A solenoid of \(1200\) turns is wound uniformly in a single layer on a glass tube \(2\,m\) long and \(0.2\,m\) in diameter. The magnetic intensity at the center of the solenoid when a current of \(2\,A\) flows through it is:

Given below are two statements: Statement \(I :\) \(PN\) junction diodes can be used to function as transistor, simply by connecting two diodes, back to back, which acts as the base terminal. Statement \(II :\) In the study of transistor, the amplification factor \(\beta\) indicates ratio of the collector current to the base current. In the light of the above statements, choose the correct answer from the options given below :

A particle moves in a straight line so that its displacement \(x\) at any time \(t\) is given by \(x^2=1+t^2\). Its acceleration at any time \(\mathrm{t}\) is \(\mathrm{x}^{-\mathrm{n}}\) where \(\mathrm{n}=\) _______.

Proton \((P)\) and electron \((e)\) will have same deBroglie wavelength when the ratio of their momentum is (assume, \(m _{ p }=1849\,m _{ e }\))

Two long parallel wires \(X\) and \(Y\), separated by a distance of 6 cm , carry currents of 5A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is \(x \times 10^{-5} \mathrm{~T}\). The value of \(x\) is__________ . Take permeability of free space as \(\mu_0=4 \pi \times 10^{-7} \mathrm{SI}\) units.

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is \(4 \mathrm{~m}\), then the time period of small oscillations will be _______ \(s\). [take \(\mathrm{g}=\pi^2 \mathrm{~ms}^{-2}\)]

A sample of an ideal gas is taken through the cyclic process \(ABCA\) as shown in figure. It absorbs, \(40\,J\) of heat during the part \(A B\), no heat during \(BC\) and rejects \(60\,J\) of heat during \(CA\). \(A\) work \(50\,J\) is done on the gas during the part \(BC\). The internal energy of the gas at \(A\) is \(1560\,J\). The work done by the gas during the part \(CA\) is.............\(J\)

A uniform sphere of weight \(W\) and radius \(5\, cm\) is being held by a string as shown in the figure. The tension in the string will be

Electron beam used in an electron microscope, when accelerated by a voltage of \(20\,kV\). has a de-Broglie wavelength of \(\lambda_0\). If the voltage is increased to \(40\,kV\). then the de-Broglie wavelength associated with the electron beam would be:

Three masses \(m_1 = 4\) kg, \(m_2 = 4\) kg and \(m_3 = 6\) kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of \(T_1/T_2\) is _____.
(take \(g = 10\) m/s\(^2\))

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of \(\lambda\). An alpha particle having certain kinetic energy has the same de-Brogle wavelength \(\lambda\). The ratio of kinetic energy of proton and that of alpha particle is: