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

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:

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

The function $f(x)=e^{a x}+e^{-a x}, x \in \mathbb{R}$ and $a<0$, is strictly decreasing for all values of ' $x$ ', where