1
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_0^{\frac{\pi}{2}} \sqrt{\cos \theta} \cdot \sin ^3 \theta d \theta=$$ ............

A
$\frac{-20}{21}$
B
$\frac{-8}{21}$
C
$\frac{20}{21}$
D
$\frac{8}{21}$
2
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\omega$ is a complex cube root of unity and $A=\left[\begin{array}{ccc}\omega & 0 & 0 \\ 0 & \omega^2 & 0 \\ 0 & 0 & 1\end{array}\right]$ then $A^{-1}=\ldots$

A
$\left[\begin{array}{ccc}\omega^2 & 0 & 0 \\ 0 & \omega & 0 \\ 0 & 0 & 1\end{array}\right]$
B
$\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$
C
$\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & \omega^2 & 0 \\ 0 & 0 & \omega\end{array}\right]$
D
$\left[\begin{array}{ccc}0 & 0 & \omega \\ 0 & \omega^2 & 0 \\ 1 & 0 & 0\end{array}\right]$
3
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $A$ and $B$ are square matrices of order 3 such that $|A|=2,|B|=4$, then $|A(\operatorname{adj} B)|=\ldots$

A
16
B
8
C
64
D
32
4
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\int \frac{1}{1-\cot x} d x=A x+B \log |\sin x-\cos x|+c$ then $A+B=\ldots \ldots$

A
1
B
$-$1
C
0
D
$-$2
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