1
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \cos ^3 x \cdot e^{\log (\sin x)} d x=$$

A
$$\frac{-e^{\sin x}}{4}+c$$
B
$$\frac{-\cos ^4 x}{4}+c$$
C
$$\frac{-\sin ^4 x}{4}+c$$
D
$$\frac{e^{\sin x}}{4}+c$$
2
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The probability distribution of a discrete random variable X is

$$\mathrm{X}$$ 1 2 3 4 5 6
$$\mathrm{P(X)}$$ K 2K 3K 4K 5K 6K

Find the value of $$\mathrm{P}(2<\mathrm{X}<6)$$

A
$$\frac{4}{21}$$
B
$$\frac{1}{21}$$
C
$$\frac{10}{21}$$
D
$$\frac{4}{7}$$
3
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{A}=(-2,2,3), \mathrm{B}=(3,2,2), \mathrm{C}=(4,-3,5)$$ and $$\mathrm{D}=(7,-5,-1)$$ Then the projection of $$\overline{\mathrm{AB}}$$ on $$\overline{\mathrm{CD}}$$ is

A
4
B
3
C
$$\frac{12}{\sqrt7}$$
D
None of these
4
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\text { If } A=\left[\begin{array}{ll} 2 & -2 \\ 2 & -3 \end{array}\right], B=\left[\begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array}\right] \text {, then }\left(B^{-1} A^{-1}\right)^{-1}=\text { ? }$$

A
$$A=\left[\begin{array}{ll}-2 & -2 \\ -3 & -2\end{array}\right]$$
B
$$A=\left[\begin{array}{cc}2 & 2 \\ -2 & -3\end{array}\right]$$
C
$$A=\left[\begin{array}{cc}3 & -2 \\ 2 & 2\end{array}\right]$$
D
$$A=\left[\begin{array}{cc}1 & -1 \\ -2 & 3\end{array}\right]$$
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