The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are \(1 \%, 2 \%\) and \(3 \%\) respectively. The maximum percentage error in the detection of the dissipated heat will be

A particle of charge \(q\) and mass \(m\) is projected from origin with an initial velocity \(\vec{v} = \left(\dfrac{v_0}{\sqrt{2}}\hat{x} + \dfrac{v_0}{\sqrt{2}}\hat{y}\right)\). There exists a uniform magnetic field \(\vec{B} = B_0 \hat{z}\) and a space varying electric field \(\vec{E} = E_0 e^{-\lambda x}\hat{x}\) within the region \(0 \leq x \leq L\). After travelling a distance such that \(x\)-coordinate has changed from \(x=0\) to \(x=L\), the change in the kinetic energy is _______.

A plane electromagnetic wave in a non-magnetic dielectric medium is given by \(\vec E\, = \,{\vec E_0}\,(4 \times {10^{ - 7}}\,x - 50t)\) with distance being in meter and time in seconds. The dielectric constant of the medium is

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through \(O\) (the centre of mass) and \(O ^{\prime}(\) corner point \()\) is 

Consider two ideal diatomic gases \(\mathrm{A}\) and \(\mathrm{B}\) at some temperature \(T\). Molecules of the gas \(A\) are rigid, and have a mass \(m\). Molecules of the gas \(\mathrm{B}\) have an additional vibrational mode, and have a mass \(\frac{\mathrm{m}}{4} .\) The ratio of the specific heats \((\mathrm{C}_{\mathrm{v}}^{\mathrm{A}}\) and \(\mathrm{C}_{\mathrm{v}}^{\mathrm{B}})\) of gas \(\mathrm{A}\) and \(\mathrm{B}\), respectively is

The de Broglie wavelength of a molecule in a gas at room temperature \((300\,K )\) is \(\lambda_1\). If the temperature of the gas is increased to \(600\,K\), then the de Broglie wavelength of the same gas molecule becomes \(..............\).

A person travels \(x\) distance with velocity \(v_1\) and then \(x\) distance with velocity \(v_2\) in the same direction. The average velocity of the person is \(v\), then the relation between \(v , v _1\) and \(v _2\) will be :

1. A wire of resistance \( R \) and length \( L \) is cut into 5 equal parts. If these parts are joined in parallel, then the resultant resistance will be:

The number of electrons flowing per second in the filament of a \(110 \mathrm{~W}\) bulb operating at \(220 \mathrm{~V}\) is _______. (Given \(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\) )

A particle is projected at an angle of \(30^{\circ}\) from horizontal at a speed of \(60 \mathrm{~m} / \mathrm{s}\). The height traversed by the particle in the first second is \(\mathrm{h}_0\) and height traversed in the last second, before it reaches the maximum height, is \(h_1\). The ratio \(h_0: h_1\) is _________
[Take, \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) ]

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of \(\theta ,\) where \(\theta \) is the angle by which it has rotated, is given as \(k\theta ^2.\) If its moment of inertia is \(I\) then the angular acceleration of the disc is

An \(n.p.n\) transistor with current gain \(\beta=100\) in common emitter configuration is shown in figure. The output voltage of the amplifier will be\(.....V\)

Given below are two statements: Statement \(I :\) \(PN\) junction diodes can be used to function as transistor, simply by connecting two diodes, back to back, which acts as the base terminal. Statement \(II :\) In the study of transistor, the amplification factor \(\beta\) indicates ratio of the collector current to the base current. In the light of the above statements, choose the correct answer from the options given below :