A electron of hydrogen atom on an excited state is having energy \(E_n=-0.85 \mathrm{eV}\). The maximum number of allowed transitions to lower energy level is _______.

Average force exerted on a non-reflecting surface at normal incidence is \(2.4 \times 10^{-4} \mathrm{~N}\). If \(360 \mathrm{~W} / \mathrm{cm}^2\) is the light energy flux during span of \(1\) hour \(30\) minutes. Then the area of the surface is _______.

A tuning fork of frequency \(480\, Hz\) is used in an experiment for measuring speed of sound \((\nu )\) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, \({\ell _1} = 30\,cm\) and \({\ell _2} = 70\,cm\). Then \(\nu\) is equal to ..... \(ms^{-1}\)

Two identical small bar magnets each of dipole moment \(3\sqrt{5}\) J/T are placed at a center to center separation of \(10\) cm, with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point P midway between the magnets is \(\alpha \times 10^{-3}\) T. The value of \(\alpha\) is ______.
(\(\mu_0=4\pi \times 10^{-7}\) Tm/A)

A cube is placed inside an electric field, \(\overrightarrow{{E}}=150\, {y}^{2}\, \hat{{j}}\). The side of the cube is \(0.5 \,{m}\) and is placed in the field as shown in the given figure. The charge inside the cube is \(.....\times 10^{-11} {C}\)

Identify the correct statements :
A. Electrostatic field lines form closed loops.
B. The electric field lines point radially outward when charge is greater than zero.
C. The Gauss-Law is valid only for inverse-square force.
D. The workdone in moving a charged particle in a static electric field around a closed path is zero.
E. The motion of a particle under Coulomb's force must take place in a plane.
Choose the correct answer from the options given below :

A sonometer wire oflength \(1.5\ m\) is made of steel. The tension in it produces an elastic strain of \(1 \%\). What is the fundamental frequency of steel if density and elasticity of steel are \(7.7 \times 10^3 \) \(kg/m^3\) and \(2.2 \times 10^{11}\) \(N/m^2\) respectively?

A bob of mass ' \(m\) ' is suspended by a light string of length ' \(L\) '. It is imparted a minimum horizontal velocity at the lowest point \(A\) such that it just completes half circle reaching the top most position B. The ratio of kinetic energies \(\frac{(\text { K.E. })_A}{(\text { K.E. })_B}\) is _______.

An expression for a dimensionless quantity \(P\) is given by \(P=\frac{\alpha}{\beta} \log _{e}\left(\frac{ kt }{\beta x }\right)\); where \(\alpha\) and \(\beta\) are constants, \(x\) is distance ; \(k\) is Boltzmann constant and \(t\) is the temperature. Then the dimensions of \(\alpha\) will be

In a Young's double slit experiment, \(16\) fringes are observed in a certain segment of the screen when light of wavelength \(700 \,nm\) is used. If the wavelength of light is changed to \(400 \,nm\), the number of fringes observed in the same segment of the screen would be........

The equation of motion of a particle is given by \(x = a \sin\left(50t + \dfrac{\pi}{3}\right)\) cm. The particle will come to rest at time \(t_1\) and it will have zero acceleration at time \(t_2\). The \(t_1\) and \(t_2\) respectively are _______.