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

The cubic equation whose roots are thrice to each of the roots of $x^3+2 x^2-4 x+1=0$ is

Consider the following reaction: $A \longrightarrow \text{Products}$. This reaction is completed in $100 \ min$. The rate constant of this reaction at $t_1 = 10 \ min$ is $10^{-2} \ min^{-1}$. What is the rate constant (in $min^{-1}$) at $t_2 = 20 \ min$?

$A$ constant voltage of $25 ~V$ is applied to a series $L-R$ circuit at $t=0$,by closing a switch. What is the potential difference across the resistor and the inductor at time $t=0$?

The solution set of the inequality $\log_{10}(x^2 - 2x - 2) \le 0$ is

If $l, m, n$ are in arithmetic progression,then the straight line $lx + my + n = 0$ will always pass through the point: