In a radioactive decay chain, the initial nucleus is \({}_{90}^{232}Th\).  At the end there are \(6\,\,\alpha -\) particles and \(4\,\,\beta -\) particles with are emitted. If the end nucleus is \({}_Z^AX\,,\,A\) and \(Z\) are given by

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

A fringe width of \(\,6 mm\) was produced for two slits separated by \(1\, mm\) apart. The screen is placed \(10\, m\) away. The wavelength of light used is \('x'\, nm.\) The value of \('x'\) to the nearest integer is

Figure shows a rod \({AB}\), which is bent in a \(120^{\circ}\) circular arc of radius \(R\). A charge \((-Q)\) is uniformly distributed over rod \({AB}\). What is the electric field \(\overrightarrow{{E}}\) at the centre of curvature \({O}\) ?

The correct match between the entries in column \(I\) and column \(II\) are              \(I\)                         \((II)\) Radiation                     Wavelength \((a)\) Microwave          \((i)\) \(100 m\) \((b)\) Gamma rays      \((ii)\) \(10^{-15} m\) \((c)\) \(A.M.\) radio waves        \((iii)\) \(10^{-10} m\) \((d)\) \(X-\)rays             \((iv)\) \(10^{-3} m\)

An \(NPN\) transistor is used in common emitter configuration as an amplifier with \(1\,k\Omega \) load resistance. Signal voltage of \(10\,mV\) is applied across the base emitter. This produces a \(3\,mA\) change in the collector current and \(15\,\mu A\) change in the base current of the amplifier. The input resistance and voltage gain are

Two capacitors having capacitance \(C _{1}\) and \(C _{2}\) respectively are connected as shown in figure. Initially, capacitor \(C _{1}\) is charged to a potential difference \(V\) volt by a battery. The battery is then removed and the charged capacitor \(C_{1}\) is now connected to uncharged capacitor \(C _{2}\) by closing the switch \(S\). The amount of charge on the capacitor \(C _{2}\), after equilibrium is

If force \(({F})\), length \(({L})\) and time \(({T})\) are taken as the fundamental quantities. Then what will be the dimension of density

For the circuit shown, the value of current at time \({t}=3.2\, {s}\) will be ...... \({A}\). [Voltage distribution \(V(t)\) is shown by Fig. \((1)\) and the circuit is shown in Fig. \((2)\)]

A thin prism \(\mathrm{P}_1\) with angle \(4^{\circ}\) made of glass having refractive index 1.54 , is combined with another thin prism \(\mathrm{P}_2\) made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism \(P_2\) in degrees is _______.