For a common emitter configuration, if $$\alpha$$ and $$\beta$$ have their usual meanings, the incorrect relationship between $$\alpha$$ and $$\beta$$ is :

If $$a,b,c,d$$ are inputs to a gate and $$x$$ is its output, then, as per the following time graph, the gate is :

Identify the semiconductor devices whose characteristics are given below, in the order $$(a),(b),(c),(d)$$ :

A particle performs simple harmonic motion with amplitude $$A.$$ Its speed is trebled at the instant that it is at a distance {{2A} \over 3} from equilibrium position. The new amplitude of the motion is:

In an engine the piston undergoes vertical simple harmonic motion with amplitude 7 cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to :

Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and I, respectively. At time t = 0 one particle has displacement A while the other one has displacement {{ - A} \over 2} and they are moving towards each other. If they cross each other at time t, then t is :

Microwave oven acts on the principle of :

Arrange the following electromagnetic radiations per quantum in the order of increasing energy : A : Blue light B : Yellow light C : X-ray D : Radiowave.

Consider an electromagnetic wave propagating in vacuum. Choose the correct statement :

A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n2 R t2 where n is a constant. The power delivered to the particle by the force acting on it, is :

Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on the body in first two seconds of the motion is :

A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km and applies a constant frictional force $$W\frac{2}{0}$$ on the car. While moving uphill on the road at a speed of 10 ms−1, the car needs power P. If it needs power {p \over 2} while moving downhill at speed v then value of $$\upsilon$$ is :

A person trying to lose weight by burning fat lifts a mass of $$10$$ $$kg$$ upto a height of $$1$$ $$m$$ $$1000$$ times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies $$3.8\times 10^{7}J$$ of energy per $$kg$$ which is converted to mechanical energy with a $$20\%$$ efficiency rate. Take $$g=9.8m{s}^{-2}$$ :

A point particle of mass $$m,$$ moves long the uniformly rough track $$PQR$$ as shown in the figure. The coefficient of friction, between the particle and the rough track equals $$\mu .$$ The particle is released, from rest from the point $$P$$ and it comes to rest at point $$R.$$ The energies, lost by the ball, over the parts, $$PQ$$ and $$QR$$, of the track, are equal to each other , and no energy is lost when particle changes direction from $$PQ$$ to $$QR$$. The value of the coefficient of friction $$\mu$$ and the distance $$x$$ $$(=QR),$$ are, respectively close to:

A series LR circuit is connected to a voltage source with V(t) = V0 sin$$\Omega$$t. After very large time, current I(t) behaves as (t0 >> {L \over R}) :

An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to :

Choose the correct statement :

A modulated signal Cm(t) has the form Cm(t) = 30 sin 300 $$\pi$$t + 10 (cos 200 $$\pi$$t −cos 400 $$\pi$$t). The carrier frequency c, the modulating frequency (message frequency) f$$\omega$$, and the modulation index $$\mu$$ are respectively given by :

An audio signal consists of two distinct sounds : one a human speech signal in the frequency band of 200 Hz to 2700 Hz, while the other is a high frequency music signal in the frequency band of 10200 Hz to 15200 Hz. The ratio of the AM signal bandwidth required to send both the signals together to the AM signal bandwidth required to send just the human speech is :

A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is :