1
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the line passing through the point of intersection of the lines $3 x-y=5$ and $x+3 y=1$ and making equal intercepts on the axes is

A
$5 x+5 y-7=0$
B
$5 x-5 y-7=0$
C
$2 x+y-7=0$
D
$x-y+7=0$
2
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{\operatorname{cosec} x d x}{\cos ^2\left(1+\log \tan \frac{x}{2}\right)}=$$

A
$\tan \left(1+\log \tan \frac{x}{2}\right)+\mathrm{c}$, where c is a constant of integration.
B
$\frac{1}{2} \tan \left(1+\log \tan \frac{x}{2}\right)+\mathrm{c}$, where c is a constant of integration.
C
$2 \tan \left(1+\log \tan \frac{x}{2}\right)+\mathrm{c}$, where c is a constant of integration.
D
$\frac{1}{4} \tan \left(1+\log \tan \frac{x}{2}\right)+\mathrm{c}$, where c is a constant of integration.
3
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The vectors $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ are not perpendicular and $\overline{\mathrm{c}}$ and $\overline{\mathrm{d}}$ are two vectors satisfying $\overline{\mathrm{b}} \times \overline{\mathrm{c}}=\overline{\mathrm{b}} \times \overline{\mathrm{d}}$ and $\overline{\mathrm{a}} \cdot \overline{\mathrm{d}}=0$, then the vector $\overline{\mathrm{d}}$ is equal to

A
$\overline{\mathrm{b}}+\left(\frac{\overline{\mathrm{b}} \cdot \overline{\mathrm{c}}}{\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}}\right) \overline{\mathrm{c}}$
B
$\overline{\mathrm{c}}-\left(\frac{\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}}{\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}}\right) \overline{\mathrm{b}}$
C
$\bar{b}-\left(\frac{\bar{b} \cdot \bar{c}}{\bar{a} \cdot \bar{b}}\right) \bar{c}$
D
$\overline{\mathrm{c}}+\left(\frac{\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}}{\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}}\right) \overline{\mathrm{b}}$
4
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the function $\mathrm{f}(x)=\left(\frac{5 x-8}{8-3 x}\right)^{\frac{3}{2 x-4}}$ if $x \neq 2$. $=\mathrm{k}$ if $x=2$. is continuous at $x=2$, then $\mathrm{k}=$

A
$\mathrm{e}^6$
B
$\mathrm{e}^2$
C
$e^{-6}$
D
$\mathrm{e}^{-2}$
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