The half-life of a radioactive substance is $20 \, min$. The approximate time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and the time $t_1$ when $\frac{1}{3}$ of it has decayed is ......... $min$.

At $550 \ K$,the $K_c$ for the following reaction is $10^4 \ L \ mol^{-1}$: $X_{(g)} + Y_{(g)} \rightleftharpoons Z_{(g)}$. At equilibrium,it was observed that $[X] = \frac{1}{2}[Y] = \frac{1}{2}[Z]$. What is the value of $[Z]$ (in $mol \ L^{-1}$) at equilibrium?

Two opposite and equal charges $4 \times 10^{-8} \, C$ are placed $2 \times 10^{-2} \, cm$ apart,forming a dipole. If this dipole is placed in an external electric field of $4 \times 10^8 \, N/C$,what are the values of the maximum torque and the work done in rotating it through $180^o$?

The velocity of a particle which starts from rest is given by the following table. The total distance travelled (in metre) by the particle in $10 \ s$,using the Trapezoidal rule is given by:

$t$ (in second)	$0$	$2$	$4$	$6$	$8$	$10$
$v$ (in m/s)	$0$	$12$	$16$	$20$	$35$	$60$

The study of the interaction of antigens and antibodies in the blood is known as:

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and $l^2+m^2-n^2=0$ is