A solenoid of length \(0.5 \mathrm{~m}\) has a radius of \(1 \mathrm{~cm}\) and is made up of ' \(m\) ' number of turns. It carries a current of \(5 \mathrm{~A}\). If the magnitude of the magnetic field inside the solenoid is \(6.28 \times 10^{-3} \mathrm{~T}\), then the value of \(m\) is _______.

A convex lens of refractive index \(1.5\) and focal length \(18 cm\) in air is immersed in water. The change in focal length of the lens will be \(...........cm\).\(\left(\right.\) Given refractive index of water \(\left.=\frac{4}{3}\right)\)

The current in a conductor is expressed as \(I=3 t^2+4 t^3\), where \(I\) is in Ampere and \(t\) is in second. The amount of electric charge that flows through a section of the conductor during \(t=1\) s to \(t=2 \mathrm{~s}\) is _______ \(\mathrm{C}\).

An infinite wire has a circular bend of radius a, and carrying a current I as shown in figure. The magnitude of magnetic field at the origin \(O\) of the arc is given by :

Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\). \(Assertion\) \((A)\) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun. \(Reason\) \((R)\): The moon takes less time to move around the earth than the time taken by the earth to move around the sun. In the light of the above statements, choose the most appropriate answer from the options given below:

Consider two uniform discs of the same thickness and different radii \(R _{1}= R\) and \(R _{2}=\alpha R\) made of the same material. If the ratio of their moments of inertia \(I_{1}\) and \(I_{2}\), respectively, about their axes is \(I _{1}: I _{2}=1: 16\) then the value of \(\alpha\) is

Hydrogen \((_1H^1),\) Deuterium \((_1H^2)\),singly ionised Helium \((_2He^4)^+\) and doubly ionised lithium \({\left( {{}_3^6Li} \right)^{ + + }}\), all have one electron around the nucleus. Consider an electron transition from \(n = 2\) to \(n = 1\). If the wavelengths of emitted radiation are \(λ_1,λ_2,λ_3\) and \(λ_4\) respectively then approximately which one of the following is correct?

Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength \(\lambda\). The value of principal quantum number ' \(n\) ' of the excited state will be: (\(R\): Rydberg constant)

A voltage regulating circuit consisting of Zener diode, having break-down voltage of 10 V and maximum power dissipation of 0.4 W , is operated at 15 V . The approximate value of protective resistance in this circuit is _________ \(\Omega\).

Least count of a vernier caliper is \(\frac{1}{20 \mathrm{~N}} \mathrm{~cm}\). The value of one division on the main scale is \(1 \mathrm{~mm}\). Then the number of divisions of main scale that coincide with \(\mathrm{N}\) divisions of vernier scale is _______.

Light source having wavelength \(331\) nm is used to generate photo-electrons whose stopping potential is \(0.2\) V. The work function of the used metal in the experiment is \(\alpha \times 10^{-19}\) J. The value of \(\alpha\) is _____.
(\(h = 6.62 \times 10^{-34}\) J s, \(e = 1.6 \times 10^{-19}\) C and \(c = 3 \times 10^8\) m/s)

\(500\, g\) of water and \(100\, g\) of ice at \(0\,^oC\) are in a calorimeter whose water equivalent is \(40\, g\). \(10\, g\) of steam at \(100\,^oC\) is added to it. Then water in the calorimeter is ....... \(g\) (Latent heat of ice \(\,= 80\, cal/g\), Latent heat of steam \(\,= 540\, cal/ g\))

A plane electromagnetic wave of frequency \(50\, MHz\) travels in free space along the positive \(x-\) direction. At a particular point in space and time, \(\vec E = 6.3\,\hat j\,V/m\) . The corresponding magnetic field \(\vec B\), at that point will be