In the following common emitter circuit,if $\beta = 100$,$V_{CE} = 7 \, V$,$V_{BE} = 0 \, V$ (negligible),and $R_C = 2 \, k\Omega$,then $I_B$ is.......$mA$.

If $u=f(r)$,where $r^2=x^2+y^2$,then $\left(\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}\right)$ is equal to

Which of the following halides does not undergo hydrolysis?

If the angles made by a straight line with the coordinate axes are $\alpha, \frac{\pi}{2}-\alpha, \beta$,then $\beta$ is equal to

In which of the following reactions,chlorine acts as an oxidising agent?
$(i)$ $CH_3CH_2OH + Cl_2 \longrightarrow CH_3CHO + HCl$
$(ii)$ $CH_3CHO + Cl_2 \longrightarrow CCl_3CHO + HCl$
$(iii)$ $CH_4 + Cl_2 \xrightarrow{hv} CH_3Cl + HCl$
The correct answer is

$A$ building has two overhead water tanks, each fitted with a sensor $(S_1, S_2)$ which goes to $0$ when the water level in the tank falls below a set value and remains $1$ otherwise. $A$ common pump is used to raise water from an underground storage tank to these overhead tanks. Of the following circuits, which one will turn on $(P = 1)$ the pump only when at least one of the tanks has a water level below the set value?