$A$ ball of mass $m$ and radius $r$ is gently released in a viscous liquid. The mass of the liquid displaced by it is $m'$ such that $m > m'$. The terminal velocity is proportional to

The differential equation of all circles which pass through the origin and whose centre lies on the $y$-axis is

The equation of the plane passing through the point $(1, 2, -3)$ and perpendicular to the planes $3x + y - 2z = 5$ and $2x - 5y - z = 7$ is:

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 maximum possible number of real roots of the equation $x^5 - 6x^2 - 4x + 5 = 0$ is

If the earth were to suddenly contract to $\frac{1}{n}^{th}$ of its present radius without any change in its mass,then the duration of the new day will be: