Inverse Trigonometric Functions Test

Result

Inverse Trigonometric Functions Test - 58

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Weekly Quiz Competition

Question 1
1 / -0

If $${ sin }^{ -1 }\left( a-\frac { { a }^{ 2 } }{ 3 } +\frac { { a }^{ 3 } }{ 9 } -...........\infty \right) +{ cos }^{ -1 }\left( 1+b+{ b }^{ 2 }+.......\infty \right) =\frac { \pi }{ 2 } $$

A
$$a=-3,b=1$$

B
$$a=1,b=\dfrac { -1 }{ 3 } $$

C
$$a=\dfrac { 1 }{ 6 } ,b=\dfrac { 1 }{ 2 } $$

D
$$a=\dfrac { 1 }{ 6 } ,b=\dfrac { 1 }{ 3 } $$

Solution
Question 2
1 / -0

If $$(cot^{-1}x)^{2}-3(cot^{-1}x)+2 > 0,$$ then x lies in

A
(cot 2, cot 1)

B
$$(-\infty , cot 2)\cup (cot 1,\infty )$$

C
$$(cot 1 \infty)$$

D
$$(-\infty , cot 1)\cup (cot 2,\infty )$$

Solution
Question 3
1 / -0

The solution of the equation $$sin^{-1}(\frac{dt}{dx})=x+y$$ is

A
tan(x+y)+sec(x+y)=x+c

B
tan(x+y)-sec(x+y)=x+c

C
tan(x+y)+sec(x+y)+x+c=0

D
None of these

Solution
Question 4
1 / -0

Thee value of $$\cos^{-1}x+\cos^{-1}\left(\dfrac {x}{2}+\dfrac {\sqrt {3-x^{2}}}{2}\right)$$, where $$\dfrac {1}{2} \le x \le 1$$.

A
$$\dfrac {\pi}{6}$$

B
$$\dfrac {\pi}{3}$$

C
$$\dfrac {\pi}{2}$$

D
$$0$$

Solution
Question 5
1 / -0

The value of $${ tan }^{ -1 }\left( \frac { xcos\theta }{ 1-xsin\theta } \right) -{ cot }^{ -1 }\left( \frac { cos\theta }{ x-sin\theta } \right) $$ is :

A
$$2\theta $$

B
$$\theta $$

C
$$\frac { \theta }{ 2 } $$

D
Independent of $$\theta $$

Solution
Question 6
1 / -0

If $${ sin }^{ -1 }\left( \frac { x }{ 5 } \right) +{ cosec }^{ -1 }\left( \frac { 5 }{ 4 } \right) =\frac { \pi }{ 2 } $$, then value of x is :

A
1

B
3

C
4

D
5

Solution
Question 7
1 / -0

Let $$S_{n}=\cot^{-1}\left(3x+\dfrac{2}{x}\right)+ \cot^{-1}\left(6x+\dfrac{2}{x}\right)+ \cot^{-1}\left(10x+\dfrac{2}{x}\right)+.....+n$$ term where $$x>0$$. If $$\displaystyle \lim_{n\rightarrow \infty}S_{n}=$$ then $$x$$ equals

A
$$\dfrac{\pi}{4}$$

B
$$1$$

C
$$\tan 1$$

D
$$\cot 1$$

Solution
Question 8
1 / -0

The number of solution of the equation $${\sin ^{ - 1}}\left( {1 - x} \right) - 2{\sin ^{ - 1}}x = \frac{\pi }{2}$$ is are

A
0

B
1

C
2

D
More then Two

Solution
Question 9
1 / -0

Let f:-$$\left\{ 0,4\pi \right\} $$$$\rightarrow \left[ 0,\pi \right] $$ be defined by f(x)=$${ cos }^{ -1 }\left( cosx \right) $$. The number of points x$$\in \left[ 0,4\pi \right] $$ satisfying the equation f(x)=$$\frac { 10-x }{ 10 } $$ is

A
2

B
1

C
3

D
4

Solution
Question 10
1 / -0

$$cos^{-1}[cos(-\frac{17}{15}\pi )]$$ is equal to-

A
$$-\frac{17\pi }{15}$$

B
$$\frac{17\pi }{15}$$

C
$$-\frac{2\pi }{15}$$

D
$$\frac{13\pi }{15}$$

Solution