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

If $y=\sin ^{-1}\left(\frac{3 x}{2}-\frac{x^3}{2}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

A
$\frac{3}{2 \sqrt{x^2-4}}$
B
$\frac{3}{\sqrt{4-x^2}}$
C
$\frac{3}{2 \sqrt{1-x^2}}$
D
$\frac{4}{\sqrt{4-x^2}}$
2
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A unit vector coplanar with $\hat{i}+\hat{j}+\hat{k}$ and $2 \hat{i}+\hat{j}+\hat{k}$ and perpendicular to $\hat{i}+\hat{j}-\hat{k}$ is

A
$+\frac{1}{\sqrt{2}}(-\hat{\mathrm{j}}-\hat{\mathrm{k}})$
B
$\frac{(\hat{j}-\hat{k})}{\sqrt{2}}$
C
$\frac{-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}}{\sqrt{5}}$
D
$+\frac{1}{\sqrt{26}}(\hat{\mathrm{j}}+5 \hat{\mathrm{k}})$
3
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Negation of the statement ' Horses have wings if and only if crows have tails. ' is

A
Horses have wings but crows do not have tails. or crows have tails but horses do not have wings.
B
Horses do not have wings if and only if crows do not have tails.
C
Horses do not have wings and crows have tails. or Horses have wings and crows have tails.
D
Horses do not have wings and crows do not have tails.
4
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A plane which is perpendicular to two planes $2 x-2 y+z=0$ and $x-y+2 z=4$, passes through $(1,2,1)$. The distance of the plane from the point $(2,3,4)$ is

A
$\sqrt{\frac{2}{5}}$ units
B
$\frac{2 \sqrt{2}}{5}$ units
C
$\frac{2}{\sqrt{5}}$ units
D
$\frac{1}{\sqrt{5}}$ units
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