If the net electric field at point \(\mathrm{P}\) along \(\mathrm{Y}\) axis is zero, then the ratio of \(\left|\frac{q_2}{q_3}\right|\) is \(\frac{8}{5 \sqrt{x}}\), where \(\mathrm{x}=\) _______.

Two light waves having the same wavelength \(\lambda\) in vacuum are in phase initially. Then the first wave travels a path \(L _{1}\) through a medium of refractive index \(n_{1}\) while the second wave travels a path of length \(L_{2}\) through a medium of refractive index \(n _{2}\). After this the phase difference between the two waves is:

The earth's magnetic field lines resemble that of a dipole at the centre of the earth. If the magnetic moment of this dipole is close to \(8 \times 10^{22}\, Am^2\), the value of earth 's magnetic field near the equator is close to....\(Gauss\) (radius of the earth \(= 6.4 \times 10^6\, m\))

Two cylindrical vessels of equal cross-sectional area \(16\,cm ^{2}\) contain water upto herghts \(100\,cm\) and \(150\,cm\) respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is \(......J\) [Take density of water \(=10^{3}\,kg / m ^{3}\) and \(g =10\,ms ^{-2}\) ]

For a uniformly charged ring of radius \(R\), the electric field on its axis has the largest magnitude at a distance \(h\) from its centre. Then value of \(h\) is

A physical quantity \(P\) is given as \(P=\frac{a^2 b^3}{c \sqrt{d}}\) The percentage error in the measurement of \(a, b, c\) and \(d\) are \(1 \%, 2 \%, 3 \%\) and \(4 \%\) respectively. The percentage error in the measurement of quantity \(P\) will be \(.......\%\)

Consider the combination of \(2\) capacitors \(C _{1}\) and \(C _{2},\) with \(C _{2}> C _{1},\) when connected in parallel, the equivalent capacitance is \(\frac{15}{4}\) time the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, \(\frac{ C _{2}}{ C _{1}}\)

In the given circuit, value of \(Y\) is

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius \(9 \mathrm{~m}\) and completes \(120\) revolutions in \(3\) minutes. The magnitude of centripetal acceleration of monkey is _______ (in \(\mathrm{m} / \mathrm{s}^2\) ).