If Rydberg's constant is \(R\), the longest wavelength of radiation in Paschen series will be \(\frac{\alpha}{7 R}\), where \(\alpha=\)____________

Critical angle of incidence for a pair of optical media is \(45^{\circ}\). The refractive indices of first and second media are in the ratio _______.

When a current of \(5\ mA\) is passed through a galvanometer having a coil of resistance \(15\ \Omega\), it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into to voltmeter of range \(0 - 10\ V\) is

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities \(d_1\) and \(d_2\) are filled in the tube. Each liquid subtends \(90^o\) angle at centre. Radius joining their interface makes an angle \(\alpha\) with vertical. Ratio \(\frac{{{d_1}}}{{{d_2}}}\) is

The position of the centre of mass of a uniform semi-circular wire of radius \('R'\) placed in \(x-y\) plane with its centre at the origin and the line joining its ends as \(x\)-axis is given by \(\left(0, \frac{x R}{\pi}\right)\). Then, the value of \(|x|\) is ...... .

The refractive index of a converging lens is \(1.4.\) What will be the focal length of this lens if it is placed in a medium of same refractive index ? (Assume the radii of curvature of the faces of lens are \(R _{1}\) and \(R _{2}\) respectively)

Given below are two statements: Statement\(-I :\) An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. Statement\(-II :\) Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed. In the light of the above statements, choose the correct answer from the options given below :

The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the \(5^{\text {th }}\) excited state of a hydrogen atom is _______.

When photons of wavelength \(\lambda _1\)  are incident on an isolated sphere, the corresponding stopping potential is found to be \(V.\)  When photons of wavelength \(\lambda _2\) are used, the corresponding stopping potential was thrice that of the above value . If light of wavelength \(\lambda _3\) is used then find the stopping potential for this case

At a given point of time the value of displacement of a simple harmonic oscillator is given as \(y = A \cos \left(30^{\circ}\right)\). If amplitude is \(40\,cm\) and kinetic energy at that time is \(200\, J\), the value of force constant is \(1.0 \times 10^{ x }\,Nm ^{-1}\). The value of \(x\) is ......