A circular conducting coil of radius \(1\, {m}\) is being heated by the change of magnetic field \(\vec {B}\) passing perpendicular to the plane in which the coil is laid. The resistance of the coil is \(2\, \mu\, \Omega\). The magnetic field is slowly switched off such that its magnitude changes in time as \(B=\frac{4}{\pi} \times 10^{-3}\, {T}\left(1-\frac{{t}}{100}\right)\) The energy dissipated by the coil before the magnetic field is switched off completely is \(E=.....\,{m} J.\)

A square shaped wire with resistance of each side \(3\, \Omega\) is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in unit of \(\Omega\) will be ......

Statement \(I:\) If three forces \(\vec{F}_{1}, \vec{F}_{2}\) and \(\vec{F}_{3}\) are represented by three sides of a triangle and \(\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}\), then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement \(II:\) A triangle made up of three forces \(\overrightarrow{{F}}_{1}, \overrightarrow{{F}}_{2}\) and \(\overrightarrow{{F}}_{3}\) as its sides taken in the same order, satisfy the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below:

Two capacitors \(C_1\) and \(C_2\) are charged to \(120\ V\) and \(200\ V\) respectively. It is found that connecting them together the potential on each one can be made zero. Then

The \(Q\)-value of a nuclear reaction and kinetic energy of the projectile particle, \(K _{ p }\) are related as

A particle is released from height \(S\) above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.

The solid cylinder of length \(80\, {cm}\) and mass \({M}\) has a radius of \(20\, {cm}\). Calculate the density of the material used if the moment of inertia of the cylinder about an axis \(CD\) parallel to \({AB}\) as shown in figure is \(2.7\, {kg} {m}^{2}\)

This question has Statement \(-1\) and Statement \(-2\) Of the four choices given after the Statements, choose the one that best describes the two Statements Statement \(1\) : No work is required to be done to move a test charge between any two points on an equipotential surface Statement \(2\) : Electric lines of force at the equipotential surfaces are mutually perpendicular to each other

Two newspaper \(A\) and \(B\) are published in a city. It is known that \(25\%\) of the city populations reads \(A\) and \(20\%\) reads \(B\) while \(8\%\) reads both \(A\) and \(B\). Further, \(30\%\) of those who read \(A\) but not \(B\) look into advertisements and \(40\%\) of those who read \(B\) but not \(A\) also look into advertisements, while \(50\%\) of those who read both \(A\)and \(B\) look into advertisements. Then the percentage of the population who look into advertisement is

If the coefficients of \(x^2\) and \(x^3\) are both zero, in the expansion of the expression \((1 + ax + bx^2) (1 -3x)^{t5}\) in powers of \(x\), then the ordered pair \((a, b)\) is equal to

Let \(\theta_1\) be the angle between two lines \(2x + 3y + c_1\, = 0\) and \(-x+5y + c_2\, = 0\) and \(\theta_2\) be the angle between two lines \(2x+ 3y + c_1\, = 0\) and \(-x+ 5y + c_3\, = 0\), where \(c_1, c_2, c_3\) are any real numbers  Statement \(-1\) : If \(c_2\) and \(c_3\) are proportional, then \(\theta_1\, = \theta_2\) Statement \(-2\) : \(\theta_1\, = \theta_2\) for all \(c_2\) and \(c_3\)

If time \((t)\), velocity \((u)\), and angular momentum \((I)\) are taken as the fundamental units. Then the dimension of mass \(({m})\) in terms of \({t}, {u}\) and \({I}\) is

Equivalent resistance between the adjacent corners of a regular \(n\)-sided polygon of uniform wire of resistance \(R\) would be: