1
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
2
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
3
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
4
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \sqrt{x^2+3 x} d x= $$

A

$\sqrt{x^2+3 x}+\log \sqrt{x^2+3 x}+c$, where c is the constant of integration.

B

$\frac{2 x+3}{4} \sqrt{x^2+3 x}-\frac{9}{8} \log \left(x+\sqrt{x^2+3 x}\right)+c$, where c is the constant of integration.

C

$x \sqrt{x^2+3 x}+\log \left(x+\sqrt{x^2+3 x}\right)+\mathrm{c}$, where c is the constant of integration.

D

$x+3 \sqrt{x^2+3 x}+\frac{3}{2} \log \left(x+\sqrt{x^2+3 x}\right)+\mathrm{c}$, where c is the constant of integration.

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