The momentum of the proton is one-fourth the momentum of the electron. What is the ratio of the de-Broglie wavelength of an electron to that of a proton?

The number of possible natural oscillations of air column in a pipe closed at one end of length \(85 \mathrm{~cm}\) whose frequencies lie below \(1250 \mathrm{~Hz}\) are (velocity of sound \(=340 \mathrm{~ms}^{-1}\))

One end of the string of length \(l\) is connected to a particle of mass \(m\) and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed \(v\), the net force on the particle (directed towards centre) will be ( \(T\) represents the tension in the string)

An inductor and a resistor are connected to an \(\mathrm{AC}\) supply of \(50 \mathrm{~V}\) and \(50 \mathrm{~Hz}\). If the voltage across the resistor is \(40 \mathrm{~V}\), then the voltage across the inductor will be

\(0.04 \mathrm{~m}\) of glass contains the same number of waves as \(0.05 \mathrm{~m}\) of water, when monochromatic light passes through them normally. Refractive index of water is \(4 / 3\). Refractive index of glass is

A photodiode fabricated from lead Selenide \([\mathrm{PbSe}]\) has a band gap energy of 0.27 eV . What is the wavelength of the signal the photodiode can detect?

A capacitor of \(10 \mu \mathrm{F}\) is connected to a \(10 \mathrm{~V}\) cell. The maximum charge on the capacitor will be

Choose the correct metal/ ion from the brackets which ..........
A. has chemical reactivity similar to that of the first few members of the Lanthanoids \((\mathrm{Zn}, \mathrm{Ca}, \mathrm{Fe}, \mathrm{Cu})\).
B. has stable \(4 \mathrm{f}^7\) electronic configuration, but acts as a strong reducing agent and converts to \(\mathrm{M}^{3+}\) state. \(\left(\mathrm{Eu}^{2+}, \mathrm{Ce}^{2+}, \mathrm{Pr}^{2+}, \mathrm{Dy}^{2+}\right)\)
C. is a colorless ion \(\left(\mathrm{Tm}^{3+}, \mathrm{Lu}^{3+}, \mathrm{Gd}^{3+}, \mathrm{Sm}^{3+}\right)\).
D. shows stable +2 oxidation state and is diamagnetic \((\mathrm{Ce}, \mathrm{Sm}, \mathrm{Ho}, \mathrm{Yb})\)

Consider the gaseous equilibrium
\(2\text{AB}_{2(g)} \rightleftharpoons 2\text{AB}_{(g)} + \text{B}_{2(g)}\)
The expression relating the degree of dissociation (\(\alpha\)) and equilibrium constant (\(K_p\)) and total pressure P is:

For what value of \(\mathrm{a}\) and \(\mathrm{b}\) the intercepts cut off on the co-ordinate axes by the line \(a x-b y+8=0\) are equal in length but opposite in signs to those cut off by the line \(2 x-3 y+6=0\) on the axes

\(\int_\limits{-1}^1 \dfrac{d}{d x}\left(\tan ^{-1} \dfrac{1}{x}\right) d x \text { is }\)

An atom has a single electron. Its ground state energy is \(-30\ eV\) and its first excited state energy is \(-8\ eV\). The atom is bombarded with a stream of photons, each of energy \(15\ eV\). Assuming the atom being in the ground state, which of the following statements is correct?

In the manufacture of ammonia by the Haber's process, \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)+92.3 \mathrm{~kJ}\), which of the following conditions is unfavourable?