$A$ conveyor belt is moving at a constant speed of $2\, m/s$. $A$ box is gently dropped on it. The coefficient of friction between them is $\mu = 0.5$. The distance that the box will move relative to the belt before coming to rest on it,taking $g = 10\, m/s^2$,is ........ $m$.

In an ellipse,the distance between its foci is $6$ and its minor axis is $8$. Then its eccentricity is

When a plane mirror is rotated through an angle $\theta$,the reflected ray turns through an angle $2\theta$. What happens to the size of the image?

The ratio of the specific heat capacities of a gas is $1.5$. When the gas undergoes an adiabatic process, its volume is doubled and pressure becomes $P_1$. When the gas undergoes an isothermal process, its volume is doubled and pressure becomes $P_2$. If $P_1 = P_2$, the ratio of the initial pressures of the gas when it undergoes adiabatic and isothermal processes is

Assertion : For a reaction $2NH_{3(g)} \to N_{2(g)} + 3H_{2(g)}$ ; $\Delta H > \Delta E$
Reason : Enthalpy change is always greater than internal energy change.

If $x^2+2px-2p+8>0$ for all real values of $x$,then the set of all possible values of $p$ is