$BX_3 + NH_3 \xrightarrow{R.T} BX_3 \cdot NH_3 + \text{Heat of adduct formation } (\Delta H)$. The numerical value of $\Delta H$ is found to be maximum for:

Which of the following oxides is the most basic oxide?

In the following common emitter circuit,if $\beta = 100$,$V_{CE} = 7\,V$,$V_{BE} = 0$,and $R_C = 2\,k\Omega$,then find the value of $I_B$ in $mA$.

An organ pipe $P_1$ closed at one end is vibrating in its first overtone. Another pipe $P_2$ open at both ends is vibrating in its third overtone. They are in resonance with a given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is:

$A$ galvanometer $G$ deflects full scale when a potential difference of $0.50 \ V$ is applied. The internal resistance of the galvanometer $r_g$ is $25 \ \Omega$. An ammeter is constructed by incorporating the galvanometer and an additional shunt resistance $R_S$. The ammeter deflects full scale when a measurement of $2.0 \ A$ is made. The resistance $R_S$ is closest to ............. $\Omega$.

The value of the series $\cos 12^{\circ} + \cos 84^{\circ} + \cos 132^{\circ} + \cos 156^{\circ}$ is