The plot given below is of the average power delivered to an \(LRC\) circuit versus frequency. The quality factor of the circuit is

A uniform electric field \(E =(8\,m / e ) V / m\) is created between two parallel plates of length \(1 m\) as shown in figure, (where \(m =\) mass of electron and \(e=\) charge of electron). An electron enters the field symmetrically between the plates with a speed of \(2\,m / s\). The angle of the deviation \((\theta)\) of the path of the electron as it comes out of the field will be........

Two factories are sounding their sirens at \(800\, Hz\) . A man goes from one factory to other at a speed of \(2\,m/s\). The velocity of sound is \(320\, m/s\). The number of beats heard by the person in one second will be

A geyser heats water flowing at a rate of \(2.0 kg\) per minute from \(30^{\circ} C\) to \(70^{\circ} C\). If geyser operates on a gas burner, the rate of combustion of fuel will be \(\dots \; g \min ^{-1}\) [Heat of combustion \(=8 \times 10^{3} Jg ^{-1}\)  Specific heat of water \(=4.2 Jg ^{-1} \; { }^{\circ} C ^{-1}\) ]

A potential divider circuit is connected with a DC source of \(20 \mathrm{~V}\), a light emitting diode of glow in voltage \(1.8 \mathrm{~V}\) and a zener diode of breakdown voltage of \(3.2 \mathrm{~V}\). The length (PR) of the resistive wire is \(20 \mathrm{~cm}\). The minimum length of \(P Q\) to just glow the LED is _______ cm.

A prism of refractive index \(\mu\) and angle \(A\) is placed in the minimum deviation position. If the angle of minimum deviation is \(A,\) then the value of \(A\) in terms of \(\mu\) is

A boy ties a stone of mass \(100 \,g\) to the end of a \(2\) \(m\) long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of \(80 \,N\). If the maximum speed with which the stone can revolve is \(\frac{ K }{\pi} rev\). / \(min\). The value of \(K\) is (Assume the string is massless and unstretchable)

A potential \(V_0\) is applied across a uniform wire of resistance \(R\). The power dissipation is \(P_1\). The wire is then cut into two equal halves and a potential of \(V _0\) is applied across the length of each half. The total power dissipation across two wires is \(P_2\). The ratio \(P_2: P_1\) is \(\sqrt{x}: 1\). The value of \(x\) is \(.............\).

A block takes \(t\) time to slide down a plane inclined at \(45°\) to the horizontal. If the surface is made smooth (frictionless), the block takes time \(\dfrac{t}{2}\) to slide down the plane. The coefficient of friction between the block and the inclined plane is \(\left(\dfrac{\alpha}{100}\right)\). The value of \(\alpha\) is __________.

A hoop of radius \(r\) and mass \(m\) rotating with an angular velocity \(\omega_0\) is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

A material has Poisson's ratio \(0.50.\) If a uniform rod of it suffers a longitudinal strain of \(2 \times {10^{ - 3}}\), then the percentage change in volume is