1
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $A=\left[\begin{array}{cc}1 & \cot \frac{\theta}{2} \\ -\cot \frac{\theta}{2} & 1\end{array}\right]$ then $A^{-1}=$

A
$\operatorname{cosec}^2 \frac{\theta}{2} \mathrm{~A}^{\mathrm{T}}$
B
$\frac{-\sin ^2 \theta}{2} A^T$
C
$\left(\frac{1+\cos \theta}{2}\right) A^T$
D
$\left(\frac{1-\cos \theta}{2}\right) A^T$
2
MHT CET 2025 21st April Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let A be a non-singular matrix of order n and $|A|=k$, then $(\operatorname{adj} A)^{-1}$ is

A
$\frac{\mathrm{A}}{\mathrm{k}}$
B
$\quad \mathrm{k}^{\mathrm{n}-1}(\operatorname{adj} \mathrm{~A})$
C
$\mathrm{k}^{n-2} \mathrm{~A}$
D
kA
3
MHT CET 2025 21st April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The distance between the lines represented by $16 x^2+9 y^2+48 x-24 x y-36 y+35=0$ is ......... units

A
$\frac{2}{5}$
B
$\frac{35}{2}$
C
$\frac{5}{2}$
D
$\frac{7}{5}$
4
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The third element in the second row of adjoint of a matrix $A=\left[a_{i j}\right]_{3 \times 3}$ (where $a_{i j}=2 i+j$ ) is

A
2
B
-2
C
4
D
-4
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