$A$ 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 masses $m_2 : m_1$ is:

The reaction $X \rightarrow \text{products}$ is a first order reaction. In $40 \text{ minutes}$,the concentration of $X$ changes from $1.0 \text{ M}$ to $0.25 \text{ M}$. What is the rate of reaction when $[X] = 0.1 \text{ M}$? $(\log 4 = 0.60)$

The locus of the complex number $z$ such that $\arg \left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}$ is:

In the process of transcription,the sigma factor is important for:

The number of turns in the primary and secondary coils of a transformer are $50$ and $200$ respectively. If the current in the primary coil is $4 ~A$,then the current in the secondary coil is: (in $~A$)

$A$ block rests on a rough inclined plane making an angle of $30^o$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8.$ If the frictional force on the block is $10\,N,$ the mass of the block (in $kg$) is (take $g = 10\,m/s^2$)