1
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the points $(1,-1, \lambda)$ and $(-3,0,1)$ are equidistant from the plane $3 x-4 y-12 z+13=0$, then the sum of all possible values of $\lambda$ is

A
$\frac{7}{3}$
B
$\frac{10}{3}$
C
$\frac{4}{3}$
D
$\frac{5}{3}$
2
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\bar{a}=\hat{i}-2 \hat{j}+3 \hat{k}$ and $\bar{b}=2 \hat{i}+3 \hat{j}-\hat{k}$, then the angle between the vectors $(2 \bar{a}+\bar{b})$ and $(\overline{\mathrm{a}}+2 \overline{\mathrm{~b}})$ is

A
$\frac{\pi}{6}$
B
$\frac{\pi}{3}$
C
$\frac{\pi}{4}$
D
$\frac{\pi}{2}$
3
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The maximum value of the objective function $\mathrm{z}=4 x+6 y$ subject to $3 x+2 y \leq 12, x+y \geq 4, x$, $y \geq 0$ is

A
24
B
46
C
56
D
36
4
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\frac{\mathrm{d}}{\mathrm{~d} x}\left(\cos ^{-1}\left(\frac{x-\frac{1}{x}}{x+\frac{1}{x}}\right)\right)=$$

A
$\frac{x^2+1}{x^2-1}$
B
$\frac{2}{1+x^2}$
C
$\frac{-1}{1+x^2}$
D
$\frac{-2}{1+x^2}$
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