An electron makes a transition from orbit $n = 4$ to the orbit $n = 2$ of the hydrogen atom. The wave number of the emitted radiation ($R =$ Rydberg's constant) will be

Focal length of a convex lens will be maximum for

$A$ particle is projected from a point at an angle $\theta$ with the horizontal direction. At any time $t$,if $p$ is the linear momentum,$y$ is the vertical displacement,and $x$ is the horizontal displacement,which of the following graphs does $NOT$ represent the variation of kinetic energy $(KE)$ of the particle?

The general solution of $y^2 dx + (x^2 - xy + y^2) dy = 0$ is:

If $f(x) = \left| \begin{array}{ccc} x - 3 & 2x^2 - 18 & 3x^3 - 81 \\ x - 5 & 2x^2 - 50 & 4x^3 - 500 \\ 1 & 2 & 3 \end{array} \right|$,then $f(1)f(3) + f(3)f(5) + f(5)f(1) = $