If ${\cos }^{-1}x>{\sin }^{-1}x$, then

(a) $\frac{1}{\sqrt{2}}<x\le 1$
(b) $0\le x<\frac{1}{\sqrt{2}}$
(c)$-1\le x<\frac{1}{\sqrt{2}}$
(d) x > 0

Q. Mark the correct alternative in each of the following:

If $y=\sqrt{x}+\frac{1}{\sqrt{x}}$, then $\frac{dy}{dx}$ at x = 1 is

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

Q. If $f\left(x\right)=\left\{\begin{array}{cc}\frac{\sin (a+1)x+\sin x}{x},& x<0\\ c,& x=0\\ \frac{\sqrt{x+b{x}^2}-\sqrt{x}}{bx\sqrt{x}},& x>0\end{array}\right.$is continuous at x = 0, then
(a) a = $-\frac{3}{2}$, b = 0, c = $\frac{1}{2}$
(b) a = $-\frac{3}{2}$, b = 1, c = $-\frac{1}{2}$
(c) a = $-\frac{3}{2}$, b ∈ R − {0}, c = $\frac{1}{2}$
(d) none of these

Q. If $\left[si{n}^{-1}x\right]+\left[co{s}^{-1}x\right]=0;x\in [0,\infty );$ the solution set for x is