The differential equation of all circles which pass through the origin and whose centres lie on the $Y$-axis is

$A$ small conducting sphere of radius $r$ is lying concentrically inside a bigger hollow conducting sphere of radius $R$. The bigger and smaller spheres are charged with $Q$ and $q$ $(Q > q)$ respectively and are insulated from each other. The potential difference between the spheres will be

The equation of a wave on a string of linear mass density $0.04 \, kg \cdot m^{-1}$ is given by: $y = 0.02 \, \sin \left[ 2\pi \left( \frac{t}{0.04} - \frac{x}{0.50} \right) \right]$. The tension in the string is ..... $N$.

Gymnosperms lack true fruits because .........

If the coefficients of the $(2r+1)$-th term and the $(r+2)$-th term in the expansion of $(1+x)^{43}$ are equal,then $r$ is equal to:

Power delivered to a mass is $P = (3t^2 - 2t + 1) \text{ W}$. The change in kinetic energy from $t = 2 \text{ s}$ to $t = 4 \text{ s}$ is $...... \text{ J}$.