The value of aluminium susceptibility is \(2.2 \times 10^{-5}\). The percentage increase in the magnetic field if space within a current carrying toroid is filled with aluminium is \(\frac{x}{10^{4}}\). Then the value of \(x\) is ...... .

The quantities \(\quad x=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}, y=\frac{E}{B}\) and \(z=\frac{l}{C R}\) are defined where \(C-\) capacitance \(R-\)Resistance, \(l-\)length, \(E-\)Electric field, \(B-\)magnetic field and \(\varepsilon_{0}, \mu_{0},\) -free space permittivity and permeability respectively. Then....

\(\frac{x}{x+4}\) is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its \((i)\) third permitted energy level to the second level and \((ii)\) the highest permitted energy level to the second permitted level. The value of \(x\) will be.

The diameter of an air bubble which was initially \(2\,mm\), rises steadily through a solution of density \(1750\,kg\,m\,m ^{-3}\) at the rate of \(0.35\,cms ^{-1}\). The coefficient of viscosity of the solution is poise (in nearest integer). (the density of air is negligible).

In an experiment with photoelectric effect, the stopping potential,

A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm . If D and d are the total distance and displacement covered by the particle in 12.5 s , then \(\frac{\mathrm{D}}{\mathrm{d}}\) is ________.

Two radioactive substances \(A\) and \(B\) have decay constants \(5\lambda \) and \(\lambda \) respectively. At \(t = 0\), a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become \((\frac {1}{e})^2\) will be

Figure represents the extension (\(\Delta l\)) of a wire of length \(1\) meter, suspended from the ceiling of the room at one end with a load \(W\) connected to the other end. If the cross-sectional area of the wire is \(10^{-5}\) m\(^2\) then the Young's modulus of the wire is __________ N/m\(^2\).

A prism of refractive index \(\mu\) and angle \(A\) is placed in the minimum deviation position. If the angle of minimum deviation is \(A,\) then the value of \(A\) in terms of \(\mu\) is

A wheatstone bridge is initially at room temperature and all arms of the bridge have same value of resistances ( \(R_1=R_2=R_3=R_4\) ). When \(R_3\) resistance is heated to some temperature, its resistance value has gone up by \(10 \%\). The potential difference \(\left( V _{ a }- V _{ b }\right)\) (after \(R _3\) is heated) is ___________ V.