In a hydrogen like ion, the energy difference between the \(2^{\text {nd }}\) excitation energy state and ground is 108.8 eV. The atomic number of the ion is

The graph shows how the magnification \(m\) produced by a thin lens varies with image distance \(v\). What is the focal length of the lens used?

In an electrical circuit, a battery is connected to pass \(20\, C\) of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at \(15\, V\). The work done by the battery is ........... \(J\).

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density \(d.\) The area of the base of both vessels is \(S\) but the height of liquid in one vessel is \(x_{1}\) and in the other, \(x_{2}\). When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is

The susceptibility of a paramagnetic material is \(99\) . The permeability of the material in \(Wb / A - m\) is : [Permeability of free space \(\left.\mu_{0}=4 \pi \times 10^{-7} Wb / A -m\right]\)

Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the \(n^{th}\) orbital will therefore be proportional to

A photon is emitted in transition from \(n =4\) to \(n =1\) level in hydrogen atom. The corresponding wavelength for this transition is \(.........\,nm\) \(\text { (given, } h =4 \times 10^{-15} eVs \text { ) : }\)

In a Young double slit experiment, the wavelength of incident light is \(6000\) Å, the separation between slits \(S_1\) and \(S_2\) is \(5\) cm and the distance between slits plane and screen is \(50\) cm, as shown in the figure below. If the resultant intensity at \(P\) is equal to the intensity due to individual slits, the path difference between interfering waves is __________ Å.

Two parallel, long wires are kept \(0.20\,m\) apart in vacuum, each carrying current of \(x\) in the same direction. If the force of attraction per meter of each wire is \(2 \times 10^{-6}\,N\), then the value of \(x\) is approximately

Which of the following expressions corresponds to simple harmonic motion along a straight line, where \(x\) is the displacement and \(a, b, c\) are positive constants?

A thin cylindrical rod of length \(10\,cm\) is placed horizontally on the principle axis of a concave mirror of focal length \(20\,cm\). The rod is placed in a such a way that mid point of the rod is at \(40\,cm\) from the pole of mirror. The length of the image formed by the mirror will be \(\frac{x}{3} cm\). The value of \(x\) is \(............\).

The current \((i)\) at time \(t =0\) and \(t =\infty\) respectively for the given circuit is

Given below are two statements Statement \(I:\) The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination. Statement \(II\) : The resistivity of the material is independent of temperature. In the light of the above statements, choose the correct answer from the options given below