The magnetic field vector of an electromagnetic wave is given by B = {B_0}{{\widehat i + \widehat j} \over {\sqrt 2 }}\cos (kz - \omega t); where $$\hat{i},\hat{j}$$ represents unit vector along x and y-axis respectively. At t = 0s, two electric charges q1 of 4$$\pi$$ coulomb and q2 of 2$$\pi$$ coulomb located at \left( {0,0,{\pi \over k}} \right) and \left( {0,0,{{3\pi } \over k}} \right), respectively, have the same velocity of 0.5 c $$\hat{i}$$, (where c is the velocity of light). The ratio of the force acting on charge q1 to q2 is :-

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by E = 20cos(2 $$\times$$ 1010 t $$-$$ 200x) V/m. The dielectric constant of the medium is equal to : (Take $$\mu$$r = 1)

A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of 20 ms-1. The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now?

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to :-

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional to :

A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (take g = 9.8 ms$$-$$2)

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that Emech = 8 J, the incorrect statement for this system is : [ where K.E. = kinetic energy ]

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :

A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of 1 : 2. If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energy is :-

A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of 0.8$$\sqrt{gh}$$. The value of workdone by the air-friction is :

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

The current (i) at time t = 0 and t = $$\infty$$ respectively for the given circuit is :

An LCR circuit contains resistance of 110$$\Omega$$ and a supply of 220 V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 45$${}^{\circ }$$. If on the other hand, only inductor is removed the current leads by 45$${}^{\circ }$$ with the applied voltage. The rms current flowing in the circuit will be :

Match List I with List II. List I List II (a) Rectifier (i) Used either for stepping up or stepping down the a.c. voltage (b) Stabilizer (ii) Used to convert a.c. voltage into d.c. voltage (c) Transformer (iii) Used to remove any ripple in the rectified output voltage (d) Filter (iv) Used for constant output voltage even when the input voltage or load current change Choose the correct answer from the options given below :

An alternating current is given by the equation i = i1 sin $$\omega$$t + i2 cos $$\omega$$t. The rms current will be :

Find the peak current and resonant frequency of the following circuit (as shown in figure).

An RC circuit as shown in the figure is driven by a AC source generating a square wave. The output wave pattern monitored by CRO would look close to :

For the given circuit, comment on the type of transformer used.

An AC current is given by I = I1 sin$$\omega$$t + I2 cos$$\omega$$t. A hot wire ammeter will give a reading :

Match List - I with List - II List - I List - II (a) Phase difference between current and voltage in a purely resistive AC circuit (i) {\pi \over 2}; current leads voltage (b) Phase difference between current and voltage in a pure inductive AC circuit (ii) zero (c) Phase difference between current and voltage in a pure capacitive AC circuit (iii) {\pi \over 2}; current lags voltage (d) Phase difference between current and voltage in an LCR series circuit (iv) {\tan ^{ - 1}}\left( {{{{X_C} - {X_L}} \over R}} \right) Choose the most appropriate answer from the options given below :