1
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\mathrm{I}=\int \frac{x^2}{(\mathrm{a}+\mathrm{bx})^2} \mathrm{dx}$ is

A
$\frac{1}{b^3}\left[a+b x+2 a \log |a+b x|-\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
B
$\frac{1}{b^3}\left[a+b x-2 a \log |a+b x|+\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
C
$\frac{1}{b^3}\left[a+b x-2 a \log |a+b x|-\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
D
$\frac{1}{b^3}\left[a+b x+2 a \log |a+b x|+\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
2
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\quad \overline{\mathrm{a}}=\alpha \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}, \overline{\mathrm{b}}=3 \hat{\mathrm{i}}-\beta \hat{j}+4 \hat{\mathrm{k}} \quad$ and $\overline{\mathrm{c}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}$, where $\alpha, \beta \in \mathbb{R}$, be three vectors. If the projection of $\overline{\mathrm{a}}$ on $\overline{\mathrm{c}}$ is $\frac{10}{3}$ and $\overline{\mathrm{b}} \times \overline{\mathrm{c}}=-6 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}$, then the value of $2 \alpha+\beta$ is

A
3
B
4
C
5
D
6
3
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $4 a b=3 h^2$, then the ratio of the slope of lines represented by $a x^2+2 \mathrm{~h} x y+\mathrm{b} y^2=0$ is

A
$\sqrt{3}: 1$
B
$1: \sqrt{3}$
C
$1: 3$
D
$3: 1$
4
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\sin \left(\cot ^{-1}(x+1)\right)=\cos \left(\tan ^{-1} x\right)$ then considering positive square roots, $x$ has the value ___________

A
0
B
$\frac{9}{4}$
C
$\frac{1}{2}$
D
$-\frac{1}{2}$
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