MCQ | Class 12 | Chapter 2
INVERSE TRIGONOMETRIC FUNCTIONS

MCQ | CHAPTER 2 | CLASS 12

Q 1) The value of $tan^{-1}\left [ sin\left ( \frac{-\pi }{2{\color{Orchid} }} \right ) \right ]$ is =

a) -1 b) 1 $c)\: \: \pi ^{2}$ $d)\: \: \frac{-\pi }{4}$

Ans: d
Q 2) The value of $cos^{-1}\left ( \frac{1}{2} \right )+2sin^{-1}\left ( \frac{1}{2} \right )$ is equal to

$a)\: \: \frac{\pi }{4}$ $b)\: \: \frac{\pi }{6}$ $c)\: \: \frac{\pi }{3}$ $d)\: \: \frac{2\pi }{3}$

Ans: d

Q 3) The value of sin^-1{cos (4095^o) is equal to

$a)\: \: \frac{-\pi }{3}$ $b)\: \: \frac{\pi }{6}$ $c)\: \: \frac{-\pi }{4}$ $d)\: \: \frac{\pi }{4}$

Ans: c

Q 4) The value of $cos(tan^{-1}x)\: =$

$a)\: \: \sqrt{1+x^{2}}$

$b)\: \: \frac{1}{\sqrt{1+x^{2}}}$

$c)\: \: 1+x^{2}$

d) None of these

Ans: b

Q 5) The value of $tan\: (sex^{-1}\sqrt{1+x^{2}})\: \: is$

$a)\: \: \frac{1}{x}$

b) x
$c)\: \: \: \frac{1}{\sqrt{1+x^{2}}}$

$d)\: \: \: \frac{x}{\sqrt{1+x^{2}}}$
Ans: b

Q 6) The value of $sec^{-1}[sec(-30^{o})]\: \: is=$
a) - 60 b) -30 c) 30 d) 150
Ans: c
Q 7) The value of $tan^{-1}\left [ \frac{cosx}{1+sinx} \right ]=$
$a)\: \: \: \frac{\pi }{4}-\frac{x}{2}$

$b)\: \: \: \frac{\pi }{4}+\frac{x}{2}$

$c)\: \: \: \frac{x}{2}$

$d)\: \: \: \frac{\pi }{4}-x$
Ans: a
Q 8) The value of $tan^{-1}\left ( \frac{1}{\sqrt{x^{2}-1}} \right )\: \: is=$

$a)\: \: \: \frac{\pi }{2}+cosec^{-1}x$

$b)\: \: \: \frac{\pi }{2}+sec^{-1}x$

$c)\: \: \: cosec^{-1}x$

$d)\: \: \: sec^{-1}x$
Ans: c
Q 9) The value of $cos^{-1}\left ( cos\frac{7\pi }{5} \right )$ is =

$a)\: \: \: \frac{3\pi }{5}$ $b)\: \: \: \frac{2\pi }{5}$ $c)\: \: \: \frac{-7\pi }{5}$ $d)\: \: \: \frac{7\pi }{5}$

Ans: a
Q 10) The principal value of $sin^{-1}\left ( \frac{-1}{2} \right )\: \: is=$

$a)\: \: \: \frac{\pi }{3}$ $b)\: \: \: \frac{\pi }{6}$ $c)\: \: \: \frac{-\pi }{3}$ $d)\: \: \: \frac{-\pi }{6}$

Ans: d

Q 11) Sec²(tan^-12) + cosec²(cot^-13) =

a) 5 b) 13 c) 15 d) 16
Ans: c

Q 12) $sin^{-1}\left [x\sqrt{1-x}-\sqrt{x}\sqrt{1-x^{2}} \right ] =$

$a)\: \: sin^{-1}x+sin^{-1}\sqrt{x}$

$b)\: \: sin^{-1}x-sin^{-1}\sqrt{x}$

$c)\: \: sin^{-1}\sqrt{x}-sin^{-1}x$

d) None of these

Ans: b

Q 13) $sin\left [ \frac{1}{2}cot^{-1}\left ( \frac{-3}{4} \right ) \right ]\: \: is=$
$a)\: \: \frac{1}{\sqrt{5}}$

