$$ \mathop {\lim }\limits_{x \to {\pi \over 2}}\left(\frac{1-\sin x}{\cos x}\right) \text { is equal to } $$
$1$
$-1$
$\frac{1}{2}$
$0$
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:
$\frac{3 \pi}{2}$
$2 \pi$
$ 0$
$\pi$
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
$\frac{7}{3}$
$\frac{7}{9}$
$\frac{9}{7}$
$\frac{3}{7}$
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:
$-729$
$-117$
$-81$
$-99$
COMEDK Papers
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