1
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{g}(x)=[\mathrm{f}(2 \mathrm{f}(x)+2)]^2$ and $\mathrm{f}(0)=-1, \mathrm{f}^{\prime}(0)=1$ then $g^{\prime}(0)$ is

A
$-$4
B
4
C
$-$3
D
3
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=\frac{a \sin x+b \cos x}{c \sin x+d \cos x}$ is decreasing for all $x$ then

A
$\mathrm{ad}-\mathrm{bc}>0$
B
$ad - bc <0$
C
$a b-c d>0$
D
$\mathrm{ab }-\mathrm{cd}<0$
3
MHT CET 2024 16th 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
$\frac{1}{2}$
B
$\frac{1}{\sqrt{2}}$
C
$\sqrt{2}$
D
1
4
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $f(1)=1, f^{\prime}(1)=5$, then the derivative of $\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$ at $x=1$ is

A
125
B
1250
C
135
D
35
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