Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is ___________ m.
\(\left( g =10 m / s ^2\right)\)

\(10\) resistors each of resistance \(10\,\Omega\) can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be \(..........\).

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is \(\sqrt{\frac{x}{5}}\) where \(\mathrm{x}=\) _____

The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by

If the maximum value of accelerating potential provided by a ratio frequency oscillator is \(12\, {kV}\). The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is ....... . \(\left[{m}_{{p}}=1.67 \times 10^{-27} {kg}, {e}=1.6 \times 10^{-19} {C},\right.\) Speed of light \(\left.=3 \times 10^{8} {m} / {s}\right]\)

A certain gas is isothermally compressed to \(\left(\dfrac{1}{3}\right)^{rd}\) of its initial volume (\(V_o = 3\) litre) by applying required pressure. If the bulk modulus of the gas is \(3 \times 10^5\) N/m\(^2\), the magnitude of work done on the gas is _______ J.

A single slit of width \(b\) is illuminated by a coherent monochromatic light of wavelength \(\lambda \). If the second and fourth minima in the diffraction pattern at a distance \(1\,m\) from the slit are at \(3\, cm\) and \(6\, cm\) respectively from the central maximum, what is the width of the central maximum ?......\(cm\) (i.e. distance between first minimum on either side of the central maximum)

A thin half ring of radius \(35\) cm is uniformly charged with a total charge of \(Q\) coulomb. If the magnitude of the electric field at centre of the half ring is \(100\) V/m, then the value of \(Q\) is _______ nC. (\(\epsilon_o = 8.85 \times 10^{-12}\) C\(^2\)/Nm\(^2\) and \(\pi = 3.14\))

A magnet of total magnetic moment \({10\,^{ - 2}}\hat i\,A - {m^2}\) is placed in a time varying magnetic field, \(B\,\hat i\,\left( {\cos \,\omega t} \right)\) where \(B = 1\, Tesla\) and \(\omega  = 0.125\, rad/s\). The work done for reversing the direction of the magnetic moment at \(t = 1\, second\), is

If the percentage errors in measuring the length and the diameter of a wire are \(0.1 \%\) each. The percentage error in measuring its resistance will be _______.

A thin disc of radius \(b = 2a\)  has a concentric hole of radius \('a'\) in it (see figure). It carries uniform surface charge \('\sigma '\) on it. If the electric field on its axis at height \('h'\) \((h << a)\) from its centre is given as \('Ch'\) then value of \('C'\) is

What is the current through the battery in the circuit shown below?