An electron in the hydrogen atom initially in the fourth excited state makes a transition to \(\mathrm{n}^{\text {th }}\) energy state by emitting a photon of energy 2.86 eV. The integer value of \(n\) will be ____.

Identify the correct statements from the following descriptions of various properties of electromagnetic waves. \(A\). In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field. \(B.\) The energy in electromagnetic wave is divided equally between electric and magnetic fields. \(C.\) Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave. \(D.\) The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other. \(E.\) The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light. Choose the most appropriate answer from the options given below:

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A :\) The escape velocities of planet \(A\) and \(B\) are same. But \(A\) and \(B\) are of unequal mass. Reason \(R :\) The product of their mass and radius must be same, \(M _{1} R _{1}= M _{2} R _{2}\) In the light of the above statements, choose the most appropriate answer from the options given below

Consider an electromagnetic wave propagating in vacuum . Choose the correct statement

A uniform magnetic field of \(2 \times 10^{-3} \mathrm{~T}\) acts along positive \(\mathrm{Y}\)-direction. A rectangular loop of sides \(20\) \(\mathrm{cm}\) and \(10 \mathrm{~cm}\) with current of \(5 \mathrm{~A}\) is \(\mathrm{Y}-\mathrm{Z}\) plane. The current is in anticlockwise sense with reference to negative \(\mathrm{X}\) axis. Magnitude and direction of the torque is _______.

In normal adjustment, for a refracting telescope, the distance between objective and eye piece is \(30\,cm\). The focal length of the objective, when the angular magnification of the telescope is \(2\) , will be \(.....cm\) 

Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is \(\mathrm{v}_1\), and that in the other string having radius of cross section \(R / 2\) is \(v_2\). Then \(\frac{v_2}{v_1}=\) ________.

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, \(\sigma=10 mho / m\). The ratio of maximum conducting current density to maximum displacement current density is _________ .
\(\left[\right.\) Take \(\left.\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 Nm ^2 / C ^2\right]\)

A parallel plate capacitor of area \(60\, cm^2\) and separation \(3\, mm\) is charged initially to \(90\, \mu C\). If the medium between the plate gets slightly conducting and the plate loses the charge initially at the rate of \(2.5\times10^{-8}\, C/s\), then what is the magnetic field between the plates ?

A particle \((\mathrm{m}=1\; \mathrm{kg})\) slides down a frictionless track \((AOC)\) starting from rest at a point \(A\) (height \(2\; \mathrm{m}\) ). After reaching \(\mathrm{C}\), the particle continues to move freely in air as a projectile. When it reaching its highest point \(P\) (height \(1 \;\mathrm{m}\) ). the kinetic energy of the particle (in \(\mathrm{J}\) ) is : (Figure drawn is schematic and not to scale; take \(\left.g=10 \;\mathrm{ms}^{-2}\right)\)

A cell of emf \(90\,V\) is connected across series combination of two resistors each of \(100\,\Omega\) resistance. A voltmeter of resistance \(400\,\Omega\) is used to measure the potential difference across each resistor. The reading of the voltmeter will be \(.........\,V\)

On a linear temperature scale \(Y\), water freezes at \(- 160^o\, Y\) and boils at \(- 50^o\, Y\). On this \(Y\) scale , a temperature of \(340\, K\) would be read as........ \(^oY\)  ( water freezes at \(273\, K\) and boils at \(373\, K\))

If \(A\, = \,\left[ {\begin{array}{*{20}{c}}
0&{ - 1}\\
1&0
\end{array}} \right],\) then which one of the following statements is not correct?