Two ions of masses \(4 \,{amu}\) and \(16\, amu\) have charges \(+2 {e}\) and \(+3 {e}\) respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :

A body travels \(102.5 \mathrm{~m}\) in \(\mathrm{n}^{\text {th }}\) second and \(115.0 \mathrm{~m}\) in \((n+2)^{\text {th }}\) second. The acceleration is what?

Four bulbs \(B_1 , B_2, B_3\) and \(B_4\) of \(100\, W\) each are connected to \(220\, V\) main as shown in the figure. The reading in an ideal ammeter will be ............... \(A\)

The correct relation between \(\gamma=\frac{ C _p}{ c _v}\) and temperature \(T\) is :

Let \(\vec A\, = \,(\hat i\, + \,\hat j)\,\)  and \(\vec B\, = \,(2\hat i\, - \,\hat j)\,.\)  The magnitude of a coplanar vector \(\vec C\) such that  \(\vec A\cdot \vec C\, = \,\vec B\cdot \vec C\, = \vec A\cdot \vec B\) is given by

A bead \(P\) sliding on a frictionless semi-circular string \((A C B)\) and it is at point \(S\) at \(t =0\) and at this instant the horizontal component of its velocity is \(v\). Another bead \(Q\) of the same mass as \(P\) is ejected from point \(A\) at \(t =0\) along the horizontal string \(A B\), with the speed \(v\), friction between the beads and the respective strings may be neglected in both cases. Let \(t_p\) and \(t_Q\) be the respective times taken by beads \(P\) and \(Q\) to reach the point \(B\), then the relation between \(t_p\) and \(t_Q\) is

The truth table for the followng logic circuit is ...... .

In a Young’s double slit experiment, the slits are placed \(0.320\,mm\) apart. Light of wavelength \(\lambda = 500\,nm\) is incident on the slits. The total number of bright fringes that are observed in the angular range \( - {30^o} \le \theta  \le {30^o}\) is

The current density in a cylindrical wire of radius \(r=4.0 \,mm\) is \(1.0 \times 10^{6} \,A / m ^{2}\). The current through the outer portion of the wire between radial distances \(r / 2\) and \(r\) is \(x \pi A\); where \(x\) is ..........

The threshold frequency of metal is \(f_0\). When the light of frequency \(2 f_0\) is incident on the metal plate, the maximum velocity of photoelectron is \(v_1\). When the frequency of incident radiation is increased to \(5 f _0\). the maximum velocity of photoelectrons emitted is \(v_2\). The ratio of \(v_1\) to \(v_2\) is:

The maximum velocity of the photoelectrons emitted from the surface is \(v\) when light of frequency \(n\) falls on a metal surface. If the incident frequency is increased to \(3n\) , the maximum velocity of the ejected photoelectrons will be 

In the following circuit, the switch \(S\)  is closed at \(t = 0.\)  The charge on the capacitor  \(C_1\)  as a function of time will be given by \(\left( {{C_{eq}}\, = {\kern 1pt} \,\frac{{{C_1}{C_2}}}{{{C_1} + {C_2}}}} \right).\)

An ideal transformer with purely resistive load operates at \(12\,kV\) on the primary side. It supplies electrical energy to a number of nearby houses at \(120\,V\). The average rate of energy consumption in the houses served by the transformer is \(60\,kW\). The value of resistive load (Rs) required in the secondary circuit will be \(.........\,m \Omega\).