1
MHT CET 2025 25th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $\mathrm{f}(x)=\log \left(\frac{1+x}{1-x}\right)$ and $\mathrm{g}(x)=\frac{3 x+x^3}{1+3 x^2}$, then $(\mathrm{fog})(x)=$
A
$2 \mathrm{f}(x)$
B
$3 \mathrm{f}(x)$
C
$\quad 4 \mathrm{f}(x)$
D
$-\mathrm{f}(x)$
2
MHT CET 2025 25th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\sec x+\tan x=2,0 < x < \frac{\pi}{2}$ then $\sin \frac{x}{4}=$

A
$\frac{1}{\sqrt{10+3 \sqrt{10}}}$
B
$\frac{1}{\sqrt{2(10+3 \sqrt{10})}}$
C
$\frac{1}{\sqrt{10-3 \sqrt{10}}}$
D
$\frac{1}{2 \sqrt{10-3 \sqrt{10}}}$
3
MHT CET 2025 25th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The eccentricity of the curve represented by $x=3(\cos t+\sin t), y=4(\cos t-\sin t)$ is

A
$\frac{\sqrt{7}}{4}$
B
$\frac{7}{16}$
C
$\frac{\sqrt{7}}{3}$
D
$\frac{\sqrt{8}}{4}$
4
MHT CET 2025 25th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The rate at which the population of a city increases varies as the population. In a period of 20 years, the population increased from 4 lakhs to 6 lakhs. In another 20 years the population will be

A
8 lakhs
B
12 lakhs
C
9 lakhs
D
10 lakhs
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