Ajay opened a cumulative time deposit account with OBC Bank for $\frac{3}{2}$ year. If the rate of interest is $10\%$ per annum and the bank pays $₹4662$ on maturity, then find how much did ajay deposit each month.

Solve the following in equation and represent the solution set on the number line.

 $4\mathrm{x}-19\le \frac{3\mathrm{x}}{5} -2\le \frac{-2}{5}+\mathrm{x}, \mathrm{x}\in \mathrm{R}$

Solve the following equation for matrix $\mathrm{X}$

$2\mathrm{X} + 4 \left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right] = 3 \left[\begin{array}{cc}4& -2\\ 0& -6\end{array}\right]$

Find the value of $\mathrm{k}$ for which the given equation has equal roots.

$\left(\mathrm{k}-12\right){\mathrm{x}}^2+2\left(\mathrm{k}-12\right)\mathrm{x}+2=0$