The work functions of metals $A$ and $B$ are in the ratio $1 : 2$. If light of frequencies $f$ and $2f$ are incident on the surfaces $A$ and $B$ respectively,the ratio of the maximum kinetic energy of photoelectrons emitted is ($f$ and $2f$ are both frequencies greater than the threshold frequency of metals $A$ and $B$ respectively).

$A$ parallel plate capacitor with air between the plates has a capacitance of $9 \, pF$. The separation between its plates is $d$. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1 = 3$ and thickness $d/3$,while the other one has dielectric constant $K_2 = 6$ and thickness $2d/3$. The new capacitance of the capacitor is .... $pF$.

If $\alpha = \frac{5}{2! 3} + \frac{5 \cdot 7}{3! 3^2} + \frac{5 \cdot 7 \cdot 9}{4! 3^3} + \ldots$,then $\alpha^2 + 4\alpha$ is equal to

The equations of motion of a projectile are given by $x = 36 t$ metre and $2 y = 96 t - 9.8 t^2$ metre. The angle of projection is:

The figure shows three resistor configurations $R_1$, $R_2$, and $R_3$ connected to a $3 \, V$ battery. If the power dissipated by the configurations $R_1$, $R_2$, and $R_3$ is $P_1$, $P_2$, and $P_3$ respectively, then:

The angle between the line joining the points $(1, -2)$ and $(3, 2)$ and the line $x + 2y - 7 = 0$ is