Two radioactive materials $X_1$ and $X_2$ have decay constants $10 \lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $1 / e$ after a time:

$A$ compound contains $69.5\%$ oxygen and $30.5\%$ nitrogen and its molecular weight is $92$. The formula of that compound is

If $ad-bc \neq 0$,then the area (in sq. units) of the parallelogram formed by the lines $ax+by+2=0$,$ax+by+5=0$,$cx+dy+3=0$ and $cx+dy+7=0$ is

$A$ source of sound of frequency $640 ~Hz$ is moving at a velocity of $\frac{100}{3} ~m/s$ along a road,and is at an instant $30 ~m$ away from a point $A$ on the road (as shown in figure). $A$ person standing at $O$,$40 ~m$ away from the road,hears sound of apparent frequency $v^{\prime}$. The value of $v^{\prime}$ is (velocity of sound $= 340 ~m/s$). (in $~Hz$)

$A$ tuning fork of frequency $392 \ Hz$ resonates with $50 \ cm$ length of a string under tension $T$. If the length of the string is decreased by $2\%$,keeping the tension constant,the number of beats heard when the string and the tuning fork are made to vibrate simultaneously is:

In the following reaction,$A$ and $B$ respectively are:
$A$ $\xrightarrow{HBr} C_2H_5Br$ $\xrightarrow{B} A$