The number of ways of choosing $10$ objects out of $31$ objects,of which $10$ are identical and the remaining $21$ are distinct,is

Two particles undergo $SHM$ along parallel lines with the same time period $(T)$ and equal amplitudes. At a particular instant,one particle is at its extreme position while the other is at its mean position. They move in the same direction. They will cross each other after a further time:

The electric field in an electromagnetic wave is given by $E = 50 \sin \frac{2 \pi}{\lambda}(ct - x) \ N/C$. Find the energy contained in a cylindrical region of cross-section $10 \ cm^2$ and length $50 \ cm$ along the $x$-axis.

Condenser $A$ has a capacity of $15 \mu F$ when it is filled with a medium of dielectric constant $15$. Another condenser $B$ has a capacity of $1 \mu F$ with air between the plates. Both are charged separately by a battery of $100 V$. After charging,both are connected in parallel without the battery and the dielectric material being removed from condenser $A$. The common potential now is.......$V$

$\sum_{n=1}^{\infty} \frac{2n^2+n+1}{n!}$ is equal to

The plant body is differentiated into which of the following parts?