90
MCQ (Single Correct Answer)
If $f(x)=|\sin x|$, then
A
$f$ is everywhere differentiable
B
$f$ is everywhere continuous but not differentiable at $x=n \pi, n \in Z$
C
$f$ is everywhere continuous but not differentiable at $x=(2 n+1) \frac{\pi}{2}, n \in Z$
D
None of the above
91
MCQ (Single Correct Answer)
If $y=\log \left(\frac{1-x^2}{1+x^2}\right)$, then $\frac{d y}{d x}$ is equal to
A
$\frac{4 x^3}{1-x^4}$
B
$\frac{-4 x}{1-x^4}$
C
$\frac{1}{4-x^4}$
D
$\frac{-4 x^3}{1-x^4}$
92
MCQ (Single Correct Answer)
If $y=\sqrt{\sin x+y}$, then $\frac{d y}{d x}$ is equal to
A
$\frac{\cos x}{2 y-1}$
B
$\frac{\cos x}{1-2 y}$
C
$\frac{\sin x}{1-2 y}$
D
$\frac{\sin x}{2 y-1}$
93
MCQ (Single Correct Answer)
The derivative of $\cos ^{-1}\left(2 x^2-1\right)$ w.r.t. $\cos ^{-1} x$ is
A
2
B
$\frac{-1}{2 \sqrt{1-x^2}}$
C
$\frac{2}{x}$
D
$1-x^2$
94
MCQ (Single Correct Answer)
If $x=t^2$ and $y=t^3$, then $\frac{d^2 y}{d x^2}$ is equal to
A
$\frac{3}{2}$
B
$\frac{3}{4 t}$
C
$\frac{3}{2 t}$
D
$\frac{3}{2 t}$