For which of the following particles will it be most difficult to experimentally verify the deBroglie relationship?

This question has statement \(1\) and statement \(2\) . Of the four choices given after the statements, choose the one that best describes the two statements. 
Statement \(- 1\): A point particle of mass m moving with speed \(u\) collides with stationary point particle of mass \(M\). If the maximum energy loss possible is given as \(f\) \(\left( {\frac{1}{2}m{v^2}} \right)\) then \( f = \left( {\frac{m}{{M + m}}} \right)\)  Statement \(-2\): Maximum energy loss occurs when the particles get stuck together as a result of the collision.

The maximum velocity of the photoelectrons emitted from the surface is \(v\) when light of frequency \(n\) falls on a metal surface. If the incident frequency is increased to \(3n\) , the maximum velocity of the ejected photoelectrons will be 

Heat energy of \(184\,kJ\) is given to ice of mass \(600\,g\) at \(-12^{\circ}\,C\), Specific heat of ice is \(2222.3\,J\,kg ^{-1^{\circ}}\,C ^{-1}\) and latent heat of ice in \(336\,kJ / kg ^{-1}\) \((A)\) Final temperature of system will be \(0^{\circ} C\). \((B)\) Final temperature of the system will be greater than \(0^{\circ} C\). \((C)\) The final system will have a mixture of ice and water in the ratio of \(5: 1\). \((D)\) The final system will have a mixture of ice and water in the ratio of \(1: 5\). \((E)\) The final system will have water only. Choose the correct answer from the options given below:

Consider two physical quantities A and B related to each other as \(E=\frac{B-x^2}{A t}\) where \(E, x\) and \(t\) have dimensions of energy, length and time respectively. The dimension of \(A B\) is _______.

Four point charges \(-q, +q, +q\) and \(-q\) are placed on \(y\) axis at \(y = -2d\), \(y = -d, y = +d\) and \(y = +2d\), respectively. The magnitude of the electric field \(E\) at a point on the \(x -\) axis at \(x = D\), with \(D > > d\), will vary as

A photon of wavelength \(\lambda \) is scattered from an electron, which was at rest. The wavelength shift \(\Delta \lambda \) is three times of \( \lambda \) and the angle of scattering \(\theta \) is \(60^o\) . The angle at which the electron recoiled is \(\phi \). The value of \(tan\,\phi \) is : ( electron speed is much smaller than the speed of light)

The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of \(176 rad / s\). The frequency of this simple harmonic oscillator is _________ Hz. \(\left[\right.\) take \(\left.\pi=\frac{22}{7}\right]\)

From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is

Given below are two statements: Statement \(I:\) Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. Statement \(II:\) Acceleration due to earth's gravity is same at a height ' \(h\) ' and depth ' \(d\) ' from earth's surface, if \(h = d\). In the light of above statements, choose the most appropriate answer form the options given below

A series combination of resistor of resistance \(100\,\Omega\), inductor of inductance \(1\,H\) and capacitor of capacitance \(6.25\,\mu F\) is connected to an ac source. The quality factor of the circuit will be \(.............\).

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency \(10\ GHz\). What is the frequency of the microwave measured by the observer?.......\(GHz\) ( speed of light \(= 3 \times  10^8 \) \(ms^{-1}\))

The value of \( \frac{\sqrt{3}\text{cosec } 20^{\circ}-\sec 20^{\circ}}{\cos 20^{\circ}\cos 40^{\circ}\cos 60^{\circ}\cos 80^{\circ}} \) is equal to