Question Bank Directory

For a parallel beam of monochromatic light of wavelength $\lambda$, diffraction is produced by a single slit whose width $a$ is much greater than the wavelength of the light. If $D$ is the distance of the screen from the slit, the width of the central maxima will be:

After two hours, one-sixteenth of the starting amount of a certain radioactive isotope remained undecayed. The half life of the isotope is

A particle executing simple harmonic motion has a kinetic energy of $K = K_0 \cos^2(\omega t)$. The values of the maximum potential energy and the total energy are, respectively:

A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current I₁ at a distance d from the conductor as shown in figure. The loop will experience

The nuclei $_{6}^{13}\text{C}$ and $_{7}^{14}\text{N}$ can be described as:

Two similar coils of radius $R$ are lying concentrically with their planes at right angles to each other. The currents flowing in them are $I$ and $2I$, respectively. The resultant magnetic field induction at the centre will be:

A long straight wire of length $2 \text{ m}$ and mass $250 \text{ g}$ is suspended horizontally in a uniform horizontal magnetic field of $0.7 \text{ T}$. The amount of current flowing through the wire will be: ($g=9.8 \text{ m s}^{-2}$)

A closely packed coil having 1000 turns has an average radius of 62.8 cm. If the current carried by the wire of the coil is 1 A, the value of the magnetic field produced at the centre of the coil will be nearly: (permeability of free space = $4\pi \times 10^{-7}$ H/m)

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an:

An astronomical telescope has an objective and eyepiece of focal lengths $40\text{ cm}$ and $4\text{ cm}$ respectively. To view an object $200\text{ cm}$ away from the objective, the lenses must be separated by a distance of:

A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices $\mu_1$ and $\mu_2$ and $R$ is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is:

The magnetic field on the axis of a circular loop of radius 100 cm carrying current I = √2 A, at a point 1 m away from the centre of the loop is given by:

For radioactive material, the half-life is 10 minutes. If initially, there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is:

At some instant, the number of radioactive atoms in a sample is $N_0$ and after time $t$, the number decreases to $N$. It is found that the graphical representation $\ln N$ versus $t$ along the $y$ and $x$ axis respectively is a straight line. Then the slope of this line is:

The half-life of radium is 1622 years. How long will it take for seven-eighth of a given amount of radium to decay?

In the nuclear decay given below: $$ _{Z}^{A}X \rightarrow _{Z+1}^{A}Y \rightarrow _{Z-1}^{A-4}B^* \rightarrow _{Z-1}^{A-4}B $$ The particles emitted in the sequence are:

The binding energy per nucleon of ${}_{3}^{7}Li$ and ${}_{2}^{4}He$ nuclei are $5.60 \text{ MeV}$ and $7.06 \text{ MeV}$, respectively. In the nuclear reaction ${}_{3}^{7}Li + {}_{1}^{1}H \rightarrow {}_{2}^{4}He + {}_{2}^{4}He + Q$, the value of energy Q released is:

A double convex lens has a focal length of 25 cm. The radius of curvature of one of the surfaces is double of the other. What would be the radii if the refractive index of the material of the lens is 1.5?

The power of a biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm. The refractive index of the material of the lens is:

If the nuclear radius of ${}^{27}\mathrm{Al}$ is 3.6 Fermi, the approximate nuclear radius of ${}^{64}\mathrm{Cu}$ in Fermi is: