A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as _______.

Given below are two statements Statement \(I\) : When the frequency of an \(a.c.\) source in a series \(LCR\) circuit increases, the current in the circuit first increases, attains a maximum value and then decreases. Statement \(II:\) In a series \(LCR\) circuit, the value of power factor at resonance is one. In the light of given statements, choose the most appropriate answer from the options given below

In the figure shown, the current in the \(10\, V\) battery is close to

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 resonance circuit having inductance and resistance \(2 \times 10^{-4} H\) and \(6.28 \Omega\) respectively oscillates at \(10\, MHz\) frequency. The value of quality factor of this resonator is ......... \([\pi=3.14]\)

A rigid square loop of side \(a\) and carrying current \(I_2\) is laying on a horizontal surface near a long current \(I_1\) wire in the same plane as shown in figure. The net force on the loop due to the wire will be

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws \(25 \%\) more charge from the battery. The dielectric constant of mica is ___________ .

In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is ___________ mm.
[Assume least count is 0.01 mm ]

The internal energy \((U),\) pressure \((P)\) and volume \(( V )\) of an ideal gas are related as \(U =\) \(3 P V+4\). The gas is :-

Four identical particles of mass \(m\) are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is \(\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{\mathrm{Gm}^2}{\mathrm{~L}^2}\), the length of the sides of the square is _______.

In a Young's double slit experiment two slits are separated by \(2\, mm\) and the screen is placed one meter away. When a light of wavelength \(500 \,nm\) is used, the fringe separation will be ........ \(mm\)

Solid sphere \(A\) is rotating about an axis \(PQ\). If the radius of the sphere is \(5\,cm\) then its radius of gyration about \(P Q\) will be \(\sqrt{x} \;cm\). The value of \(x\) is \(................\).

A cyclotron is used to accelerate protons. If the operating magnetic field is \(1.0\,T\) and the radius of the cyclotron 'dees' is \(60 cm\), the kinetic energy of the accelerated protons in \(MeV\) will be. [use \(m _{p}=1.6 \times 10^{-27} kg , e =1.6 \times 10^{-19} C\) ]