The $pH$ of a buffer solution made by mixing $25 \ mL$ of $0.02 \ M \ NH_4OH$ and $25 \ mL$ of $0.2 \ M \ NH_4Cl$ at $25^{\circ}C$ is ($pK_b$ of $NH_4OH = 4.8$).

An elevator weighing $6000\, kg$ is pulled upward by a cable with an acceleration of $5\, m/s^2$. Taking $g$ to be $10\, m/s^2$,then the tension in the cable is ........... $N$.

If $D, E$ and $F$ are respectively the mid-points of $AB, AC$ and $BC$ in $\triangle ABC$,then $\overrightarrow{BE} + \overrightarrow{AF}$ is equal to :

$A$ ray of light refracts from medium $1$ into a thin layer of medium $2$,crosses the layer,and is incident at the critical angle on the interface between medium $2$ and $3$ as shown in the figure. If the angle of incidence of the ray is $\theta$,the value of $\theta$ is

The minimum value of $(x-\alpha)(x-\beta)$ is

Which of the following is the correct order of lattice energy for the given ionic compounds?