The value of $k$ for which the equation $2x^2 - kx + x + 8 = 0$ has equal and real roots is:

If the values of $k$ for which the equation $x^2+2(k+2)x+6k+7=0$ has equal roots are $k_1$ and $k_2$,then $k_1^2+k_2^2=$

The number of real solutions of the equation $x^{2}-|x|-12=0$ is:

$A$ building construction work can be completed by two masons $A$ and $B$ together in $22.5$ days. Mason $A$ alone can complete the work in $24$ days less than mason $B$ alone. Then mason $A$ alone will complete the work in: (in $days$)

For the equation $|x^2| + |x| - 6 = 0$,the roots are

If $x = \sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}$,then $x^2(x-4)^2$ is equal to :