An \(LCR\) circuit as shown in the figure is connected to a voltage source \(V_{ac}\) whose frequency can be varied. The frequency, at which the voltage across the resistor is maximum, is......\(Hz\)

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from \(440\, Hz\) to \(480 \,Hz ,\) when it gets reflected from the wall. If the speed of sound in air is \(345 \,m / s ,\) then the speed of the car is \(.......km/hr\)

A proton (mass \(m\) ) accelerated by a potential difference \(V\)  flies through a uniform transverse magnetic field \(B.\) The field occupies a region of space by width \('d'\). If \(\alpha \) be the angle of deviation of proton from initial direction of motion (see figure), the value of \(sin\,\alpha \) will be

In the given figure, a battery of emf \(E\) is connnected across a conductor \(P Q\) of length \('Y'\) and different area of cross-sections having radii \(r_{1}\) and \(r_{2}\left(r_{2}\,<\,r_{1}\right)\). Choose the correct option as one moves from \(P\) to \(Q\) :

Eight copper wire of length \(l\) and diameter \(d\) are joined in parallel to form a single composite conductor of resistance \(R\). If a single copper wire of length \(2\,l\) have the same resistance \((R)\) then its diameter will be \(.....d\).

The half-life of \({ }^{198} {Au}\) is \(3 \,days.\) If atomic weight of \({ }^{198} {Au}\) is \(198\, {g} / {mol}\) then the activity of \(2 \,{mg}\) of \({ }^{198} {Au}\) is ..... \(\times 10^{12}\,disintegration/second\)

A body is performing simple harmonic with an amplitude of \(10 \,cm\). The velocity of the body was tripled by air Jet when it is at \(5 \,cm\) from its mean position. The new amplitude of vibration is \(\sqrt{ x } \,cm\). The value of \(x\) is________

A spherical body of radius \(r\) and density \(\sigma\) falls freely through a viscous liquid having density \(\rho\) and viscosity \(\eta\) and attains a terminal velocity \(v _0\). Estimated maximum error in the quantity \(\eta\) is : (Ignore errors associated with \(\sigma, \rho\) and g , gravitational acceleration)