$b)\: \: \frac{-2}{\sqrt{5}}$

$c)\: \: \frac{2}{\sqrt{5}}$

$d)\: \: \frac{-1}{\sqrt{5}}$

Ans: c

Q 14) If $tan^{-1}\left ( \frac{1-x}{1+x} \right )=\frac{1}{2}tan^{-1}x$ , then x =

a) 1

$b)\:\: \sqrt{3}$

$c)\:\: \frac{1}{\sqrt{3}}$

d) None of these

Ans: c

Q 15) The value of $cos^{-1}\left ( cos\frac{7\pi }{6} \right )$

$a)\:\:\frac{7\pi }{6}$

$b)\:\:\frac{5\pi }{6}$

$c)\:\:\frac{\pi }{6}$

d) None of these

Ans: b

Q 16) If $cos^{-1}\left ( \frac{5}{13} \right )-sin^{-1}\left ( \frac{12}{13} \right )=cos^{-1}x$ , then x is equal to

a) 1 $b)\:\:\frac{1}{\sqrt{2}}$ c) 0 $d)\:\:\frac{\sqrt{3}}{2}$

Ans: a

Q 17) Principal value of $sin^{-1}\left ( \frac{-1}{2} \right )$ is

$a)\: \: \frac{\pi }{3}$ $b)\: \: \frac{-\pi }{3}$ $c)\: \: \frac{5\pi }{6}$ $d)\: \: \frac{-\pi }{6}$

Ans: d

Explanation:

$\theta =sin^{-1}\left ( \frac{-1}{2} \right )$

$\Rightarrow \: \: sin\theta =\frac{-1}{2}=sin\left ( \frac{-\pi }{6} \right )$

$\Rightarrow \: \: \theta =\frac{-\pi }{6}$

Q 18) If $sin^{-1}x+sin^{-1}y=\frac{2\pi }{3}$ , then find the value of $cos^{-1}x+cos^{-1}y$
$a)\: \: \frac{2\pi }{3}$

$b)\: \: \frac{-2\pi }{3}$

$c)\: \: \frac{\pi }{3}$

$d)\: \: \pi$

Ans: c

Explanation

$sin^{-1}x+sin^{-1}y=\frac{2\pi }{3}$

$\left ( \frac{\pi }{2}-cos^{-1} \right )+\left ( \frac{\pi }{2}-cos^{-1}y \right )=\frac{2\pi }{3}$

$\pi -cos^{-1}x-cos^{-1}y=\frac{2\pi }{3}$

$cos^{-1}x+cos^{-1}y=\pi -\frac{2\pi }{3}$

$cos^{-1}x+cos^{-1}y=\frac{\pi }{3}$

Q 19) $tan^{-1}\left [ sin\left ( \frac{-\pi }{2} \right ) \right ]$ is equal to

a) -1 b) 1 $c)\: \: \frac{\pi }{2}$ $d)\: \: \frac{-\pi }{4}$
Ans: d

Q 20) $sin\left [ cot^{-1}\left\{ cos\left ( tan^{-1}x \right )\right\} \right ] =$

$a)\: \: \sqrt{\frac{1+x^{2}}{2+x^{2}}}$

$b)\: \: \sqrt{\frac{1-x^{2}}{2+x^{2}}}$

$c)\: \: \sqrt{\frac{1+x^{2}}{2-x^{2}}}$

$d)\: \: \sqrt{\frac{2+x^{2}}{1+x^{2}}}$

Ans: a

Q21) The value of $sec\left\{tan^{-1}\left ( \frac{-y}{3} \right ) \right\}$ is equal to

a) $\frac{\sqrt{9+y^{2}}}{9}$

b) $\frac{\sqrt{9+y^{2}}}{3}$

c) $\frac{3}{\sqrt{9+y^{2}}}$

d) $\frac{9}{\sqrt{9+y^{2}}}$

Ans b

Explanation

$sec\left ( tan^{-1}\frac{y}{3} \right )=\sqrt{sec^{2}\left ( tan^{-1}\frac{y}{3} \right )}$

