Calculate the surface temperature of the planet,if the energy radiated by unit area in unit time is $5.67 \times 10^4 \, W$. (Assume the planet is a black body).

Two wires are made of the same material and have the same volume. Wire $1$ has cross-sectional area $A$ and wire $2$ has cross-sectional area $3A$. If the length of wire $1$ increases by $\Delta x$ on applying force $F$,how much force is needed to stretch wire $2$ by the same amount $\Delta x$?

Companion cells in plants are associated with

If $f: R \rightarrow R$ is an even function having derivatives of all orders,then which of the following is an odd function?

If three unit vectors $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ satisfy $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$, then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

Two wooden blocks of masses $M$ and $m$ are placed on a smooth horizontal surface as shown in the figure. If a force $P$ is applied to the system as shown in the figure such that the mass $m$ remains stationary with respect to the block of mass $M$, then the magnitude of the force $P$ is