The order of reactivity of phenol $(I)$,nitrobenzene $(II)$ and benzene $(III)$ towards nitration is

In the adjacent circuit,a voltmeter of internal resistance $R$,when connected across $B$ and $C$,reads $\frac{100}{3} \text{ V}$. Neglecting the internal resistance of the battery,the value of $R$ is

$A$ string is vibrating in its fifth overtone between two rigid supports $2.4 ~m$ apart. The distance between successive node and antinode is (in $~m$)

If $2 \vec{a} + 3 \vec{b} + \vec{c} = \vec{0}$,then $\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}$ is equal to

The coefficient of static friction,$\mu_s$ between block $A$ of mass $2\,kg$ and the table as shown in the figure is $0.2$. What would be the maximum mass value of block $B$ so that the two blocks do not move (in $,kg$)? The string and the pulley are assumed to be smooth and massless. $(g = 10\,m/s^2)$

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ $(\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ $(k > 0)$. The terminal speed of the ball is