1
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The curve satisfying the differential equation $y \mathrm{~d} x-\left(x+3 y^2\right) \mathrm{dy}=0$ and passing through the point $(1,1)$ also passes through the point

A
$\left(\frac{1}{4}, \frac{1}{2}\right)$
B
$\left(\frac{1}{4},-\frac{1}{2}\right)$
C
$\left(\frac{1}{3},-\frac{1}{3}\right)$
D
$\left(-\frac{1}{3}, \frac{1}{3}\right)$
2
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The maximum value of $z=x+y$, subjected to $x+y \leq 10,5 x+3 y \geq 15, x \leq 6, x, y \geq 0$

A
occurs only at unique point.
B
occurs only at two distinct points.
C
occurs at infinitely many points.
D
does not exist.
3
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The distance of the point $(1,3,-7)$ from the plane passing through the point $(1,-1,-1)$ having normal perpendicular to both the lines $\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z-4}{3}$ and $\frac{x-2}{2}=\frac{y+1}{-1}=\frac{z+7}{-1}$ is

A
$\frac{10}{\sqrt{83}}$ units.
B
$\frac{5}{\sqrt{83}}$ units.
C
$\frac{10}{\sqrt{74}}$ units.
D
$\frac{20}{\sqrt{74}}$ units.
4
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Domain of definition of the real valued function $f(x)=\sqrt{\sin ^{-1}(2 x)+\frac{\pi}{6}}$ is

A
$\left[-\frac{1}{4}, \frac{1}{2}\right]$
B
$\left[\frac{-3}{2}, \frac{1}{2}\right]$
C
$\left[\frac{-3}{2}, \frac{1}{9}\right]$
D
$\left[-\frac{1}{4}, \frac{3}{4}\right]$
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