A collimated beam of light of diameter 2 mm is propagating along x -axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm , then the focal length of second lens is _________ mm.

The surface tension of a soap bubble is \(0.03\) N/m. The work done in increasing the diameter of bubble from \(2\) cm to \(6\) cm is \(\alpha \pi \times 10^{-4}\) J. The value of \(\alpha\) is _______. (Take \(\pi = 3.14\))

A plane electromagnetic wave of frequency \(20\,MHz\) propagates in free space along \(x\)-direction. At a particular space and time, \(\overrightarrow{ E }=6.6 \hat{ j } V / m\). What is \(\overrightarrow{ B }\) at this point?

In an experiment of \(CE\) configuration of \(n-p-n\) transistor, the transfer characteristics are observed as given in figure. If the input resistance is \(200 \Omega\) and output resistance is \(60 \Omega\) the voltage gain in this experiment will be..........

The value of the resistor, \(R_S\), needed in the \(dc\) voltage regulator circuit shown here, equals

The equation of a plane progressive wave is given by \(y = 5\cos\pi\left(200t - \dfrac{x}{150}\right)\) where \(x\) and \(y\) are in cm and \(t\) is in second. The velocity of the wave is _______ m/s.

Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is

A coil of \(200\) turns and area \(0.20 \mathrm{~m}^2\) is rotated at half a revolution per second and is placed in uniform magnetic field of \(0.01 \mathrm{~T}\) perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is \(\frac{2 \pi}{\beta}\) volt. The value of \(\beta\) is _______.

Two masses \(m\) and \(\frac{m}{2}\) are connected at the two ends of a massless rigid rod of length \(l\). The rod is suspended by a thin wire of torsional constant \(k\) at the centre of mass of the rodmass system (see figure). Because of torsional constant \(k\), the restoring torque is \(\tau  = k\,\theta \) for angular displacement \(\theta \). If the rod is rotated by \(\theta _0\) and released, the tension in it when it passes through its mean position will be

The center of mass of a thin rectangular plate (fig - x ) with sides of length \(a\) and \(b\), whose mass per unit area \((\sigma)\) varies as \(\sigma=\frac{\sigma_0 x}{a b}\) (where \(\sigma_0\) is a constant), would be \(\qquad\)

Two bodies of masses \(1\, kg\) and \(4\, kg\) are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency \(25\, rad/s\), and amplitude \(1.6\, cm\) while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is ..... \(N\) ( take \(g = 10\, ms^{-2}\))