The magnetic field at the centre of a current carrying circular coil of area ' \(A\) ' is ' \(B\) '. The magnetic moment ( M ) of the coil is ( \(\mu_0=\) permeability of free space)
A uniform solid sphere of mass ' \(m\) ' and radius ' r ' is surrounded by a uniform thin spherical shell of radius ' \(2 r\) ' and mass ' \(m\) ' then the gravitational field
A particle is executing linear S.H.M. starting from mean position. The ratio of the kinetic energy to the potential energy of the particle at a point of half the amplitude is
A parallel plate air capacitor has capacity ' \(C\) ' and distance of separation between plates is ' \(d\) '. If a conducting sheet of thickness \(\frac{2 d}{3}\) is inserted in between the plates, the capacitance becomes \(C_1\). The ratio of \(\frac{C_1}{C}\) is
A polyatomic gas is compressed to \(\left(\frac{1}{8}\right)^{\text {th }}\) of its volume adiabatically. If its initial pressure is \(\mathrm{P}_0\), its new pressure will be [Given, \(\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{4}{3}\) ]
The energy that should be added to an electron to reduce its de-Broglie wavelength from \(\lambda\) to \(\frac{\lambda}{2}\) is \(n\) times the initial energy. The value of ' \(n\) ' is
In an a.c. circuit with pure capacitance ' C ' and a.c. source \(E=E_0 \sin \omega t\), the equation of instantaneous current is given by
Radius of curved road is ' \(R\) ', width of road is ' \(b\) '. The outer edge of road is raised by ' \(h\) ' with respect to inner edge so that a car with velocity ' \(V\) ' can pass safe over it, then value of ' \(h\) ' is ( \(\mathrm{g}=\) acceleration due to gravity)
Which of the following comes under the category of random errors?
In the case of common emitter transistor amplifier, the ratio of collector current to emitter current is 0.96 , then the current gain \((\beta)\) of the amplifier is
Let the speed of light and the polarising angle for a given medium be ' \(V\) ' and ' \(i_p\) ' respectively. The relation between them is : ( \(\mathrm{C}=\) speed of light in vacuum)
The equivalent resistance of the following circuit when no current flows in the resistance of \(5 \Omega\) is nearly
Two tuning forks when sounded together produce 4 beats per second. One of the forks is in unison with 23 cm length of sonometer wire and other with 24 cm length of the same wire. The frequencies of the two tuning forks are
A disc of paper of radius ' \(R\) ' has a hole of radius ' \(r\) '. It is floating on a liquid of surface tension ' T '. The force of surface tension on the disc is
Figure shows the north pole of a magnet moving away from a thick conducting loop containing a capacitor. The excess positive charge will arrive on
An a. c. source is connected across a pure inductor. Which one of the following figures shows the correct phase relation between the current and e.m.f.?
An observer moves towards a stationary source of sound with a velocity of one fifth of the velocity of sound. The percentage increase in the apparent frequency is
In hydrogen atom, the energy of electron in first and third orbit is ' \(E_1\) ' and' \(E_3\) ' respectively. If \(E_3=x E_1\) then the value of \(x\) will be
A ray of light is incident on first face of an equilateral glass prism at an angle of incidence ' \(I\) '. The emergent ray just grazes along the adjacent face. The refractive index of the the prism is \(\sqrt{2}\). The value of angle of incidence at first face is \(\left(\sin 45^{\circ}=\frac{1}{\sqrt{2}}, \sin 90^{\circ}=1\right)\)
Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously with tensions ' \(\mathrm{T}_1\) ' and ' \(\mathrm{T}_2\) ' respectively. On changing the tension slightly in one of them, the beat frequency remains unchanged. This will happen when (Given \(\rightarrow \mathrm{T}_1>\mathrm{T}_2\) )
In a common emitter transistor amplifier circuit, the current gain \(\alpha=0.8\). If the base current changes by \(3 \mu \mathrm{~A}\) then the collector current changes by
How much should the pressure be increased in order to reduce the volume of a given mass of gas by \(5 \%\) at the constant temperature?
A square coil ABCD of side ' L ' is carrying a current in clockwise direction. A straight conductor carrying current \(\mathrm{I}_2\) (upward direction) is kept parallel to side AB at a distance \(\frac{\mathrm{L}}{3}\) in the plane of \(A B C D\). The net force on the coil ABCD is ( \(\mu_0=\) magnetic permeability)
In Young's double slit experiment the wavelength of light used is \(6000 \mathop {\rm{A}}\limits^{\rm{o}}\), the screen is 40 cm from the slits and the fringe width is 0.012 cm , the distance between two slits is
A regular hexagon of side 6 cm has a charge of \(2 \mu \mathrm{C}\) at each of its vertices, what is the potential at the centre of the hexagon?
\[ \left[\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text { SI unit }\right] \]
