A square loop of side \(10 \mathrm{~cm}\) and resistance \(0.7\  \Omega\) is placed vertically in east-west plane. A uniform magnetic field of \(0.20 \mathrm{~T}\) is set up across the plane in north east direction. The magnetic field is decreased to zero in \(1 \mathrm{~s}\) at a steady rate. Then, magnitude of induced emf is \(\sqrt{\mathrm{x}} \times 10^{-3} \mathrm{~V}\). The value of \(x\) is _______.

A \(1\,m\) long copper wire carries a current of \(1\,A\). If the cross section of the wire is \(2.0\,mm ^{2}\) and the resistivity of copper is \(1.7 \times 10^{-8}\,\Omega\,m\). the force experienced by moving electron in the wire is \(\times 10^{-23}\,N\). (charge on electron \(=1.6 \times 10^{-19}\,C\) )

A uniform solid cylindrical roller of mass \('m'\) is being pulled on a horizontal surface with force \(F\) parallel to the surface and applied at its centre. If the acceleration of the cylinder is \('a'\) and it is rolling without slipping then the value of \('F'\) is 

A teacher in his physics laboratory allotted an experiment to determine the resistance \((G)\) of a galvanometer. Students took the observations for \(\frac{1}{3}\) deflection in the galvanometer. Which of the below is true for measuring value of \(G\) \(?\)

In a radioactive material, fraction of active material remaining after time \(t\) is \(\frac{9}{16}\) The fraction that was remaining after \(\frac{t}{2}\) is 

Initial pressure and volume of a monoatomic ideal gas are \(P\) and \(V\). The change in internal energy of this gas in adiabatic expansion to volume \(V_{final}=27V\) is ________ J.

A particle is moving in a circle of radius \(r\) under the action of a force \(F\, = \alpha r^2\) which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy \(= 0\) for \(r\, = 0\))

If minimum possible work is done by a refrigerator in converting \(100\; grams\) of water at \(0^{\circ} C\) to ice, how much heat (in calories) is released to the surrounding at temperature \(27^{\circ} C\) (Latent heat of ice \(=80 Cal / gram\) ) to the nearest integer?

A piston of mass \(M\) is hung from a massless spring whose restoring force law goes as \(\mathrm{F}=-\mathrm{kx}^3\), where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' \(n\) ' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height \(\mathrm{L}_0\) to \(\mathrm{L}_1\), the total energy delivered by the filament is (Assume spring to be in its natural length before heating)

If some three consecutive in the binomial expansion of \({\left( {x + 1} \right)^n}\) in powers of \(x\) are in the ratio \(2 : 15 : 70\), then the average of these three coefficient is

A body of mass \(1000 \mathrm{~kg}\) is moving horizontally with a velocity \(6 \mathrm{~m} / \mathrm{s}\). If \(200 \mathrm{~kg}\) extra mass is added, the final velocity (in \(\mathrm{m} / \mathrm{s}\) ) is:

Let \(x , y , z > 1\) and \(A=\left[\begin{array}{lll}1 & \log _x y & \log _x z \\ \log _y x & 2 & \log _y z \\ \log _z x & \log _z y & 3\end{array}\right]\) .Then \(\left|\operatorname{adj}\left(\operatorname{adj} A^2\right)\right|\) is equal to

Let \(f : (-1, 1) \to R\) be a function defined by \(f\left( x \right) = \left\{ { - \left| x \right|, - \sqrt {1 - {x^2}} } \right\}\). if \(K\) be the set of all points at which \(f\) is not differentiable, then \(K\) has exactly