If $x > 0, y > 0, z > 0, xy + yz + zx < 1$ and if $\tan^{-1} x + \tan^{-1} y + \tan^{-1} z = \pi$,then $x + y + z$ equals to

$A$ weak acid $HX$ has the dissociation constant $1 \times 10^{-5} \ M$. It forms a salt $NaX$ on reaction with alkali. The percentage hydrolysis of $0.1 \ M$ solution of $NaX$ is ........ $\%$.

If $3 \cos x \neq 2 \sin x$,then the general solution of $\sin^2 x - \cos 2x = 2 - \sin 2x$ is

The species having tetrahedral shape is

Magnesium wire is heated in the atmosphere of $CO_2$ because

Let the relation $R$ be defined on the set of natural numbers $N$ by $a R b$ if $3 a + 2 b = 27$. Then $R$ is: