Magnetic fields at two points on the axis of a circular coil at a distance of \(0.05\, m\) and \(0.2\, m\) from the centre are in the ratio \(8: 1.\) The radius of coil is .......... \(m\)

The force is given in terms of time \(t\) and displacement \(x\) by the equation \({F}={A} \cos {Bx}+{C} \sin {Dt}\) The dimensional formula of \(\frac{{AD}}{{B}}\) is -

A concave mirror of focal length \(10\) cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is __________ cm.

In a photoelectric experiment ultraviolet light of wavelength \(280\, {nm}\) is used with lithium cathode having work function \(\phi=2.5\, {eV}\). If the wavelength of incident light is switched to \(400\, {nm}\), find out the change in the stopping potential (in \({V}\)). \(\left({h}=6.63 \times 10^{-34}\, {J} \cdots\right.\), \(\left.{c}=3 \times 10^{8} \,{ms}^{-1}\right)\) 

A musician using an open flute of length \(50\,cm\) produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of \(10 \,km/h.\) If the wave speed is \(330\,m/s,\) the frequency heard by the running person shall be close to...... \(Hz\)

Two sitar strings, \(A\)  and \(B,\)  playing the note \('Dha'\)  are slightly out of tune and produce beats and frequency  \(5\,Hz.\)  The tension of the string \(B\) is slightly increased and the beat frequency is found to decrease by  \(3\,Hz\) . If the frequency of \(A\) is \(425\,Hz,\)  the original frequency of \(B\) is  ... \(Hz\)

A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is \({\theta _{iC}}\) and Brewster's angle of incidence is \({\theta _{iB}}\), such that \(\sin \,{\theta _{iC}}/\sin \,{\theta _{iB}} = \eta  = 1.28\). The  relative refractive index of the two media is

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Consider a ferromagnetic material :
Assertion (A) : The individual atoms in a ferromagnetic material possess a magnetic dipole moment and interact with one another in such a way that they spontaneously align themselves forming domains.
Reason (R) : At high enough temperature, the domain structure of ferromagnetic material disintegrates. Thus, magnetization will disappear at high enough temperature known as Curie temperature.
In the light of the above statements, choose the correct answer from the options given below :

N equally spaced charges each of value q , are placed on a circle of radius R . The circle rotates about its axis with an angular velocity \(\omega\) as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, \(I_A-I_B\), for the given Amperian loops is:

The centre of a wheel rolling on a plane surface moves with a speed \(v_{0} .\) A particle on the rim of the wheel at the same level as the centre will be moving at a speed \(\sqrt{x}\, v_{0}\). Then the value of \(x\) is ...... .

The temperature of a body in air falls from \(40^{\circ} \mathrm{C}\) to \(24^{\circ} \mathrm{C}\) in 4 minutes. The temperature of the air is \(16^{\circ} \mathrm{C}\). The temperature of the body in the next 4 minutes will be:

A force \(\mathrm{f}=\mathrm{x}^2 \mathrm{y} \hat{\mathrm{i}}+\mathrm{y}^2 \hat{\mathrm{j}}\) acts on a particle in a plane \(\mathrm{x}+\mathrm{y}=10\). The work done by this force during a displacement from \((0,0)\) to \((4 \mathrm{~m}, 2 \mathrm{~m})\) is Joule (round off to the nearest integer)

In the given figure, there is a circuit of potentiometer of length \(A B=10 \,{m}\). The resistance per unit length is \(0.1 \,\Omega\) per \({cm}\). Across \({AB}\), a battery of emf \({E}\) and internal resistance ' \({r}^{\prime}\) is connected. The maximum value of emf measured by this potentiometer is : (In \(V\))