The diameter of the objective of a telescope is $1 \ m$. Its resolving limit for light of wavelength $4538 \ \mathring{A}$ will be:

Evaluate the determinant: $\left|\begin{array}{cc}2 & 4 \\ -5 & -1\end{array}\right|$

If $\frac{1}{x(x^2 + 1)} = \frac{A}{x} + \frac{Bx + C}{x^2 + 1}$,then $(A, B, C) = $

$A$ body of mass $m$ is moving in a circle of radius $r$ with a constant speed $v$. The force on the body is $\frac{mv^2}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle?

In an experiment of a simple pendulum,the errors in the measurement of length of the pendulum $(L)$ and time period $(T)$ are $3 \%$ and $2 \%$,respectively. The maximum percentage error in the value of $\frac{L}{T^2}$ is (in $\%$)

When zeolite,which is a hydrated sodium aluminium silicate,is treated with hard water,the sodium ions are exchanged with which of the following?