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A rocket is going away from the earth at a speed $0.2c$, where c = speed of light. It emits a signal of frequency $4\times {10}^{7}Hz$. What will be the frequency observed by an observer on the earth?

A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 10m from the lamp will be

A block of mass 'm' is suspended by different
springs of spring constants shown in the figure.

Let time period of oscillation in these four
positions be T_1, T₂, T₃
and T₄. Then

A train moves towards a stationary observer with a speed $34\text{m/s}$. The train sounds a whistle and its frequency registered by the observer is $f_1$. If the speed of the train is reduced to $17\text{m/s}$, the frequency registered is $f_2$. If the speed of sound is $340\text{m/s}$ , then the ratio $\frac{f_1}{f_2}$ is



[Assume, medium is stationary ]

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Seven resistors are connected as shown in the diagram.



The equivalent resistance in $\Omega$ of this network between $A$ and $B$ is:

When a long wire carrying a steady current is bent into a circular coil of one turn, the magnetic induction at its centre is B. When the same wire carrying the same current is bent to form a circular coil of n turns of a smaller radius, the magnetic induction at the centre will be

A balloon starts rising from the surface of the earth. The ascension rate is constant and equal to $V_0$. Due to the wind the balloon gathers a horizontal velocity component $V_x=Ky$ where K is a constant and y is the height of ascent.
The tangential and normal acceleration of the balloon at a height of ascent equal to h is

A body dropped from the top of a tower falls through $40m$ during the last two seconds of its fall. The height of tower is $(g=10m/s^2)$

A thin rod of length $L$ and mass $M$, is bent into a circular loop. Find the moment of inertia of the loop about one of its diameters. Take mass $M=3\text{Kg}$ and $L=2\text{m}.$

A body traveling along a straight line traversed first one third of the total distance with a velocity $4\text{m/s}$. The remaining part of the distance was covered with a velocity $2\text{m/s}$ for half the time and with velocity $6\text{m/s}$ for the other half of time. The average velocity over the whole time of motion is

Find the equivalent resistance of the infinite ladder circuit shown in figure across terminal
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$\text{A}$ and $\text{B}$.

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is $B$. It is then bent into a circular coil of $n$ turns. The magnetic field at the centre of this coil of $n$ turns will be

4 ideal diodes are connected as shown in the circuit. The current through $50\Omega$ resistance is

The frequency of a car horn is 400 Hz. If the horn is honked as the car moves with a speed $u_s$ = 34 m/s through still air towards a stationary receiver, the wavelength of the sound passing the receiver is [velocity of sound is 340 m/s]

By Huygen's wave theory of light, we cannot explain the phenomenon of

[CPMT 1989; AFMC 1993, 99; MP PET 1995, 2003;RPMT 2003; BCECE 2003; Pb PMT 2004]

A transverse wave on a string has an amplitude of 0.2 m and a frequency of 175 Hz. Consider a particle of the string at x = 0. It begins with a displacement y = 0, at t = 0, according to equation $y=0.2sin(kx\pm \omega t)$. How much time passes between the first two instant when this particle has a displacement of y = 0.1 m?

Two parallel glass plates are dipped partly in the liquid of density $d$ keeping them vertical. If the distance between the plates is $x$, surface tension for the liquid is $T$ and angle of contact is $\theta$, then rise of liquid between the plates due to capillary will be

1. 1000

A gas at NTP is suddenly compressed to one-fourth of its original volume.If $\gamma$ is supposed to be $\frac{3}{2}$,n then the final pressure is

The relation between time $t$ and distance $x$ for a moving body is given as $t=m{x}^2+nx$, where $m$ and $n$ are constants. The retardation of the motion is :
$\left(\text{Where}v\text{stands for velocity}\right)$

An angular magnification of $30\text{X}$ is to be obtained from a compound microscope, having an eyepiece of focal length $5\text{cm}$. Find the magnification produced by the objective lens.



Given angular magnification is achieved in case of the least strain on the eye.

Two discs are mounted on frictionless bearings on a common shaft. The first disc has rotational inertia $I$ and is spinning with angular velocity $\omega$. The second disc has rotational inertia $2I$ and is spinning in opposite direction with angular velocity $3\omega$, as shown in figure. If the two discs are slowly forced towards each other along the shaft, until they couple. Then final common angular velocity is

A force $F$ acting on a particle varies with position $x$ as shown in figure. The work done by this force in displacing the particle from $x=-1\text{m}$ to $1\text{m}$.

The energy of an electron in a hydrogen atom in the $n^{th}$ orbit is $E_n$. Then, the energy in the $n^{th}$ orbit of double ionized helium atom will be

Find the friction force between block $A$ and the surface for system at rest given below:
$m_A=9\text{kg},m_B=4\text{kg},{\mu }_s={\mu }_k=0.8$