A \(10\, \Omega, 20 \; mH\) coil carrying constant current is connected to a battery of \(20 \; V\) through a switch is opened current becomes zero in \(100 \; \mu s\). The average emf induced in the coil is \(\dots \; V\).

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 wire of resistance \(R\) is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points \(A\) and \(B\) is \(R / n\). The value of \(n\) is :

A transformer has an efficiency of \(80 \%\) and works at \(10 \mathrm{~V}\) and \(4 \mathrm{~kW}\). If the secondary voltage is \(240 \mathrm{~V}\), then the current in the secondary coil is _______.

A thermodynamic system is taken through cyclic process. The total work done in the process is \(.........\,J\)

A uniformly charged ring of radius \(3a\) and total charge \(q\) is placed in \(xy-\) plane centered at origin. A point charge \(q\) is moving towards the ring along the \(z-\) axis and has speed \(v\) at \(z = 4a\). The minimum value of \(v\) such that it crosses the origin is

The ratio of heat dissipated per second through the resistance \(5 \Omega\) and \(10 \Omega\) in the circuit given below is _______.

The total internal energy of two mole monoatomic ideal gas at temperature \(T=300\,K\) will be ...........\(J\). \(\text { (Given } R =8.31\,J / mol.K )\)

Let \(A,B\) and \(C\) be the vertices of a variable right angled triangle inscribed in the parabola \(y^2=16x\). Let the vertex \(B\) containing the right angle be \((4,8)\) and the locus of the centroid of \(\triangle ABC\) be a conic \(C_o\). Then three times the length of latus rectum of \(C_o\) is ______

Young's modulus is determined by the equation given by \(\mathrm{Y}=49000 \frac{\mathrm{m}}{\ell} \frac{\text { dyne }}{\mathrm{cm}^2}\) where \(\mathrm{M}\) is the mass and \(\ell\) is the extension of wre used in the experiment. Now error in Young modules \((\mathrm{Y})\) is estimated by taking data from \(M-\ell\) plot in graph paper. The smallest scale divisions are \(5 \mathrm{~g}\) and \(0.02\) \(\mathrm{cm}\) along load axis and extension axis respectively. If the value of \(M\) and \(\ell\) are \(500 \mathrm{~g}\) and \(2 \mathrm{~cm}\) respectively then percentage error of \(\mathrm{Y}\) is _______.

If \(\int {{x^5}\,{e^{ - {x^2}}}\,dx\, = \,g\,(x)\,{e^{ - {x^2}}} + \,c,} \) where \(c\) is a constant of integration, then \(g(-1)\) is equal to

If the shortest distance between the lines \(\frac{x+\sqrt{6}}{2}=\frac{y-\sqrt{6}}{3}=\frac{z-\sqrt{6}}{4}\) and \(\frac{x-\lambda}{3}=\frac{y-2 \sqrt{6}}{4}=\frac{z+2 \sqrt{6}}{5}\) is 6 , then sum of squares of all possible values(s) of \(\lambda\) is

The temperature of a gas having \(2.0 \times 10^{25}\) molecules per cubic meter at \(1.38 \mathrm{~atm}\) (Given, \(\mathrm{k}=\) \(\left.1.38 \times 10^{-23} \mathrm{JK}^{-1}\right)\) is _______.