A boy standing on a moving truck throws a projectile such that he is able to catch it back after the truck has moved \(100 \mathrm{~m}\). If the truck is moving horizontally along a straight line with a constant speed \(30 \mathrm{~m} / \mathrm{s}\), at what speed (relative to the truck) must the projectile is thrown. (Assume, \(g=10 \mathrm{~m} / \mathrm{s}^2\) )

1. The focal lengths of the objective and the eyepiece of a compound microscope are \(2 \mathrm{~cm}\) and \(3 \mathrm{~cm}\) respectively and the distance between them is \(15 \mathrm{~cm}\). The final image formed by the eyepiece is at infinity. The distances of the object and the image produced by the object from the objective lens are respectively

The thickness of a uniform rectangular metal plate is 5 mm and the area of each surface is \(5 \mathrm{~cm}^2\). In steady state, the temperature difference between the two surfaces of the plate is \(14^{\circ} \mathrm{C}\). If the heat flowing through the plate in one second from one surface to the other surface is 42 J , then the thermal conductivity of the metal is

The dimension of \(\frac{E^2}{\mu_0}\) in mass \((M)\), length \((L)\) and time \((T)\) is ( \(E=\) electric field, \(\mu_0=\) permeability of free space)

If the reading in Fahrenheit scale is twice the reading in Celsius scale, then the reading in Fahrenheit scale is

The average energy of a neutron produced in the fission of \({ }_{92}^{235} \mathrm{U}\) is

 A sheet of steel at \(20^{\circ} \mathrm{C}\) has size as shown in figure below. If the co-efficient of linear expansion for steel is \(10^{-5 \circ} \mathrm{C}^{-1}\), then what is the change in the area at \(60^{\circ} \mathrm{C}\) ?

If \(200 \mathrm{MeV}\) of energy is released in the fission of one nucleus of \({ }_{92}^{236} \mathrm{U}\), the number of nuclei that must undergo fission to release an energy of \(1000 \mathrm{~J}\) is

An auditorium has volume of \(10^5 \mathrm{~m}^3\) and surface area of absorption \(2 \times 10^4 \mathrm{~m}^2\). Its average absorption coefficient is 0.2 . The reverberation time of the auditorium in seconds is

A metre stick is balanced on a knife edge at its centre. When four coins, each of mass \(2 \mathrm{~g}\) are put one on top of the other at \(10.0 \mathrm{~cm}\) mark, the stick it found to be balanced at \(46.0 \mathrm{~cm}\) mark. The mass of the metre stick is

A particle executes simple harmonic motion according to the equation \(x(t)=A \sin ^2(\alpha t)\). If the time period of the SHM is \(0.2 \mathrm{~s}\), then the value of \(\alpha\) (in units of \(\mathrm{rad} / \mathrm{s}\) ) is

The potential difference \(V\) across the filament of the bulb shown in the given Wheatstone bridge varies as \(V=i(2 i+1)\), where ' \(t\) ' is the current in ampere through the filament of the bulb. The emf of the battery \(\left(V_{\mathrm{a}}\right)\) so that the bridge becomes balanced is

Two identical bar magnets of magnetic moment \(M\) each, are placed along \(X\) and \(Y\)-axes, respectively at a distance \(d\) from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on \(X\)-axis and on the magnetic axis of magnet placed on \(Y\)-axis. If the magnitude of total magnetic field at the origin is \(B=\alpha\left[\frac{\mu_0}{4 \pi} \frac{M}{d^3}\right]\), then the value of constant \(\alpha\) will be \(\langle d>>l\), where \(l\) is the length of the bar magnets and direction of \(\mathrm{N}\) to \(\mathrm{S}\) in magnets is opposite with respect to each other)