If $\vec{P}=b \hat{i}+6 \hat{j}+\hat{k} \quad$ and $\quad \vec{Q}=\hat{i}-a \hat{j}+4 \hat{k} \quad$ are perpendicular to each other, also $3 \mathrm{~b}-\mathrm{a}=5$. The value of $a$ and $b$ is

Two polaroids are oriented with their planes perpendicular to incident light and transmission axis making an angle $30^{\circ}$ with each other. What fraction of incident unpolarised light is transmitted?

$$ \left(\cos 30^{\circ}=\sqrt{3} / 2\right) $$

The acceleration (a) - time (T) graph for the body starting from rest is given below. The maximum speed of the body is

Two spherical black bodies have radii ' $R_1$ ' and ' $R_2$ '. Their surface temperatures are $T_1 K$ and $T_2 K$ respectively. If they radiate the same power, the ratio $\frac{R_1}{R_2}$ is