$=\sqrt{1+tan^{2}\left ( tan^{-1}\frac{y}{3} \right )}$

$=\sqrt{1+\frac{y^{2}}{9}}=\frac{\sqrt{9+y^{2}}}{3}$

Q22) If $sin^{-1}x+sin^{-1}y+sin^{-1}z = \frac{3\pi }{2}$ then the value of x + y² + z³is

a) 1 b) 3 c) 2 d) 5

Ans: b

Explanation

$sin^{-1}x+sin^{-1}y+sin^{-1}z = \frac{3\pi }{2}$

$\Rightarrow sin^{-1}x=\frac{\pi}{2}$ $\Rightarrow x=1$

$\Rightarrow sin^{-1}y=\frac{\pi}{2}$ $\Rightarrow y=1$

$\Rightarrow sin^{-1}z=\frac{\pi}{2}$ $\Rightarrow z=1$

$x+y^{2}+z^{3}=1+1+1=3$

Q23 Principal value of the expression $cos^{-1}\left [ cos\left ( -680^{o} \right ) \right ]$ is

a) $\frac{2\pi }{9}$

b) $-\frac{2\pi }{9}$

c) $\frac{34\pi }{9}$

d) $\frac{\pi }{9}$

Ans : a

Q24) The value of tan²(sec^-12) + cot²(cosec^-13) is

a) 5 b) 11 c) 13 d) 15

Ans: b

Q25) The value of $tan^{-1}\left ( \frac{1}{2} \right )+tan^{-1}\left ( \frac{1}{3} \right )+tan^{-1}\left ( \frac{7}{8} \right )$ is

a) $tan^{-1}\left ( \frac{7}{8} \right )$

b) $cot^{-1}(15)$

c) $tan^{-1}(15)$

d) $tan^{-1}\left ( \frac{25}{24} \right )$

Ans : c

Q26) Find the value of $tan^{-1}\left ( \sqrt{3} \right )-cot^{-1}\left ( -\sqrt{3} \right )$

a) π

b) $-\frac{\pi }{2}$

c) - π

d) $\frac{\pi }{2}$

Answer: b

Explanation

$tan^{-1}\sqrt{3}-cot^{-1}(-\sqrt{3})$

$=tan^{-1}\sqrt{3}-\left [\pi - cot^{-1}(\sqrt{3}) \right ]$

$=\left [ tan^{-1}\sqrt{3}+cot^{-1}(\sqrt{3}) \right ]-\pi$

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

Q27) If sec^-1x + sec^-1y = $\frac{\pi }{2}$ , then the value of cosec^-1x + cosec^-1y is

a) π b) π/2 c) 3π/2 d) -π

Answer b

Explanation

sec^-1x + sec^-1y = $\frac{\pi }{2}$

⇒ $\frac{\pi }{2}$ - cosec^-1x + $\frac{\pi }{2}$ - cosec^-1y = $\frac{\pi }{2}$

⇒ $\frac{\pi }{2}$ - cosec^-1x - cosec^-1y = 0

⇒ cosec^-1x + cosec^-1y = $\frac{\pi }{2}$

Q28) $cot\left ( \frac{\pi }{4}-2cot^{-1}3 \right )=$

a) 5 b) 9 c) 12 d) 7

Answer 7

Explanation

$2cot^{-1}(3)=2tan^{-1}\left ( \frac{1}{3} \right )$

= $tan^{-1}\left ( \frac{\frac{2}{3}}{1-\frac{1}{9}} \right )=tan^{-1}\left ( \frac{2/3}{8/9} \right )$

