1
MHT CET 2025 21st April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\sin ^2\left(\cot ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

A
-1
B
1
C
$-\frac{1}{4}$
D
$\frac{1}{2}$
2
MHT CET 2025 21st April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{\sin x}{\sqrt{5 \sin ^2 x+6 \cos ^2 x}} d x $$

A

$\quad \log \left(\cos x+\sqrt{\cos ^2 x+5}\right)+\mathrm{c}$, where c is the constant of integration

B

$\quad \log \left(\sin x+\sqrt{6 \cos ^2 x+5}\right)+\mathrm{c}$, where c is the constant of integration

C

$-\log \left(\cos x+\sqrt{\cos ^2 x+6}\right)+\mathrm{c}$, where c is the constant of integration

D

$-\log \left(\cos x+\sqrt{\cos ^2 x+5}\right)+\mathrm{c}$, where c is the constant of integration

3
MHT CET 2025 21st April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=\frac{\mathrm{k} \sin x+2 \cos x}{\sin x+\cos x}$ is strictly increasing for all real values of $x$, then

A
$\mathrm{k}=1$
B
$\mathrm{k}>1$
C
$\mathrm{k}<2$
D
$\mathrm{k}>2$
4
MHT CET 2025 21st April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The locus of the points represented by $|z+3|-|z-3|=6$, where $z$ is a complex number, is ….

A
Circle with radius 1 unit
B
Straight line with slope 1.
C
Parabola with focus $(1,0)$
D
X -axis
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