Inverse Trigonometric Functions: 1 mark Questions (CBSE Class 12)

If $2{\cos }^{-1}x=y$, then

1. (A)$0\le y\le \pi$
2. (B)$-\pi \le y\le \pi$
3. (C)$0\le y\le 2\pi$
4. (D)$-\pi \le y\le 0$

If ${\tan }^{-1}x=3y$, then

1. (A)$-\frac{\pi }{2}<y<\frac{\pi }{2}$
2. (B)$-\frac{3\pi }{2}<y<\frac{3\pi }{2}$
3. (C)$-\frac{\pi }{6}<y<\frac{\pi }{6}$
4. (D)$-\frac{\pi }{6}\le y\le \frac{\pi }{6}$

If ${\sin }^{-1}x+\pi =y$, then

1. (A)$-\frac{\pi }{2}\le y\le \frac{\pi }{2}$
2. (B)$-\frac{3\pi }{2}\le y\le -\frac{\pi }{2}$
3. (C)$\frac{\pi }{2}\le y\le \frac{3\pi }{2}$
4. (D)$0\le y\le \pi$

The domain of $f(x)={\cos }^{-1}(2x-5)$ is :

1. (A)$[-1,1]$
2. (B)$[4,6]$
3. (C)$[-7,-3]$
4. (D)$[2,3]$

The domain of ${\sin }^{-1}(1-2x)$ is :

1. (A)$[-1,1]$
2. (B)$[-1,3]$
3. (C)$[-2,2]$
4. (D)$[0,1]$

The domain of ${\cos }^{-1}(4x+1)$ is :

1. (A)$[-1,1]$
2. (B)$[-3,5]$
3. (C)$[-4,4]$
4. (D)$\left[-\frac{1}{2},0\right]$

The following graph represents :

1. (A)$y={\cos }^{-1}x$
2. (B)$y={\sec }^{-1}x$
3. (C)$y={\tan }^{-1}x$
4. (D)$y={\text{cosec}}^{-1}x$

The principal value of ${\sec }^{-1}(\sqrt{2})+2{\text{cosec}}^{-1}(-\sqrt{2})$ is :

1. (A)$-\frac{\pi }{2}$
2. (B)$-\frac{\pi }{4}$
3. (C)$\frac{\pi }{4}$
4. (D)$\frac{\pi }{2}$

The following graph represents :

1. (A)$y={\sec }^{-1}x$
2. (B)$y={\cot }^{-1}x$
3. (C)$y={\tan }^{-1}x$
4. (D)$y={\text{cosec}}^{-1}x$

The following graph represents :

1. (A)$y={\cos }^{-1}x$
2. (B)$y={\sec }^{-1}x$
3. (C)$y={\sin }^{-1}x$
4. (D)$y={\tan }^{-1}x$

For the inverse trigonometric functions, which of the following Principal Value Branch is not correctly defined ?

1. (A)${\tan }^{-1}:R\to \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$
2. (B)${\sec }^{-1}:R-(-1,1)\to [0,\pi ]-\left\{\frac{\pi }{2}\right\}$
3. (C)${\cot }^{-1}:R\to (0,\pi )$
4. (D)${\text{cosec}}^{-1}:R-(-1,1)\to \left[-\frac{\pi }{2},\frac{\pi }{2}\right]$