$A$ galvanometer has resistance $G$ and range $V_g$. How much resistance is required to read voltage up to $V$ volt?

$\sinh^{-1}(2^{3/2})$ is equal to :

If a body is projected with an angle $\theta$ to the horizontal,then

Identify the organism shown in the given figure.

The acceleration due to gravity on the moon is $\left(\frac{1}{6}\right)$ times the acceleration due to gravity on the earth. If the ratio of the density of the earth $\rho_{e}$ to the density of the moon $\rho_{m}$ is $\frac{5}{3}$,then the radius of the moon $R_{m}$ in terms of the radius of the earth $R_{e}$ is:

If $f(x) = \begin{cases} x-5, & \text{for } x \leq 1 \\ 4x^2-9, & \text{for } 1 < x < 2 \\ 3x+4, & \text{for } x \geq 2 \end{cases}$,then $f^{\prime}(2^{+})$ is equal to