$A$ determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that the determinant chosen is non-zero is

$A$ solid sphere and a disc of same mass $M$ and radius $R$ are kept such that their curved surfaces are in contact and their centers lie along the same horizontal line. The moment of inertia of the two-body system about an axis passing through their point of contact and perpendicular to the plane of the disc is

Along the $x$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at a point $P$ located at a distance $r$ from the charge $-q$ (where $r > a$) is ($\varepsilon_0$ is the permittivity of free space):

The potential difference between $A$ and $B$ in the figure is ................. $V$.

Which of the following is a prokaryotic kingdom?

$A$ small source of sound vibrating at a frequency $500 ~Hz$ is rotated along a circle of radius $\frac{100}{\pi} ~cm$ at a constant angular speed of $5 ~revolutions ~per ~second$. The minimum and maximum frequency of the sound observed by a listener situated in the plane of the circle is (speed of sound is $332 ~ms^{-1}$).