The energy required to remove the electron from a singly ionized Helium atom is \(2.2\, times\) the energy required to remove an electron from Helium atom . The total energy required to ionize the Helium atom completely is......\(eV\)

A piece of wood of mass \(0.03\, kg\) is dropped from the top of a \(100\, m\) height building. At the same time, a bullet of mass \(0.02\, kg\) is fired vertically upward, with a velocity \(100\, ms^{- 1}\), from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is ........ \(m\). \((g = 10\, ms^{-2})\)

The disintegration rate of a certain radioactive sample at any instant is \(4250\) disintegrations per minute.\(10\) minutes later, the rate becomes \(2250\) disintegrations per minute. The approximate decay cons \(.........\min^{-1}\)

Mass per unit area of a circular disc of radius \(\mathrm{a}\) depends on the distance \(\mathrm{r}\) from its centre as \(\sigma(\mathrm{r})=\mathrm{A}+\mathrm{Br} .\) The moment of inertia of the disc about the the axis, perpendicular to the plane and passing through its centre is

A moving coil galvanometer has a coil with \(175\, turns\) and area \(1\, cm^2\) It uses a torsion band of torsion constant \(10^{-6}\, N\, -m/rad\). The coil is placed in a magnetic field \(B\) parallel to its plane. The coil deflects by \(10\) for a current of \(1\, mA\). The value of \(B\) (in Tesla) is approximately

An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes \(32\) times of its initial value. If the final pressure of gas is \(128\) atmosphers, the value of \(\gamma\) the gas is

A car accelerates from rest to \(u\,m / s\). The energy spent in this process is \(E\,J\). The energy required to accelerate the car from \(u\,m / s\) to \(2u\,m / s\) is \(nE\,J\). The value of \(n\) is ..............

Two wires \(A\) and \(B\) made of different materials of length 6.0 cm and 5.4 cm, respectively and area of cross sections \(3.0 \times 10^{-5} m^2\) and \(4.5 \times 10^{-5} m^2\), respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of \(A\) to that of \(B\) is \(x : 3\). The value of x is ___________.

A circuit connected to an \(ac\) source of \(emf\) \(e = e_0\, sin\, (1000t)\) with \(t\) in seconds, gives a phase difference of \(\frac{\pi }{4}\) between the \(emf\) \(e\) and current \(i\). Which of the following circuits will exhibit this?

A tube of length \(50\,cm\) is filled completely with an incompressible liquid of mass \(250\,g\) and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity \(x \sqrt{ F }\) rad \(s ^{-1}\). If \(F\) be the force exerted by the liquid at the other end then the value of \(x\) will be\(....\)

If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is _________ m.
(Atomic number of gold \(=79\) and \(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9\)in SI units)

Two radioactive materials \(A\) and \(B\) have decay constants \(25 \lambda\) and \(16 \lambda\) respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of \(B\) to that of \(A\) will be "\(e\)" after a time \(\frac{1}{a \lambda}\). The value of \(a\) is \(......\)