The half-life of \(Au ^{198}\) is \(2.7\, days.\) The activity of \(1.50\, mg\) of \(Au ^{198}\) if its atomic weight is \(198\, g mol ^{-1}\) is .......\(Ci\) \(\left( N _{ A }=6 \times 10^{23}\, / mol \right)\)

A wire of resistance \(R\) and radius \(r\) is stretched till its radius became \(r / 2\). If new resistance of the stretched wire is \(xR\), then value of \(x\) is _______.

The relation between time \(t\) and distance \(x\) for a moving body is given as \(t=m x^{2}+n x\), where \({m}\) and \({n}\) are constants. The retardation of the motion is - (Where \(v\) stands for velocity)

In the circuit shown, charge on the \(5\, \mu F\) capacitor is\(........\mu C\)

A closed vessel contains \(0.1\) mole of a monoatomic ideal gas at \(200\, K\). If \(0.05\) mole of the same gas at \(400\, K\) is added to it, the final  equilibrium temperature (in \(K\) ) of the gas in the vessel will be closed to

A vessel contains \(16 \,g\) of hydrogen and \(128 \,g\) of oxygen at standard temperature and pressure. The volume of the vessel in \(cm ^{3}\) is

An oil drop of radius \(2\, mm\) with a density \(3\, g\) \(cm ^{-3}\) is held stationary under a constant electric field \(3.55 \times 10^{5}\, V\, m ^{-1}\) in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess ? (consider \(\left. g =9.81\, m / s ^{2}\right)\)

If the maximum load carried by an elevator is \(1400\,kg\) (\(600\,kg\) - Passenger \(+800\,kg\) - elevator), which is moving up with a uniform speed of \(3\,ms ^{-1}\) and the frictional force acting on it is \(2000\,N\), then the maximum 10.Power used by the motor is \(...........\,kW \left( g =10\,m / s ^2\right)\).

A mosquito is moving with a velocity \(\overrightarrow{ v }=0.5 t ^{2} \hat{ i }+3 t \hat{ j }+9 \hat{ k }\, m / s\) and accelerating in uniform conditions. What will be the direction of mosquito after \(2 \,s\) ?

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be..... \(\%\).

A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now ..... \(f\)