If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon \(=27\) days and gravitational attraction between the satellite and the moon is neglected.

An electron of mass \(\mathrm{m}\) and magnitude of charge \(|e|\) initially at rest gets accelerated by a constant electric field \(\mathrm{E}\). The rate of change of de-Broglie wavelength of this electron at time \(t\) ignoring relativistic effects is 

The circuit contains two diodes each with a forward resistance of \(50\, \Omega\) and with infinite reverse resistance. If the battery voltage is \(6\, V\), the current through the \(120\, \Omega\) resistance is \(mA\)

Two discs have moments of intertia \({I}_{1}\) and \({I}_{2}\) about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, \(\omega_{1}\) and \(\omega_{2}\) respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :

An object moves with speed \(v_1, v_2\), and \(v_3\) along a line segment \(A B, B C\) and \(C D\) respectively as shown in figure. Where \(AB = BC\) and \(AD =3 AB\), then average speed of the object will be :

A \(2\,mW\) laser operates at a wavelength of \(500\,nm.\) The number of photons that will be emitted per second is [Given Planck’s constant \(h = 6.6 \times 10^{-34}\,Js,\) speed of light \(c = 3.0\times 10^8\,m/s\) ]

Read the following statements: \(A.\) When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice. \(B.\) Two bodies \(P\) and \(Q\) having equal surface areas are maintained at temperature \(10^{\circ}\,C\) and \(20^{\circ}\,C\). The thermal radiation emitted in a given time by \(P\) and \(Q\) are in the ratio \(1: 1.15\) \(C.\) A carnot Engine working between \(100\,K\) and \(400\,K\) has an efficiency of \(75 \%\) \(D.\) When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below :

The value of \(\frac{e^{-\frac{\pi}{4}}+\int \limits_0^{\frac{\pi}{4}} e^{-x} \tan ^{50} x d x}{\int \limits_0^{\frac{\pi}{4}} e^{-x}\left(\tan ^{49} x+\tan ^{51} x\right) d x}\) is

In an experiment for determination of refractive index of glass of a prism by \(i - \delta\) , plot it was found thata ray incident at angle \(35 ^o \), suffers a deviation of \(40 ^o \) and that it emerges at angle \(7 9 ^o \). In that case which of the following is closest to the maximum possible value of the refractive index?

Let a tangent to the Curve \(9 x^2+16 y^2=144\) intersect the coordinate axes at the points \(A\) and \(B\). Then, the minimum length of the line segment \(A B\) is \(.........\)

The area (in sq. units) of the region \(\left\{ {x \in R:x \ge } \right.0,\,y \ge 0,\,y \ge x - 2\,and\,y \le \sqrt x \} \,,\,\) is

Two blocks of masses \(m\) and \(M\) are connected by means of a metal wire of cross-sectional area \(A\) passing over a frictionless fixed pulley as shown in the figure. The system is then released. If \(M = 2\, m\), then the stress produced in the wire is

A mass of \(1\text{ kg}\) is kept on an inclined plane with \(30°\) inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of \(4\text{ m/s}\). The work done by the frictional force in time \(2\text{ s}\) is _______ J. (Take \(g = 10\text{ m/s}^2\))