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

The equation of the normal to the curve $x=\theta+\sin \theta, y=1+\cos \theta$ at $\theta=\frac{\pi}{2}$ is

A
$2 x+2 y+\pi=0$
B
$2 x-2 y-\pi=0$
C
$x+y+\pi=0$
D
$x+y-2 \pi=0$
2
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The co-ordinates of a point on the curve $y=x \log x$ at which the normal is parallel to the line $2 x-2 y=3$ are

A
$\left(-\mathrm{e}^{-2}, 2 \mathrm{e}^{-2}\right)$
B
$\left(-\mathrm{e}^{-2},-2 \mathrm{e}^{-2}\right)$
C
$\left(\mathrm{e}^{-2}, 2 \mathrm{e}^{-2}\right)$
D
$\left(\mathrm{e}^{-2},-2 \mathrm{e}^{-2}\right)$
3
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of C for which Mean value Theorem holds for the function $\mathrm{f}(x)=\log _e x$ on the interval $[1,3]$ is

A
$\log _3 \mathrm{e}$
B
$\log _{\mathrm{e}} 3$
C
$\frac{1}{2} \log _{\mathrm{c}} 3$
D
$ 2 \log _3 \mathrm{e}$
4
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The maximum value of the function

$$f(x)=3 x^3-18 x^2+27 x-40$$

on the set $\mathrm{S}=\left\{x \in \mathbb{R} / x^2+30 \leq 11 x\right\}$ is

A
$-$122
B
$-$222
C
222
D
122
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