Conductor wire ABCDE with each \(\operatorname{arm} 10 \mathrm{~cm}\) in length is placed in magnetic field of \(\frac{1}{\sqrt{2}}\) Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of \(10 \mathrm{~cm} / \mathrm{s}\), induced emf between points A and E is _____ mV.

Some distant star is to be observed by some telescope of diameter of objective lens \(a\), at an angular resolution of \(3.0\times 10^{-7}\) radian. If the wavelength of light from the star reaching the telescope is \(500\) nm, the minimum diameter of the objective lens of the telescope is ________ cm. (nearest integer)

In an open organ pipe \(v_3\) and \(v_6\) are \(3^{\text {rd }}\) and \(6^{\text {th }}\) harmonic frequencies, respectively.
If \(v_6-v_3=2200 \) Hz then length of the pipe is ______ mm.
(Take velocity of sound in air is 330 m/s.)

The half life period of radioactive element \({x}\) is same as the mean life time of another radioactive element \(y.\) Initially they have the same number of atoms. Then:

The transfer characteristic curve of a transistor, having input and output resistance \(100\,\Omega \) and \(100\,k\Omega \) respectively, is shown in the figure. The Voltage and Power gain, are respectively

A ray of light of intensity \(I\) is incident on a parallel glass slab at point \(A\) as shown in diagram. It undergoes partial reflection and refraction. At each reflection, \(25\%\) of incident energy is reflected. The rays \(AB\) and \(A'B'\) undergo interference. The ratio of \(I_{max}\) and \(I_{min}\) is

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool.
\(\left(\right.\)Take \(g=10 \mathrm{~m} / \mathrm{s}^2\), specific heat of water \(\left.=4200 \mathrm{~J} /(\mathrm{kg} \mathrm{K})\right)\)

A mixture of carbon dioxide and oxygen has volume \(8310\) cm\(^3\), temperature \(300\) K, pressure \(100\) kPa and mass \(13.2\) g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are _______.
(Assume both carbon dioxide and oxygen gases behave like ideal gases) \([R = 8.31\) J/mol.K\(]\)

In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative \(z\)-axis and magnetic field is along the positive \(x\)-axis. Then the direction of propagation of electromagnetic wave is

The energy released when \(\dfrac{7}{17.13}\) kg of \(^{7}_{3}\text{Li}\) is converted into \(^{4}_{2}\text{He}\) by proton bombardment is \(\alpha \times 10^{32}\) eV. The value of \(\alpha\) is _______. (Nearest integer) (Mass of \(^{7}_{3}\text{Li} = 7.0183\) u, mass of \(^{4}_{2}\text{He} = 4.004\) u, mass of proton \(= 1.008\) u and \(1\) u \(= 931\) MeV/c\(^2\) and Avogadro number \(= 6.0 \times 10^{23}\))

An \(\alpha\) particle and a carbon \(12\) atom has same kinetic energy \(K\). The ratio of their de-Broglie wavelength \(\left(\lambda_{a}: \lambda_{C 12}\right)\) is