1
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
$\mathrm{ab }-\mathrm{cd}<0$
2
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
3
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
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

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

A
0
B
2
C
3
D
6
MHT CET Subjects
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