1
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $0 \leqslant \cos ^{-1} x \leqslant \pi$ and $\frac{-\pi}{2} \leqslant \sin ^{-1} x \leqslant \frac{\pi}{2}$, then at $x=\frac{1}{5}$ the value of $\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)$ is

A
$-\sqrt{\frac{24}{25}}$
B
$\sqrt{\frac{24}{25}}$
C
$\frac{\sqrt{24}}{25}$
D
$\frac{-\sqrt{24}}{25}$
2
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0
In a triangle ABC with usual notations if $b \sin C(b \cos C+c \cos B)=42$, then area of triangle $\mathrm{ABC}=$
A
42 sq. units
B
21 sq. units
C
24 sq. units
D
12 sq. units
3
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{x}{1+x^4} d x= $$

A
$\frac{1}{2} \tan ^{-1} x^2+c$, where $c$ is the constant of integration
B
$2 \tan ^{-1} x+c$, where $c$ is the constant of integration
C
$\frac{1}{2} \tan ^{-1} x+c$, where c is the constant of integration
D
$\tan ^{-1} x^2+\mathrm{c}$, where c is the constant of integration
4
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let the plane passing through point $(2,1,-1)$ containing line joining the points $(1,3,2)$ and $(1,2,1)$ makes intercepts $\mathrm{p}, \mathrm{q}, \mathrm{r}$ on co-ordinate axes, then $\mathrm{p}+\mathrm{q}+\mathrm{r}=$

A
0
B
3
C
2
D
-2

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