If $\tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\frac{\pi}{2}$,then $1-xy-yz-zx$ is equal to

In a gene bank,valuable plant materials are stored in a living state. $A$ gene bank is a part of which of the following?

$A$ short magnetic needle is pivoted in a uniform magnetic field of induction $1 ~T$. Now,simultaneously another magnetic field of induction $\sqrt{3} ~T$ is applied at right angles to the first field; the needle deflects through an angle $\theta$ whose value is (in $^{\circ}$)

The value of the series $x \log _e a + \frac{x^3}{3!} (\log _e a)^3 + \frac{x^5}{5!} (\log _e a)^5 + \dots$ is

$A$ solution of concentration $C \ g \ \text{equiv}/L$ has a specific resistance $R$. The equivalent conductance of the solution is

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio $2 : 3$. The ratio of their partial pressures,when enclosed in a vessel kept at a constant temperature,is $4 : 3$. The ratio of their densities is :-