Two forces \(P\) and \(Q\), of magnitude \(2F\) and \(3F\), respectively, are at an angle \(\theta \) with each other. If the force \(Q\) is doubled, then their resultant also gets doubled. Then, the angle \(\theta \) is ....... \(^o\)

The fractional change in the magnetic field intensity at a distance \('r'\) from centre on the axis of current carrying coil of radius \('a'\) to the magnetic field intensity at the centre of the same coil is : (Take \(r << a )\)

de-Broglie wavelength of an electron accelerated by a voltage of \(50\,\,V\) is close to ............. \(\mathop {\rm{A}}\limits^o \)  \((\left| e \right| = 1.6 \times {10^{ - 19}}\,\,C,\,\,{m_e} = 9.1 \times {10^{ - 31}}\,kg,\,\,h = 6.6 \times {10^{ - 34}}\,\,Js)\)

The recoil speed of a hydrogen atom after it emits a photon in going from \(n =5\) state to \(n =1\) state will be ..... \(m/s\)

A cone of base radius \(R\) and height \(h\) is located in a uniform electric field \(\vec E\) parallel to its base. The electric flux entering the cone is

An electron of a hydrogen like atom, having \(Z=4\), jumps from \(4^{\text {th }}\) energy state to \(2^{\text {nd }}\) energy state, The energy released in this process, will be \(.........eV\) \((\) Given \(Rch =13.6\,eV )\) Where \(R =\) Rydberg constant \(c=\) Speed of light in vacuum \(h =\) Planck's constant

What equal length of an iron wire and a copper-nickel alloy wire, each of \(2 \; {mm}\) diameter connected parallel to give an equivalent resistance of \(3 \Omega ?\) (Given resistivities of iron and copper-nickel alloy wire are \(12 \;\mu \Omega {cm}\) and \(51\; \mu \Omega {cm}\) respectively) (in \({m}\))

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant k=3 and permeability \(\mu=2\mu_{0}\), is
( \(\mu_0=\) permeability of vacuum)

\(A, B, C\) and \(D\) are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation \(AD = C\, ln\, (BD)\) holds true. Then which of the combination is not a meaningful quantity ?

A thin uniform bar of length \(L\) and mass \(8\,m\) lies on a smooth horizontal table. Two point masses \(m\) and \(2\,m\) moving in the same horizontal plane from opposite sides of the bar with speeds \(2v\) and \(v\) respectively. The masses stick to the bar after collision at a distance \(\frac{L}{3}\) and \(\frac{L}{6}\) respectively from the centre of the bar. If the bar starts rotating about its center of mass as a result of collision, the angular speed of the bar will be

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: If the average kinetic energy of \(H_2\) and \(O_2\) molecules, kept in two different sized containers are same, then their temperatures will be same.

Reason R: The r.m.s. speed of \(H_2\) and \(O_2\) molecules are same at same temperature.

Choose the correct answer from the options given below

The electric current in the circuit is given as \(i=i_{ o }(t / T)\). The r.m.s current for the period \(t=0\) to \(t=T\) is ___________

An infinite plane sheet of charge having uniform surface charge density \(+\sigma_5 \mathrm{C} / \mathrm{m}^2\) is placed on \(\mathrm{x}-\mathrm{y}\) plane. Another infinitely long line charge having uniform linear charge density \(+\lambda_e \mathrm{C} / \mathrm{m}\) is placed at \(z=4 \mathrm{~m}\) plane and parallel to \(y\)-axis. If the magnitude values \(\left|\sigma_s\right|=2\left|\lambda_{\mathrm{e}}\right|\) then at point \((0,0,2)\), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is \(\pi \sqrt{\mathrm{n}}: 1\). The value of \(n\) is _______.