The normal freezing point $(f.p.)$ of nitrobenzene is $278.82\, K$. If a non-volatile solute is dissolved in it and a solution of $0.25\, m$ (molality) is prepared,the observed $f.p.$ of the solution is $276.82\, K$. Evaluate $K_f$ of nitrobenzene in $K\, kg\, mol^{-1}$.

Which one of the following does not involve coagulation?

$A$ fireman of mass $60 \, kg$ slides down a pole. He is pressing the pole with a force of $600 \, N$. The coefficient of friction between the hands and the pole is $0.5$. With what acceleration will the fireman slide down (in $, m/s^2$)? (Take $g = 10 \, m/s^2$)

Zirconium phosphate $[Zr_3(PO_4)_4]$ dissociates into three zirconium cations of charge $+4$ and four phosphate anions of charge $-3$. If molar solubility of zirconium phosphate is denoted by $S$ and its solubility product by $K_{sp}$,then which of the following relationships between $S$ and $K_{sp}$ is correct?

If in a $\triangle ABC$,$r_1 < r_2 < r_3$,then:

When the engine is switched off,a vehicle of mass $M$ is moving on a rough horizontal road with momentum $p$. If the coefficient of friction between the road and the tyres of the vehicle is $\mu_k$,what is the distance travelled by the vehicle before it comes to rest?