1
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $A+B=\left[\begin{array}{cc}1 & \tan \frac{\theta}{2} \\ -\tan \frac{\theta}{2} & 1\end{array}\right]$ where $A$ is symmetric and $B$ is skew-symmetric matrix, then the matrix $\left(A^{-1} B+A B^{-1}\right)$ at $\theta=\frac{\pi}{6}$ is given by

A
$\left[\begin{array}{cc}1 & 2 \sqrt{3} \\ 2 \sqrt{3} & 1\end{array}\right]$
B
$\left[\begin{array}{cc}-1 & -2 \sqrt{3} \\ 2 \sqrt{3} & 1\end{array}\right]$
C
$\left[\begin{array}{cc}0 & 2 \sqrt{3} \\ 2 \sqrt{3} & 0\end{array}\right]$
D
$\left[\begin{array}{cc}0 & -2 \sqrt{3} \\ 2 \sqrt{3} & 0\end{array}\right]$
2
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If, $\int \frac{d \theta}{\cos ^2 \theta(\tan 2 \theta+\sec 2 \theta)}=\lambda \tan \theta+2 \log _{\mathrm{e}}|\mathrm{f}(\theta)|+\mathrm{c}$ (where c is a constant of integration), then the ordered pair $(\lambda,|f(\theta)|)$ is equal to

A
$(1,|1+\tan \theta|)$
B
$(1,1-1-\tan \theta \mid)$
C
$(-1,|1+\tan \theta|)$
D
$(-1,|1-\tan \theta|)$
3
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The domain of definition of the function $y(x)$ is given by the equation $2^x+2^y=2$, is

A
$0< x \leq 1$
B
$0 \leq x \leq 1$
C
$-\infty< x \leq 0$
D
$-\infty< x<1$
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\cos x \frac{\mathrm{~d} y}{\mathrm{~d} x}-y \sin x=6 x, 0

A
$y=\cos x+3 x^2+\mathrm{c}$, where c is a constant of integration.
B
$y+\cos x=3 x^2+\mathrm{c}$, where c is a constant of integration.
C
$y=3 x^2 \cos x+\cos x$, where c is a constant of integration.
D
$y \cdot \cos x=3 x^2+\mathrm{c}$, where c is a constant of integration.
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