The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is \(25 \%\) of the velocity of light, then the ratio of \(K.E.\) of electron and \(K.E.\) of photon will be:

Binding energy of a certain nucleus is \(18 \times 10^8 J\). How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus?

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:

A convex lens made of glass (refractive index \(=1.5\) ) has focal length 24 cm in air. When it is totally immersed in water (refractive index \(=1.33\) ), its focal length changes to ________.

As shown in figure, a cuboid lies in a region with electric field \(E=2 x^2 \hat{i}-4 y \hat{j}+6 \hat{k} \quad N / C\). The magnitude of charge within the cuboid is \(n \varepsilon_0 C\). The value of \(n\) is \(............\) (if dimension of cuboid is \(1 \times 2 \times 3 \;m ^3\) )

From the photoelectric effect experiment, following observations are made. Identify which of these are correct \(A.\) The stopping potential depends only on the work function of the metal. \(B.\) The saturation current increases as the intensity of incident light increases. \(C.\) The maximum kinetic energy of a photo electron depends on the intensity of the incident light. \(D.\) Photoelectric effect can be explained using wave theory of light. Choose the correct answer from the options given below:

A uniform sphere of mass \(500\; g\) rolls without slipping on a plane horizontal surface with its centre moving at a speed of \(5.00\; \mathrm{cm} / \mathrm{s}\). Its kinetic energy is

Five identical cells each of internal resistance \(1\, \Omega\) and \(emf \;5\, {V}\) are connected in series and in parallel with an external resistance \('R'.\) For what value of \('R',\) current in series and parallel combination will remain the same ? (in \(\Omega\))

Two equal positive point charges are separated by a distance \(2 a\). The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge \(q_0\) becomes maximum is \(\frac{a}{\sqrt{x}}\). The value of \(x\) is \(................\)

A circle of radius \(2\) unit passes through the vertex and the focus of the parabola \(y^{2}=2 x\) and touches the parabola \(y=\left(x-\frac{1}{4}\right)^{2}+\alpha\), where \(\alpha>0\). Then \((4 \alpha-8)^{2}\) is equal to

If the function \(f:(-\infty,-1] \rightarrow(a, b]\) defined by \(f(x)=e^{x^3-3 x+1}\) is one-one and onto, then the distance of the point \(\mathrm{P}(2 \mathrm{~b}+4, \mathrm{a}+2)\) from the line \(x+e^{-3} y=4\) is :

The probability that two randomly selected subsets of the set \(\{1,2,3,4,5\}\) have exactly two elements in their intersection, is :

The minimum value of \(f ( x )= a ^{ a ^{ x }}+ a ^{1- a ^{ x }},\) where \(a, x \in R\) and \(a > 0\), is equal to ..... .