1
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $P(3,2,6)$ be a point in space and $Q$ be a point on the line $\bar{r}=\hat{i}-\hat{j}+2 \hat{k}+\mu(-3 \hat{i}+\hat{j}+5 \hat{k})$. Then the value of $\mu$ for which the vector $\overline{\mathrm{PQ}}$ is parallel to the plane $x-4 y+3 z=1$ is

A
$\frac{1}{4}$
B
$-\frac{1}{4}$
C
$\frac{1}{8}$
D
$-\frac{1}{8}$
2
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{f}(x)=\frac{x}{\sqrt{\mathrm{a}^2+x^2}}-\frac{\mathrm{d}-x}{\sqrt{\mathrm{~b}^2+(\mathrm{d}-x)^2}}, x \in \mathbb{R}$ where $\mathrm{a}, \mathrm{b}, \mathrm{d}$ are non-zero real constants. Then

A
$\mathrm{f}^{\prime}$ is not a continuous function of $x$.
B
f is neither increasing nor decreasing function of $x$.
C
f is an increasing function of $x$.
D
f is a decreasing function of $x$.
3
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the vectors $\overline{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overline{\mathrm{c}}=\lambda \hat{\mathrm{i}}+\hat{\mathrm{j}}+\mu \hat{\mathrm{k}}$ are mutually orthogonal, then $(\lambda, \mu) \equiv$

A
$(-3,2)$
B
$(2,-3)$
C
$(-2,3)$
D
$(3,-2)$
4
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=(\sin x)^{\tan x}$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

A
$(\sin x)^{\tan x}\left(1+\sec ^2 x \log (\sin x)\right)$
B
$\tan x(\sin x)^{\tan x-1} \cos x$
C
$(\sin x)^{\tan x} \sec ^2 x \log \sin x$
D
$\tan x(\sin x)^{\tan x-1}$
MHT CET Papers
EXAM MAP