1
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The shaded area in the given figure is a solution set for some system of inequalities. The maximum value of the function $\mathrm{z}=4 x+3 y$ subject to linear constraints given by the system is

MHT CET 2024 16th May Evening Shift Mathematics - Linear Programming Question 1 English

A
38
B
36
C
33
D
34
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $z_1=5-2 i$ and $z_2=3+i$, where $i=\sqrt{-1}$, then $\arg \left(\frac{z_1+z_2}{z_1-z_2}\right)$ is

A
$\tan ^{-1}\left(\frac{22}{19}\right)$
B
$\tan ^{-1}\left(\frac{22}{13}\right)$
C
$\tan ^{-1}\left(\frac{21}{19}\right)$
D
$\tan ^{-1}\left(\frac{19}{22}\right)$
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The co-ordinates of the foot of the perpendicular from the point $(0,2,3)$ on the line $\frac{x+3}{5}=\frac{y+1}{2}=\frac{z+4}{3}$ is

A
$\left(\frac{48}{19}, \frac{23}{19}, \frac{-13}{19}\right)$
B
$\left(\frac{-48}{19}, \frac{23}{19}, \frac{-13}{19}\right)$
C
$\left(\frac{-48}{19}, \frac{-23}{19}, \frac{-13}{19}\right)$
D
$\left(\frac{48}{19}, \frac{-23}{19}, \frac{-13}{19}\right)$
4
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The slope of tangent at $(x, y)$ to a curve passing through $\left(1, \frac{\pi}{4}\right)$ is $\frac{y}{x}-\cos ^2 \frac{y}{x}$, then the equation of curve is

A
$y=\tan ^{-1}\left(\log \left(\frac{\mathrm{e}}{x}\right)\right)$
B
$y=x^2\left(\tan ^{-1}\left(\log \frac{\mathrm{e}}{x}\right)\right)$
C
$y=x\left(\tan ^{-1}\left(\log \frac{\mathrm{e}}{x}\right)\right)$
D
$y=\frac{1}{x}\left(\tan ^{-1}\left(\log \frac{\mathrm{e}}{x}\right)\right)$
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