$A$ light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $\frac{g}{8}$,then the ratio of the masses is

$A$ sphere $P$ of mass $m$ moving with velocity $v$ undergoes an oblique and perfectly elastic collision with an identical sphere $Q$ initially at rest. The angle $\theta$ between the velocities of the spheres after the collision shall be ............... $^o$.

Which of the following statements is incorrect regarding viruses?

$A$ long straight wire carrying a current of $30 ~A$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4} ~T$. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2.0 ~cm$ away from the wire is
$\left(\mu_0=4 \pi \times 10^{-7} ~H/m\right)$

One litre of oxygen at a pressure of $1 ~atm$ and two litres of nitrogen at a pressure of $0.5 ~atm$ are introduced into a vessel of volume $1 ~L$. If there is no change in temperature,the final pressure of the mixture of gas (in $atm$) is

If $\frac{4 + 3\sqrt{3}}{\sqrt{7 + 4\sqrt{3}}} = a + \sqrt{b}$,then $(a, b) = $