If it takes \(5\,minutes\) to fill a \(15\,litre\) bucket from a water tap of diameter \(\frac{2}{{\sqrt \pi  }}cm\) then the Reynolds number for the flow is (density of water \(= 10^3\,kg/m^3\) ) and viscosity of water \(= 10^{-3}\,Pa.s\) ) close to

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is \(7 \times 10^8 \mathrm{~V} / \mathrm{s}\) then the integer value of the distance between the parallel plates is \(\left(\right.\) Take, \(\left.\epsilon_0=9 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}, \pi=\frac{22}{7}\right)\) ________ \(\mu \mathrm{m}\).

An ideal gas is expanding such that \({PT}^{3}=\) constant. The coefficient of volume expansion of the gas is:

In a photoelectric experiment ultraviolet light of wavelength \(280\, {nm}\) is used with lithium cathode having work function \(\phi=2.5\, {eV}\). If the wavelength of incident light is switched to \(400\, {nm}\), find out the change in the stopping potential (in \({V}\)). \(\left({h}=6.63 \times 10^{-34}\, {J} \cdots\right.\), \(\left.{c}=3 \times 10^{8} \,{ms}^{-1}\right)\) 

A \(16\, \Omega\) wire is bend to form a square loop. A \(9 \,{V}\) supply having internal resistance of \(1 \,\Omega\) is connected across one of its sides. The potential drop across the diagonals of the square loop is \(.......\,\times 10^{-1} \,{V}\)

A quantity \(f\) is given by \(f=\sqrt{\frac{{hc}^{5}}{{G}}}\) where \(c\) is speed of light, \(G\) universal gravitational constant and \(h\) is the Planck's constant. Dimension of \(f\) is that of

A rod of length \(60 \mathrm{~cm}\) rotates with a uniform angular velocity \(20 \mathrm{rad} \mathrm{s}^{-1}\) about its perpendicular bisector, in a uniform magnetic field \(0.5 \mathrm{~T}\). The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is________\(V\).

The radius of \(2^{\text {nd }}\) orbit of \(He ^{+}\)of Bohr's model is \(r _1\) and that of fourth orbit of \(Be ^{3+}\) is represented as \(r _2\). Now the ratio \(\frac{r_2}{r_1}\) is \(x : 1\). The value of \(x\) is .........

On celcius scale the temperature of body increases by \(40^{\circ} \mathrm{C}\). The increase in temperature on Fahrenheit scale is _______.

The average kinetic energy of a molecule of the gas is

A capacitor of capacitance \(C=1\, \mu \,{F}\) is suddenly connected to a battery of \(100\, volt\) through a resistance \({R}=100\, \Omega\). The time taken for the capacitor to be charged to get \(50 \,{V}\) is \(....\,\times \,10^{-4}\,s.\) [Take \(\ln 2=0.69]\)

Given below are two statements: Statement \(I\) : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit \(\left( E _{1}\right)\) to higher energy orbit \(\left( E _{2}\right)\), is given as \(hf = E _{1}- E _{2}\). Statement \(II\) : The jumping of electron from higher energy orbit \(\left(E_{2}\right)\) to lower energy orbit \(\left(E_{1}\right)\) is associated with frequency of radiation given as \(f\) \(=\left( E _{2}- E _{1}\right) / h\) This condition is Bohr's frequency condition. In the light of the above statements, choose the correct answer from the options given below