MCQ
If $\sin ^{-1} x=y$ then
  • A
    $0 \leq y \leq \pi$
  • $-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$
  • C
    $0 < y < \pi$
  • D
    $-\frac{\pi}{2} < y < \frac{\pi}{2}$

Answer

Correct option: B.
$-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$
B

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

If $\theta$ is the angle between any two vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ then $\big|\vec{\text{a}}.\vec{\text{b}}\big|=\big|\vec{\text{a}}\times\vec{\text{b}}\big|$ when $\theta$ is equal to:
  1. $0$
  2. $\frac{\pi}{4}$
  3. $\frac{\pi}{2}$
  4. $\pi$
$\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{a}}\times\vec{\text{b}}\big]+\big(\vec{\text{a}}.\vec{\text{b}}\big)^2=$
  1. $\big|\vec{\text{a}}\big|^2\big|\vec{\text{b}}\big|^2$
  2. $\big|\vec{\text{a}}+\vec{\text{b}}\big|^2$
  3. $\big|\vec{\text{a}}\big|^2+\big|\vec{\text{b}}\big|^2$
  4. $2\big|\vec{\text{a}}\big|^2\big|\vec{\text{b}}\big|^2$
For the following LPP, maximise $Z=3 x+4 y$ subject to constraints $x-y \geq-1, x \leq 3, x \geq 0, y \geq 0$, the maximum value is
If  (0, 0),(a, 0)  and  (0, b)  are collinear, then:
  1. ab = 0
  2. a = b
  3. a = −b
  4. a - b = c
$A B C D$ is a rhombus whose diagonals intersects at $E$. Then $\overrightarrow{E A}+\overrightarrow{E B}+\overrightarrow{E C}+\overrightarrow{E D}$ equals to
If $|A|=|k A|$, where $A$ is a square matrix of order 2 , then sum of all possible values of $k$ is
$\int\text{x}\sec\text{x}^2\text{ dx}$ is equal to:
  1. $\frac{1}{2}\log\big(\sec\text{x}^2+\tan\text{x}^2\big)+\text{C}$
  2. $\frac{\text{x}^2}{2}\log\big(\sec\text{x}^2+\tan\text{x}^2\big)+\text{C}$
  3. $2\log\big(\sec\text{x}^2+\tan\text{x}^2\big)+\text{C}$
  4. none of these.
The value of $\int\frac{\cos\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$ is:
  1. $2\cos\sqrt{\text{x}}+\text{C}$
  2. $\sqrt{\frac{\cos\text{x}}{\text{x}}}+\text{C}$
  3. $\sin\sqrt{\text{x}}+\text{C}$
  4. $2\sin\sqrt{\text{x}}+\text{C}$
The corner points of the bounded feasible region determined by a system of linear constraints are $(0,3),(1,1)$ and $(3,0)$. Let $Z=p x+q y$, where $p, q>0$,. The condition on $p$ and $q$ so that the minimum of $Z$ occurs at $(3,0)$ and $(1,1)$ is
The function $f(x)=x+\sin x$ is