The half-life of a radioactive isotope $X$ is $50$ years. It decays to another element $Y$,which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1:15$ in a sample of a given rock. The age of the rock was estimated to be ......... years.

Observe the following statements :
$I$. The physical and chemical properties of elements are periodic functions of their electronic configuration.
$II$. Electronegativity of fluorine is less than the electronegativity of chlorine.
$III$. Electropositive nature decreases from top to bottom in a group.
The correct answer is :

The horizontal and vertical displacements $x$ and $y$ of a projectile at a given time $t$ are given by $x = 6t \text{ m}$ and $y = 8t - 5t^2 \text{ m}$. The range of the projectile in metres is

Extranuclear inheritance is a consequence of the presence of genes in

The perpendicular distance from the point $(1, \pi)$ to the line joining $(1, 0^{\circ})$ and $(1, \frac{\pi}{2})$ (in polar coordinates) is:

The number of possible straight lines passing through $(2, 3)$ and forming a triangle with the coordinate axes,whose area is $12 \, sq. \, units$,is