1
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 $x$.
2
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
$(3,-2)$
3
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
$\tan x(\sin x)^{\tan x-1}$
4
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0
 

If for some $x \in \mathbb{R}^{+} \cup\{0\}$, the frequency distribution of the marks obtained by 20 students in a test is

Marks : 2 3 5 7
Frequency : $(x+1)^2$ $2x-5$ $x^2-3x$ $x$

then the mean of the marks is

A
3.0
B
2.5
C
2.8
D
3.2
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