1
COMEDK 2026 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

If $X=\tan ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]+\cos ^{-1}\left[\cos \left(\frac{7 \pi}{6}\right)\right]$ and $Y=\sin ^{-1}\left[\sin \left(\frac{11 \pi}{6}\right)\right]+\tan ^{-1}\left[\tan \left(\frac{4 \pi}{3}\right)\right]$ then the value of $\mathbf{2} \boldsymbol{X}-\boldsymbol{Y}$ is:

A

$\frac{3 \pi}{2}$

B

$2 \pi$

C

$ 0$

D

$\pi$

2
COMEDK 2026 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

If the coefficients of $x^2$ and $x^3$ in the expansion of $(3+k x)^9$ are equal, then the value of ' $\boldsymbol{k}$ ' is

A

$\frac{7}{3}$

B

$\frac{7}{9}$

C

$\frac{9}{7}$

D

$\frac{3}{7}$

3
COMEDK 2026 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

Matrix $A=\left[\begin{array}{ccc}1 & 1 & 2 \\ 1 & -2 & 2 \\ 1 & 0 & -1\end{array}\right]$,

Given $\boldsymbol{M}_{\mathbf{2 2}}$ and $\boldsymbol{A}_{\mathbf{3 2}}$ are the minor and cofactor of the adjoint matrix of $\boldsymbol{A}$ respectively then the value of the expression $\boldsymbol{M}_{\mathbf{2 2}}+\boldsymbol{A}_{\mathbf{3 2}}-|\boldsymbol{a} \boldsymbol{d} \boldsymbol{j}|$ is:

A

$-729$

B

$-117$

C

$-81$

D

$-99$

4
COMEDK 2026 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_0^{\frac{\pi}{2}} \frac{3 \sin x+4 \cos x}{\sin x+\cos x} d x= $$

A

$$ \frac{\pi}{4} $$

B

$$ \frac{7\pi}{4} $$

C

$\pi$

D

$$ \frac{7\pi}{2} $$