For the plane electromagnetic wave given by $$E=E_0\sin (\omega t-kx)$$ and $$B=B_0\sin (\omega t-kx)$$, the ratio of average electric energy density to average magnetic energy density is

The energy density associated with electric field $$\vec{E}$$ and magnetic field $$\vec{B}$$ of an electromagnetic wave in free space is given by $$({ϵ}_0-$$ permittivity of free space, $${\mu }_0-$$ permeability of free space)

Identify the correct statements from the following : A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative. C. Work done by friction on a body sliding down an inclined plane is positive. D. Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero. E. Work done by the air resistance on an oscillating pendulum is negative. Choose the correct answer from the options given below :

A stone is projected at angle $$30^{\circ }$$ to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be -

The ratio of powers of two motors is $$\frac{3\sqrt{x}}{\sqrt{x}+1}$$, that are capable of raising $$300\mathrm{kg}$$ water in 5 minutes and $$50\mathrm{kg}$$ water in 2 minutes respectively from a well of $$100\mathrm{m}$$ deep. The value of $$x$$ will be

Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is :

Given below are two statements: Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal retarding forces. Both come to rest in equal distance. Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. In the light of given statements, choose the most appropriate answer from the options given below

A bullet of mass $$0.1\mathrm{kg}$$ moving horizontally with speed $$400{\mathrm{ms}}^{-1}$$ hits a wooden block of mass $$3.9\mathrm{kg}$$ kept on a horizontal rough surface. The bullet gets embedded into the block and moves $$20\mathrm{m}$$ before coming to rest. The coefficient of friction between the block and the surface is __________. (Given $$g=10\mathrm{m}/{\mathrm{s}}^2$$ )

An alternating voltage source $\mathrm{V}=260\sin (628\mathrm{t}$ ) is connected across a pure inductor of $5\mathrm{mH}$ Inductive reactance in the circuit is :

Match List - I with List - II : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-amwm{font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0lax{text-align:left;vertical-align:top} List I List II A. AC generator I. Presence of both L and C B. Transformer II. Electromagnetic Induction C. Resonance phenomenon to occur III. Quality factor D. Sharpness of resonance IV. Mutual Induction Choose the correct answer from the options given below :

If $$\mathrm{R},{\mathrm{X}}_{\mathrm{L}}$$, and $${\mathrm{X}}_{\mathrm{C}}$$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless :

In the given circuit, rms value of current $\left(I_{\mathrm{rms}}\right)$ through the resistor $R$ is:

In a series LR circuit with $${\mathrm{X}}_{\mathrm{L}}=\mathrm{R}$$, power factor P1. If a capacitor of capacitance C with $${\mathrm{X}}_{\mathrm{C}}={\mathrm{X}}_{\mathrm{L}}$$ is added to the circuit the power factor becomes P2. The ratio of P1 to P2 will be :

For the given figures, choose the correct options :

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes $$x$$ times its initial resonant frequency $${\omega }_0$$. The value of $$x$$ is :

Given below are two statements: Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor. Statement II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor. In the light of above statements, choose the correct answer form the options given below:

Given below are two statements: Statement I : When the frequency of an a.c source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases. Statement II : In a series LCR circuit, the value of power factor at resonance is one. In the light of given statements, choose the most appropriate answer from the options given below.

As per the given graph, choose the correct representation for curve $$\mathrm{A}$$ and curve B. Where $${\mathrm{X}}_{\mathrm{C}}=$$ reactance of pure capacitive circuit connected with A.C. source $${\mathrm{X}}_{\mathrm{L}}=$$ reactance of pure inductive circuit connected with $$\mathrm{A}.\mathrm{C}$$. source R = impedance of pure resistive circuit connected with A.C. source. $$\mathrm{Z}=$$ Impedance of the LCR series circuit $$\}$$

Given below are two statements: Statement I : Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs Statement II : Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage. In the light of the above statements, choose the correct answer from the options given below:

A capacitor of capacitance $$150.0\mu \mathrm{F}$$ is connected to an alternating source of emf given by $$\mathrm{E}=36\sin (120\pi \mathrm{t})\mathrm{V}$$. The maximum value of current in the circuit is approximately equal to :