$A$ sample of a radioactive element has a mass of $10 \, g$ at an instant $t = 0$. The approximate mass of this element in the sample after two mean lives is ........ $g$.

The major product formed in the reaction is

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$a$. Sodium laurylsulphate	$i$. Toilet soap
$b$. Cetyltrimethyl ammonium chloride	$ii$. Non-ionic detergent
$c$. Sodium stearate	$iii$. Anionic detergent
$d$. Polyethyleneglycyl stearate	$iv$. Cationic detergent

Choose the correct answer from the options given below:

For a first order reaction at $27^{\circ} C$,the ratio of time required for $75 \%$ completion to $25 \%$ completion of reaction is

If the pair of lines $ax^2 + 2(a + b)xy + by^2 = 0$ represent the diameters of a circle and divide the circle into four sectors such that the area of one sector is three times the area of the other,then:

Consider the following statements $A$ and $B$ and identify the correct answer given below.
$A$. Peltier coefficient is numerically equal to the potential difference across the junctions of the thermocouple through which current is flowing.
$B$. According to Thomson,energy is neither absorbed nor evolved at the junction of a thermocouple but is absorbed or evolved only along the lengths of both the conductors.