The point on the line $3x + 4y = 5$ which is equidistant from $(1, 2)$ and $(3, 4)$ is

$A$ body of mass $6 ~kg$ is under a force which causes displacement in it given by $s = \frac{t^2}{4}$ metres,where $t$ is time. The work done by the force in $2$ seconds is: (in $~J$)

In which of the following is lead sulfate $(PbSO_4)$ soluble?

The velocities of three particles of masses $20 \ g$,$30 \ g$ and $50 \ g$ are $10 \hat{i}$,$10 \hat{j}$ and $10 \hat{k}$,respectively. The velocity of the centre of mass of the three particles is

There is some change in length when a $33000 ~N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} ~m^2$. The change of temperature required to produce the same elongation,if the steel rod is heated,is (The modulus of elasticity is $3 \times 10^{11} ~N/m^2$ and the coefficient of linear expansion of steel is $1.1 \times 10^{-5} /{ }^{\circ} C$). (in $^{\circ} C$)

The required amount of $KBr$ (molar mass $= 119 \, g/mol$) in grams to start the precipitation of $AgBr$ in $500 \, mL$ solution of $0.05 \, M \, AgNO_3$ will be ($K_{sp}$ of $AgBr = 5 \times 10^{-13}$)