If one of the roots of the equation $6x^3-25x^2+2x+8=0$ is an integer and $\alpha > 0$,$\beta < 0$ are the other two roots,then $\frac{4}{\alpha}+\frac{1}{\beta}=$

The number of real roots of the equation $\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}=\frac{13}{6}$ is

If the resultant of two forces of magnitudes $P$ and $Q$ acting at a point at an angle of $60^\circ$ is $\sqrt{7}Q$,then $P/Q$ is

If $x = 2^{1/3} - 2^{-1/3}$,then $2x^3 + 6x = $

Suppose the height of a pyramid with a square base is decreased by $p \%$ and the lengths of the sides of its square base are increased by $p \%$ (where $p > 0$). If the volume remains the same,then:

$A$ 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 $days$)