1
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
If $ 2 y=\left[\cot ^{-1}\left(\frac{\sqrt{3} \cos x+\sin x}{\cos x-\sqrt{3} \sin x}\right)\right]^2 \forall x \in\left(0, \frac{\pi}{2}\right)$ then $\frac{d y}{d x}$ is equal to :
A
$x-\frac{\pi}{6}$
B
$2 x-\frac{\pi}{3}$
C
$\frac{\pi}{6}-x$
D
$\frac{\pi}{3}-x$
2
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

If $y=\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2$,

then $\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}=$

A
2
B
3
C
0
D
4
3
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
Differentiate $\log _a x$ with respect to $a^x$
A
$\frac{1}{x a^x}$
B
$\frac{1}{x a^x(\log a)^2}$
C
$\frac{a^x}{x(\log a)^2}$
D
$\frac{a^x}{x}$
4
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $f(x)=\left(\frac{3+x}{1+x}\right)^{2+3 x}$, then $f^{\prime}(0)=$
A
$12+\log 3$
B
$-12+3 \log 3$
C
$-\frac{4}{3}+3 \log 3$
D
$-12+27 \log 3$
COMEDK Subjects
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