions 2020 - 2021

12th Standard

Reg.No. :
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Maths

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

10 x 1 = 10
1. The value of sin-1 (cos x),0$\le x\le\pi$ is

(a)

$\pi-x$

(b)

$x-\frac{\pi}{2}$

(c)

$\frac{\pi}{2}-x$

(d)

$\pi-x$

2. If cot−1x=$\frac{2\pi}{5}$ for some x$\in$R, the value of tan-1 x is

(a)

$\frac{-\pi}{10}$

(b)

$\frac{\pi}{5}$

(c)

$\frac{\pi}{10}$

(d)

$-\frac{\pi}{5}$

3. If x=$\frac{1}{5}$, the valur of cos (cos-1x+2sin-1x) is

(a)

$-\sqrt { \frac { 24 }{ 25 } }$

(b)

$\sqrt { \frac { 24 }{ 25 } }$

(c)

$\frac{1}{5}$

(d)

-$\frac{1}{5}$

4. ${ sin }^{ -1 }\left( tan\frac { \pi }{ 4 } \right) -{ sin }^{ -1 }\left( \sqrt { \frac { 3 }{ x } } \right) =\frac { \pi }{ 6 }$.Then x is a root of the equation

(a)

x2−x−6=0

(b)

x2−x−12=0

(c)

x2+x−12=0

(d)

x2+x−6=0

5. If sin-1 $\frac{x}{5}+ cosec^{-1}\frac{5}{4}=\frac{\pi}{2}$, then the value of x is

(a)

4

(b)

5

(c)

2

(d)

3

6. If ${ tan }^{ -1 }\left\{ \cfrac { \sqrt { 1+{ x }^{ 2 } } -\sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 1+{ x }^{ 2 } } +\sqrt { 1-{ x }^{ 2 } } } \right\} =\alpha$ then x2 =

(a)

$sin2\alpha$

(b)

$sin\alpha$

(c)

$cos2\alpha$

(d)

$cos\alpha$

7. The number of solutions of the equation ${ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\cfrac { \pi }{ 4 }$

(a)

2

(b)

3

(c)

1

(d)

none

8. ${ tan }^{ -1 }\left( \cfrac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \cfrac { 2 }{ 11 } \right)$ =

(a)

0

(b)

$\cfrac { 1 }{ 2 }$

(c)

-1

(d)

none

9. If ${ cos }^{ -1 }x>x>{ sin }^{ -1 }x$ then

(a)

$\cfrac { 1 }{ \sqrt { 2 } } <x\le 1$

(b)

$0\le x<\cfrac { 1 }{ \sqrt { 2 } }$

(c)

$-1\le x<\cfrac { 1 }{ \sqrt { 2 } }$

(d)

x>0

10. 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]