A travelling microscope has \(20\) divisions per \(cm\) on the main scale while its Vernier scale has total \(50\) divisions and \(25\) Vernier scale divisions are equal to \(24\) main scale divisions, what is the least count of the travelling microscope \(..........\,cm\)

The diameter of a wire measured by a screw gauge of least count \(0.001\) cm is \(0.08\) cm. The length measured by a scale of least count \(0.1\) cm is \(150\) cm. When a weight of \(100\) N is applied to the wire, the extension in length is \(0.5\) cm, measured by a micrometer of least count \(0.001\) cm. The error in the measured Young's modulus is \(\alpha \times 10^9\) N/m\(^2\). The value of \(\alpha\) is _______.
(Ignore the contribution of the load to Young's modulus error calculation)

Two projectile thrown at \(30^{\circ}\) and \(45^{\circ}\) with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

Two coherent monochromatic light beams of intensities \(I\) and \(4I\) are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is \(x\)I. The value of \(x\) is _______.

An effective power of a combination of \(5\) identical convex lenses which are kept in contact along the principal axis is \(25 \mathrm{D}\). Focal length of each of the convex lens is _______.

An object is kept at rest at a distance of 3 R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is :
(Assume \(\mathrm{M}=\) mass of earth, \(\mathrm{G}=\) Universal gravitational constant)

The area of cross-section of a railway track is \(0.01\, {m}^{2}\). The temperature variation is \(10^{\circ} {C}\). Coefficient of linear expansion of material of track is \(10^{-5} /{ }^{\circ} {C}\). The energy stored per meter in the track is ...... \({J} / {m} .\) (Young's modulus of material of track is \(10^{11} \,{Nm}^{-2}\) ))

From \(18\) m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is _____ m.
(Take \(g = 10\) m/s\(^2\) and neglect the air resistance)

A bar magnet of length \(14 \,cm\) is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at a distance of \(18\, cm\) from the center of the magnet. If \(B _{ H }=0.4 \,G ,\) the magnetic moment of the magnet is \(\left(1\, G =10^{-4} T \right)\)

When Uranium is bombarded with neutrons, it undergoes fission. The fission reaction can be written as  \({}_{92}{U^{235}} + {}_0{n^1} \to {}_{56}B{a^{141}} + {}_{36}K{r^{92}} + 3x + Q{\rm{( energy)}}\) where three particles named \(x\) are produced and energy \(Q\) is released. What is the name of the particle \(x\) ?

Match List \(I\) (Wavelength range of electromagnetic spectrum) with List \(II\) (Method of production of these waves) and select the correct option from the options given below the lists

List \(I\)	List \(II\)
\((1)\) \(700\, nm\) to \(1\,mm\)	\((i)\) Vibration of atoms and molecules
\((2)\) \(1\,nm\) to \(400\, nm\)	\((ii)\) Inner shell electrons in atoms moving from one energy level to a lower level
\((3)\) \( < 10^{-3}\,nm\)	\((iii)\) Radioactive decay of the nucleus
\((4)\) \(1\,mm\) to \(0.1\,m\)	\((iv)\) Magnetron valve

Young's moduli of the material of wires \(A\) and \(B\) are in the ratio of \(1: 4\), while its area of cross sections are in the ratio of \(1: 3\). If the same amount of load is applied to both the wires, the amount of elongation produced in the wires \(A\) and \(B\) will be in the ratio of [Assume length of wires \(A\) and \(B\) are same]