1
MHT CET 2020 16th October Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$f(x)=\log (\sec x+\tan x)$$, then $$f^{\prime}\left(\frac{\pi}{4}\right)=$$

A
$$\frac{1}{\sqrt{2}}$$
B
$$\sqrt{2}$$
C
1
D
$$\frac{2}{\sqrt{3}}$$
2
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\log \left[\frac{x+\sqrt{x^2+25}}{\sqrt{x^2+25}-x}\right]$ then $\frac{d y}{d x}=\ldots \ldots$

A
$\frac{1}{\sqrt{x^2+25}}$
B
$\frac{2}{\sqrt{x^2+25}}$
C
$\frac{-1}{\sqrt{x^2+25}}$
D
$\frac{-2}{\sqrt{x^2+25}}$
3
MHT CET 2019 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $x=\sin \theta, y=\sin ^3 \theta$ then $\frac{d^2 y}{d x^2}$ at $\theta=\frac{\pi}{2}$ is ............

A
3
B
6
C
$\frac{1}{6}$
D
$\frac{1}{3}$
4
MHT CET 2019 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $x^y=e^{x-y}$, then $\frac{d y}{d x}$ at $x=1$ is ...........

A
$e$
B
1
C
0
D
$-$1
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