Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by \({E}=20 \cos \left(2 \times 10^{10} {t}-200 {x}\right) \,{V} / {m} .\) The dielectric constant of the medium is equal to : (Take \(\mu_{{r}}=1\) )

The de Broglie wavelength of an oxygen molecule at \(27^{\circ} C\) is \(x \times 10^{-12} m\). The value of \(x\) is (take Planck's constant \(=6.63 \times 10^{-34} J . s\), Boltzmann constant \(=1.38 \times 10^{-23} J / K\), mass of oxygen. Molecule \(\left.=5.31 \times 10^{-26} kg\right)\).

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is \(5 / x\). The value of \(x\) is _________ .

Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm . When released from rest the heavier mass is observed to fall 81 cm in 9 s . The rotational inertia of the pulley is _________ \(kg \cdot m ^2\).\(\left( g =9.8 m / s ^2\right)\)

A rigid massless road of length \(3l\) has tow masses attached at each end as shown in the figure. The rod is pivoted at point \(P\) on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be

A series \(LR\) circuit is connected to an ac source of frequency \(\omega \) and the inductive reactance is equal to \(2R\). A capacitance of capacitive reactance equal to \(R\) is added in series with \(L\) and \(R\). The ratio of the new power factor to the old one is

Match the List-I with List-II

	List-I		List-II
A	Radio-wave	I	is produced by Magnetron value
B	Micro-wave	II	Due to change in the vibrational modes of atoms
C	Infrared-wave	II	Due to inner shell electrons moving from higher energy level to lower energy level
D	X-ray	IV	Due to rapid acceleration of electrons

Choose the correct answer from the options given below:

A stone tide to a string of length \(L\) is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed \(u\). The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is \(\sqrt{ x \left( u ^{2}- gL \right)}\). The value of \(x\) is .............

A system consists of two identical spheres each of mass \(1.5\, {kg}\) and radius \(50\, {cm}\) at the end of light rod. The distance between the centres of the two spheres is \(5\, {m}\). What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint ? (in \({kgm}^{2}\))

Let \(B_1\) be the magnitude of magnetic field at center of a circular coil of radius \(R\) carrying current \(I\). Let \(B_2\) be the magnitude of magnetic field at an axial distance ' \(x\) ' from the center. For \(x: R=3: 4, \frac{B_2}{B_1}\) is :