For a gas $\frac{R}{C_v} = 0.4$,where $R$ is the universal gas constant and $C_v$ is the molar specific heat at constant volume. The gas is made up of molecules which are

$ \cos^4 \frac{\pi}{8} + \cos^4 \frac{3\pi}{8} + \cos^4 \frac{5\pi}{8} + \cos^4 \frac{7\pi}{8} = $

The resolving power of an astronomical telescope is $0.2\, sec$. If the central half portion of the objective lens is covered,the resolving power will be....$sec$

What is the chemical name of Vitamin $B_1$?

Match the following columns and select the correct option:

$(a)$ Eosinophils	$(i)$ Immune response
$(b)$ Basophils	$(ii)$ Phagocytosis
$(c)$ Neutrophils	$(iii)$ Release histaminase enzyme
$(d)$ Lymphocytes	$(iv)$ Release granules containing histamine

$(a)\quad (b)\quad (c)\quad (d)$

If $p$-th,$q$-th,and $r$-th terms of a geometric progression are the positive numbers $a, b,$ and $c$ respectively,then the angle between the vectors $(\log a^2) i + (\log b^2) j + (\log c^2) k$ and $(q-r) i + (r-p) j + (p-q) k$ is