A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains:

A particle is moving in a straight line such that its velocity is increasing at \(5\,ms ^{-1}\) per meter. The acceleration of the particle is \(ms ^{-2}\) at a point where its velocity is \(20\,ms ^{-1}\).

The angular width of the central maximum in a single slit diffraction pattern is \(60^o \) . The width of the slit is \(1\ \mu m\). The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at  distance \(50\ cm\) from the slits. If the observed fringe width is \(1\ cm\), what is slit separation distance?.........\(\mu m\)
(i.e. distance between the centres of each slit. )

A body is performing simple harmonic with an amplitude of \(10 \,cm\). The velocity of the body was tripled by air Jet when it is at \(5 \,cm\) from its mean position. The new amplitude of vibration is \(\sqrt{ x } \,cm\). The value of \(x\) is________

A \(750\, Hz,\) \(20\) \(V\) (rms ) source is connected to a resistance of \(100\, \Omega\) an inductance of \(0.1803\, H\) and a capacitance of \(10\mu ,\) \(F\) all in series. The time in which the resistance (heat capacity \(2 J /{ }^{\circ} C\) ) will get heated by \(10^{\circ} C\). (assume no \(105 s\) of heat to the surroundings) is close to\(.....s\)

A tennis ball (treated as hollow spherical shell) starting from \(O\) rolls down a hill. At point \(A\) the ball becomes air borne leaving at an angle of \(30^o\) with the horizontal. The ball strikes the ground at \(B\). What is the value of the distance \(AB\) ? (Moment of inertia of a spherical shell of mass \(m\) and radius \(R\) about its diameter .......... \(m\). \(= \frac {2}{3}\,mR^2\))

A block of ice of mass \(120\,g\) at temperature \(0^{\circ} C\) is put in \(300\,gm\) of water at \(25^{\circ} C\). The \(xg\) of ice melts as the temperature of the water reaches \(0^{\circ} C\). The value of \(x\) is [Use: Specific heat capacity of water \(=4200\) \(J\,kg ^{-1} K ^{-1}\), Latent heat of ice \(\left.=3.5 \times 10^{5} J\,kg ^{-1}\right]\)

In a physical balance working on the principle of moments, when \(5\, mg\) weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

The half-life of \({ }^{198} {Au}\) is \(3 \,days.\) If atomic weight of \({ }^{198} {Au}\) is \(198\, {g} / {mol}\) then the activity of \(2 \,{mg}\) of \({ }^{198} {Au}\) is ..... \(\times 10^{12}\,disintegration/second\)