$=tan^{-1}\left ( \frac{2\times 9}{3\times 8} \right )=tan^{-1}\left ( \frac{3}{4} \right )$

Now by using the formula

$cot\left(\frac{\pi}{4}-\theta\right)=\frac{1+tan\theta}{1-tan\theta}$

Given equations becomes

$cot\left ( \frac{\pi }{4}-2cot^{-1}3 \right )=cot\left ( \frac{\pi }{4}-tan^{-1}\frac{3}{4} \right )$

$cot\left ( \frac{\pi }{4}-tan^{-1}\frac{3}{4} \right )=\frac{1+tan\left(tan^{-1}\frac{3}{4}\right)}{1-tan\left(tan^{-1}\frac{3}{4}\right)}$

$\frac{1+tan\left(tan^{-1}\frac{3}{4}\right)}{1-tan\left(tan^{-1}\frac{3}{4}\right)}=\frac{1+\frac{3}{4}}{1-\frac{3}{4}}=7$

Q29) If 3sin^-1x + cos^-1x = π, then x is equal to

a) 0

b) $\frac{1}{\sqrt{2}}$

c) -1

d) 1/2

Answer b

Explanation

3sin^-1x + cos^-1x = π

2sin^-1x + (sin^-1x + cos^-1x) = π

2sin^-1x + π / 2 = π

2sin^-1x = π - π / 2 = π / 2

sin^-1x = π / 4

x = sin(π / 4) = $\frac{1}{\sqrt{2}}$

Q30) If $sin^{-1}\left ( \frac{2\alpha }{1+\alpha ^{2}} \right )+cos^{-1}\left ( \frac{1-\beta ^{2}}{1+\beta ^{2}} \right )=tan^{-1}\left ( \frac{2x}{1-x^{2}} \right )$ , then the value of x is

a) $x=\frac{\alpha +\beta }{1-\alpha \beta }$

b) $x=\frac{\alpha -\beta }{1-\alpha \beta }$

c) $x=\frac{\alpha -\beta }{1+\alpha \beta }$

d) None of these

Ans: a

Explanation

$sin^{-1}\left ( \frac{2\alpha }{1+\alpha ^{2}} \right )=2tan^{-1}\alpha$

$cos^{-1}\left ( \frac{1-\beta ^{2}}{1+\beta ^{2}} \right )=2tan^{-1}\beta$

$tan^{-1}\left ( \frac{2x}{1-x^{2}} \right )=2tan^{-1}x$

Using these values in the given equation we get

$2tan^{-1}\alpha +2tan^{-1}\beta =2tan^{-1}x$

$tan^{-1}\alpha +tan^{-1}\beta =tan^{-1}x$

$\Rightarrow tan^{-1}\left ( \frac{\alpha +\beta }{1-\alpha \beta } \right )=tan^{-1}x$

$\Rightarrow x=\frac{\alpha +\beta }{1-\alpha \beta }$

Q31) The value of : $tan\left ( \frac{1}{2}cos^{-1}\frac{\sqrt{5}}{3} \right )$ is

a) $\frac{3-\sqrt{5}}{2}$

b) $\frac{3+\sqrt{5}}{2}$

c) $\frac{5+\sqrt{3}}{2}$

d) $\frac{\sqrt{5}}{3}$

Answer a

Q32) The value of : $sin^{-1}\left ( \frac{2\sqrt{2}}{3} \right )+sin^{-1}\left ( \frac{1}{3} \right )$

a) $\frac{\pi }{6}$

b) $\frac{\pi }{4}$

c) $\frac{\pi }{2}$

d) 0

Answer c

Q33) The value of expression $2sec^{-1}2 + sin^{-1}\left ( \frac{1}{2} \right )$ is

a) $\frac{\pi }{6}$ b) $\frac{5\pi }{6}$ c) $\frac{7\pi }{6}$ d) 1

Answer b

Q34) The value of : $sec^{2}(tan^{-1}3)+cosec^{2}(cot^{-1}2)$ is

a) 5 b) 13 c) 15 d) 25

Answer c

Q35) $sin\left [ \frac{\pi }{3}-sin^{-1}\left ( -\frac{1}{2} \right ) \right ]$ is equal to

a) 1/2 b) 1/3 c) 1/4 d) 1

Ans d

Q36) $cos\left [ 2cos^{-1}\left ( \frac{1}{5} \right ) +sin^{-1}\left ( \frac{1}{5} \right )\right ]$ is equal to

a) 1/5

b) $-\frac{2\sqrt{6}}{5}$

c) -1/5

d) $-\frac{2\sqrt{6}}{5}$

Answer: d

Q37) The value of $sin^{-1}\left [ sin\left ( \frac{-17\pi }{8} \right ) \right ]$ is

a) $-\frac{\pi }{6}$ b) $\frac{\pi }{8}$ c) $\frac{-\pi }{8}$ d) $\frac{\pi }{12}$

Answer c

Q38) Evaluate: $sin^{-1}\left\{sin\left ( \frac{5\pi }{6} \right ) \right\}+tan^{-1}\left\{ tan\left ( \frac{\pi }{6} \right )\right\}$ is

a) $\frac{\pi }{6}$ b) $\frac{2\pi }{3}$ c) $\frac{\pi }{3}$ d) $\frac{5\pi }{6}$

Answer: c

Q39) Find the value of : $sin\left [\frac{\pi }{3}-sin^{-1}\left ( -\frac{1}{2} \right ) \right ]$

Ans: 1

Q40) $sin^{-1}\left [ sin\left ( \frac{2\pi }{3} \right ) \right ]=\frac{2\pi }{3}$ , state true or false

Ans: False

Q41) What is the Principal branch of tan^-1x

Ans $\left ( -\frac{\pi }{2},\frac{\pi }{2} \right )$

Q42) If $tan^{-1}x=sin^{-1}\left ( \frac{1}{\sqrt{2}} \right )$ then find the value of x

Ans 1

Q43) $cos^{-1}\left ( cos\frac{7\pi }{6} \right )=\frac{7\pi }{6}$ state true or false

Ans : False

Download Complete PDF of MCQ

👉 Click Here to Go Back to MCQ Home Page

THANKS FOR YOUR VISIT

PLEASE COMMENT BELOW

🙏

Search This Blog

FEATURED POST ON MATHS MCQ

Assertion & Reason Questions For Math Class 10 | Arithmetic Progression

Maths MCQ Class 12 Ch-2 | Inverse Trigonometric Functions

MCQ | Class 12 | Chapter 2
INVERSE TRIGONOMETRIC FUNCTIONS

Comments

Post a Comment

CLICK HERE FOR OTHER POSTS ON MATHEMATICS MCQ

Popular Post on this Blog

Multiple Choice Questions (MCQ) On Mathematics

Maths MCQ Class IX Ch-10 | Heron's Formula

Maths MCQ Class IX Ch-6 | Lines & Angles

SUBSCRIBE THIS BLOG FOR GETTING NEW POSTS

Get new posts by email:

Followers

FEATURED POST ON MATHS MCQ

Assertion & Reason Questions For Math Class 10 | Arithmetic Progression

Maths MCQ Class 12 Ch-2 | Inverse Trigonometric Functions

MCQ | Class 12 | Chapter 2INVERSE TRIGONOMETRIC FUNCTIONS

Comments

Post a Comment

CLICK HERE FOR OTHER POSTS ON MATHEMATICS MCQ

Popular Post on this Blog

Multiple Choice Questions (MCQ) On Mathematics

Maths MCQ Class IX Ch-10 | Heron's Formula

Maths MCQ Class IX Ch-6 | Lines & Angles

SUBSCRIBE THIS BLOG FOR GETTING NEW POSTS

Get new posts by email:

Followers

MCQ | Class 12 | Chapter 2
INVERSE TRIGONOMETRIC FUNCTIONS