A certain charge \(Q\) is divided into two parts \(q\) and \((Q-q) .\) How should the charges \(Q\) and \(q\) be divided so that \(q\) and \((Q-q)\) placed at a certain distance apart experience maximum electrostatic repulsion?

Find the correct combination of A, B, C and D inputs which can cause the LED to glow

A big drop is formed by coalescing \(1000\) small droplets of water. The ratio of surface energy of \(1000\) droplets to that of energy of big drop is \(\frac{10}{x}\). The value of \(x\) is _______.

Distance between an object and three times magnified real image is 40 cm . The focal length of the mirror used is _________ cm .

Identify the correct statements from the following descriptions of various properties of electromagnetic waves. \(A\). In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field. \(B.\) The energy in electromagnetic wave is divided equally between electric and magnetic fields. \(C.\) Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave. \(D.\) The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other. \(E.\) The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light. Choose the most appropriate answer from the options given below:

The typical output characteristics curve for a transistor working in the common-emitter configuration is shown in the figure. The estimated current gain from the figure is

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following (Assume negligible air friction)

Let \(f, g:(0, \infty) \rightarrow R\) be two functions defined by \(f(x)=\int_{-x}^x\left(|t|-t^2\right) e^{-t^2} d t\) and \(g(x)=\int_0^{x^2} t^{1 / 2} e^{-t} d t\). Then the value of \(\left(\mathrm{f}\left(\sqrt{\log _{\mathrm{e}} 9}\right)+\mathrm{g}\left(\sqrt{\log _{\mathrm{e}} 9}\right)\right)\) is

For \(n \in N\), let \(S _{ n }=\left\{ z \in C :| z -3+2 i |=\frac{ n }{4}\right\}\) and \(T _{ n }=\left\{ z \in C :| z -2+3 i |=\frac{1}{ n }\right\}\) Then the number of elements in the set \(\left\{ n \in N : S _{ a } \cap T _{ n }=\phi\right\}\) is.

\(\lim _{x \rightarrow \frac{\pi}{2}}\left(\frac{1}{\left(x-\frac{\pi}{2}\right)^2} \int_{x^3}^{\left(\frac{\pi}{2}\right)^3} \cos \left(\frac{1}{t^3}\right) d t\right)\) is equal to

An ellipse has its center at (1,-2), one focus at (3,-2) and one vertex at \((5,-2)\). Then the length of its latus rectum is :

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths \(r\) =\(\frac{{{\lambda _1}}}{{{\lambda _2}}}\) is given by

Let \(\mathrm{A}\) be a \(3 \times 3\) real matrix. If \(\operatorname{det}(2 \operatorname{Adj}(2 \operatorname{Adj}(\operatorname{Adj}(2 \mathrm{~A}))))=2^{41}\), then the value of \(\operatorname{det}\left(A^{2}\right)\) equal ..... .