1
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\sec \left(\tan ^{-1} x\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ is equal to

A
$\frac{-1}{\sqrt{2}}$
B
$\frac{1}{2}$
C
$\frac{1}{\sqrt{2}}$
D
$\sqrt{2}$
2
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=\log _{x^2}\left(\log _{\mathrm{e}} x\right)$, then $\mathrm{f}^{\prime}(x)$ at $x=\mathrm{e}$ is

A
1
B
$\frac{1}{\mathrm{e}}$
C
$\frac{1}{2 \mathrm{e}}$
D
$\frac{1}{4 \mathrm{e}}$
3
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $x=\sec \theta-\cos \theta, y=\sec ^{10} \theta-\cos ^{10} \theta$ and $\left(x^2+4\right)\left(\frac{d y}{d x}\right)^2=k\left(y^2+4\right)$, then the value of $k$ is

A
$\frac{1}{100}$
B
1
C
10
D
100
4
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=\sin ^{-1}\left(\frac{2 \cdot 3^x}{1+9^x}\right)$, then $\mathrm{f}^{\prime}\left(\frac{1}{2}\right)$ equals

A
$\sqrt{3} \log (\sqrt{3})$
B
$-\sqrt{3} \log 3$
C
$-\sqrt{3} \log (\sqrt{3})$
D
$\sqrt{3} \log 3$
MHT CET Subjects
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