Arrange $NH_4^+$,$H_2O$,$H_3O^{+}$,$HF$,and $OH^{-}$ in increasing order of acidic nature.

$A$ body of mass $2 ~kg$ starts from rest and moves with uniform acceleration. It acquires a velocity $20 ~ms^{-1}$ in $4 ~s$. The power exerted on the body in $2 ~s$ in watts is

$A$ solid cylinder $30 \ cm$ in diameter at the top of an inclined plane $2.0 \ m$ high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom is .......... $m/s$.

Fraunhofer lines are produced by the absorption of light in

An organ pipe $P_1$,closed at one end and containing a gas of density $\rho_1$ is vibrating in its first harmonic. Another organ pipe $P_2$,open at both ends and containing a gas of density $\rho_2$ is vibrating in its third harmonic. Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes,the ratio of the lengths of $P_1$ and $P_2$ is (assume the given gases to be monoatomic).

If $\cos ^{-1}\left(\frac{y}{b}\right)=2 \log \left(\frac{x}{2}\right)$, where $x>0$, then $x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}$ is equal to