Radius of a certain orbit of hydrogen atom is \(8.48\mathring A \). If energy of electron in this orbit is \(\mathrm{E} / \mathrm{x}\), then \(\mathrm{x}=\) _______. (Given \(a_0=0.529 \mathring A, E=\) energy of electron in ground state)

A uniform conducting wire of length is \(24 {a}\), and resistance \({R}\) is wound up as a current carrying coil in the shape of an equilateral triangle of side \('a'\) and then in the form of a square of side \('a'.\) The coil is connected to a voltage source \({V}_{0}\). The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is \(1: \sqrt{y}\) where \(y\) is ..... .

The electric field in a region is given \(\overrightarrow{ E }=\left(\frac{3}{5} E _{0} \hat{ i }+\frac{4}{5} E _{0} \hat{ j }\right) \frac{ N }{ C } .\) The ratio of flux of reported field through the rectangular surface of area \(0.2\, m ^{2}\) (parallel to \(y - z\) plane) to that of the surface of area \(0.3\, m ^{2}\) (parallel to \(x - z\) plane \()\) is \(a : b ,\) where \(a =\) ............. [Here \(\hat{ i }, \hat{ j }\) and \(\hat{ k }\) are unit vectors along \(x , y\) and \(z-\)axes respectively]

A point charge \(q_1=4 q_0\) is placed at origin. Another point charge \(q_2=-q_0\) is placed at \(x =12\,cm\). Charge of proton is \(q_0\). The proton is placed on \(x\)-axis so that the electrostatic force on the proton in zero. In this situation, the position of the proton from the origin is \(..........cm\).

A particle \(A\) of mass \(‘m’\) and charge \(‘q’\) is accelerated by a potential difference of \(50\, V\). Another particle \(B\) of mass \(‘4\, m’\) and charge \(‘q’\) is accelerated by a potential difference of \(2500\, V\). The ratio of de-Broglie wavelength \(\frac{{{\lambda _A}}}{{{\lambda _B}}}\) is close to

If \(a,\, b,\,c,\,d\) are inputs to a gate and \(x\) is its output, then, as per the following time graph, the gate is

A block moving horizontally on a smooth surface with a speed of \(40\, {m} / {s}\) splits into two parts with masses in the ratio of \(1: 2\). If the smaller part moves at \(60\, {m} / {s}\) in the same direction, then the fractional change in kinetic energy is :-

An oscillator of mass \(M\)  is at rest in its equilibrium position in a potential \(V\, = \,\frac{1}{2}\,k{(x - X)^2}.\) A particle of mass \(m\)  comes from right with speed \(u\)  and collides completely inelastically with \(M\) and sticks to it . This process repeats every time the oscillator crosses its equilibrium position .The amplitude of oscillations after \(13\)  collisions is: \((M = 10,\, m = 5,\, u = 1,\, k = 1 ).\) 

A uniform electric field of \(10\,N / C\) is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy \(0.5\,eV\). The length of each plate is \(10\,cm\). The angle \((\theta)\) of deviation of the path of electron as it comes out of the field is  \(.........\)(in degree).

A ball of radius r and density \(\rho\) dropped through a viscous liquid of density \(\sigma\) and viscosity \(\eta\) attains its terminal velocity at time t , given by \(t = A \rho^{ a } r ^{ b } \eta^{ c } \sigma^{ d }\), where A is a constant and a , b c and d are integers. The value of \(\frac{b+c}{a+d}\) is ___________.

In the given figure, the charge stored in \(6 \ \mu \mathrm{F}\) capacitor, when points \(A\) and \(B\) are joined by a connecting wire is _______ \(\mu \mathrm{C}\).