The density of a cube is measured by measuring its mass and length of its sides. The \% error in the measurement of mass and length are $5 \%$ and $6 \%$ respectively. The percentage error in the measurement of density is

A mass attached to a spring performs S.H.M. whose displacement is $\mathrm{x}=3 \times 10^{-3} \cos 2 \pi \mathrm{t}$ metre. The time taken to obtain maximum speed for the first time is

If a gas is compressed isothermally then the r.m.s. velocity of its molecules

Three vectors are expressed as $\vec{a}=4 \hat{i}-\hat{j}, \vec{b}=-3 \hat{i}+2 \hat{j}$ and $\vec{c}=-\hat{k}$. The unit vector along the direction of sum of these vectors is