Plotting Graphs

Q. The equation sin^–1x = 3sin^–1α has a solution, then the set of exhaustive values of ‘α’ is

समीकरण sin^–1x = 3sin^–1α का एक हल है, तब ‘α’ के सम्पूर्ण मानों का समुच्चय है

1. $\left(-\infty ,-\frac{1}{2}\right)\cup \left(\frac{1}{2},\infty \right)$
2. $\left(-\frac{\sqrt{3}}{2},\frac{\sqrt{3}}{2}\right)$
3. $\left[-\frac{\sqrt{3}}{2},\frac{\sqrt{3}}{2}\right]$
4. $\left[-\frac{1}{2},\frac{1}{2}\right]$

Q. For the interval $[-2\pi ,2\pi ],\sin x>0$ in the interval:

1. $(-2\pi ,-\pi )\cup (0,\pi )$
2. $[-\frac{\pi }{2},\frac{\pi }{2}]$
3. $(-2\pi ,2\pi )-\left\{0\right\}$
4. $[-2\pi ,-\frac{\pi }{2}]\cup [\frac{\pi }{2},2\pi ]$

Q. ${\sin }^{-1}x$ ${\tan }^{-1}x$
when $x\in (0,1]$

1. $\ge$
2. $\le$
3. >
4. <

Q. The interval of $x$ for which $cotx<0,(2\pi <x<4\pi )$ is:

1. $x\in (\pi /2,3\pi )\cup (7\pi /2,4\pi )$
2. $x\in (5\pi /2,3\pi )\cup (7\pi /2,4\pi ]$
3. $x\in (5\pi /2,3\pi ]\cup (7\pi /2,4\pi )$
4. $x\in (5\pi /2,3\pi )\cup (7\pi /2,4\pi )$

Q. ${\sin }^{-1}x$ ${\tan }^{-1}x$
when $x\in (0,1]$

1. $\ge$
2. $\le$
3. >
4. <

Q. If [.] denotes the greatest integer function then $\underset{x\to 0}{lim}\left[\frac{x^2}{tanx.sinx}\right]=$

1. -1
2. 1
3. 0
4. does not exist

Q. For the interval $[-2\pi ,2\pi ],\sin x<0$ in the interval

1. $(-\pi ,0)\cup (\pi ,2\pi )$
2. $(-2\pi ,2\pi )-\left\{0\right\}$
3. $(-2\pi ,-\pi )\cup (0,\pi )$
4. $[-\frac{\pi }{2},\frac{\pi }{2}]$

Q. In the interval $[-2\pi ,2\pi ],\sin x=-1\text{or}1$ for which of the following?

1. $x=\frac{3\pi }{2}$
2. $x=\frac{-3\pi }{2}$
3. $x=\frac{-5\pi }{2}$
4. $x=\frac{-\pi }{2}$