The heat generated in 1 minute between points A and B in the given circuit, when a battery of 9 V with internal resistance of \(1 \Omega\) is connected across these points is _________ J.

Which of the four resistances \(P, Q, R\) and \(S\) generate the greatest amount of heat when a current flows from \(A\) to \(B\) ?

Given below are two statements :
Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division.
Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions.
In the light of the above statements, choose the correct answer from the options given below.

The pressure \(( P )\) and temperature \(( T )\) relationship of an ideal gas obeys the equation \(PT ^2=\) constant. The volume expansion coefficient of the gas will be:

If the refractive index of the material of a prism is \(\cot \left(\frac{A}{2}\right)\), where \(A\) is the angle of prism then the angle of minimum deviation will be

Three concentric spherical metallic shells \(X , Y\) and \(Z\) of radius \(a , b\) and c respectively \([ a < b < c ]\) have surface charge densities \(\sigma,-\sigma\) and \(\sigma\), respectively. The shells \(X\) and \(Z\) are at same potential. If the radii of \(X\) and \(Y\) are \(2\,cm\) and \(3\,cm\), respectively.The radius of shell \(Z\) is \(......cm\).

The source of time varying magnetic field may be \((A)\) a permanent magnet \((B)\) an electric field changing linearly with time \((C)\) direct current \((D)\) a decelerating charge particle \((E)\) an antenna fed with a digital signal Choose the correct answer from the options given below:

An inclined plane making an angle of \(30^{\circ}\) with the horizontal is placed in a uniform horizontal electric field \(200 \, \frac{ N }{ C }\) as shown in the figure. A body of mass \(1\, kg\) and charge \(5\, mC\) is allowed to slide down from rest at a height of \(1\, m\). If the coefficient of friction is \(0.2,\) find the time (in \(s\) )taken by the body to reach the bottom. \(\left[ g =9.8 \,m / s ^{2}, \sin 30^{\circ}=\frac{1}{2}\right.\); \(\left.\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right]\)

In the given figure, the value of \(V_{0}\) will be \(.....V\).

An \(\alpha\) particle and a proton are accelerated from rest by a potential difference of \(200\, V\). After this, their de Broglie wavelengths are \(\lambda_{\alpha}\) and \(\lambda_{p}\) respectively. The ratio \(\frac{\lambda_{p}}{\lambda_{a}}\) is