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With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength \( 5890 \, \displaystyle \overset{\circ}{\text{A}} \) is observed at \( 5896 \, \displaystyle \overset{\circ}{\text{A}} \) ?

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is \( 50\% \) of its translational kinetic energy. The body is:

At an angle of \( 30^\circ \) to the magnetic meridian, the apparent dip is \( 45^\circ \). Find the true dip:

Two small drops of mercury each of radius \( R \) coalesce to form a single large drop. The ratio of total surface energy before and after the change is:

For a certain radioactive process the graph between \( \ln R \) and \( t \, (\text{sec}) \) is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately:

The length of a metal wire is \( l_{1} \) when the tension in it is \( T_{1} \) and is \( l_{2} \) when the tension is \( T_{2} \). The natural length of the wire is:

Two vectors \( \vec{P} \) and \( \vec{Q} \) have equal magnitudes. If the magnitude of \( \vec{P} + \vec{Q} \) is \( n \) times the magnitude of \( \vec{P} - \vec{Q} \), then angle between \( \vec{P} \) and \( \vec{Q} \) is:

For a series LCR circuit with \( R = 100\,\Omega \), \( L = 0.5\,\text{mH} \) and \( C = 0.1\,\text{pF} \) connected across \( 220\,\text{V} - 50\,\text{Hz} \) AC supply, the phase angle between current and supplied voltage and the nature of the circuit is:

A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time \( t_{1} \). If he remains stationary on a moving escalator then the escalator takes him up in time \( t_{2} \). The time taken by him to walk up on the moving escalator will be:

If time \( (t) \), velocity \( (v) \), and angular momentum \( (l) \) are taken as the fundamental units. Then the dimension of mass \( (m) \) in terms of \( t \), \( v \), and \( l \) is:

An electron having de-Broglie wavelength \( \lambda \) is incident on a target in a X-ray tube. Cut-off wavelength of emitted X-ray is:

Consider a binary star system of star A and star B with masses \( m_{A} \) and \( m_{B} \) revolving in a circular orbit of radii \( r_{A} \) and \( r_{B} \) respectively. If \( T_{A} \) and \( T_{B} \) are the time period of star A and star B, respectively, then:

If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be:

The correct relation between the degrees of freedom \( f \) and the ratio of specific heat \( \gamma \) is:

A particle is making simple harmonic motion along the X-axis. If at a distances \( x_1 \) and \( x_2 \) from the mean position the velocities of the particle are \( v_1 \) and \( v_2 \) respectively. The time period of its oscillation is given as:

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:

Which of the following graphs represent the behavior of an ideal gas? Symbols have their usual meaning.

The magnetic susceptibility of a material of a rod is \( 499 \). Permeability in vacuum is \( 4\pi \times 10^{-7} \ \text{H/m} \). Absolute permeability of the material of the rod is:

A satellite is launched into a circular orbit of radius \( R \) around earth, while a second satellite is launched into a circular orbit of radius \( 1.02R \). The percentage difference in the time periods of the two satellites is:

In an electromagnetic wave the electric field vector and magnetic field vector are given as \( \vec{E} = E_0 \hat{i} \) and \( \vec{B} = B_0 \hat{k} \) respectively. The direction of propagation of electromagnetic wave is along:

One mole of an ideal gas at \( 27^\circ \text{C} \) is taken from A to B as shown in the given PV indicator diagram. The work done by the system will be \( \_\_\_\_\_\_\_\_ \times 10^{-1} \, \text{J} \).
[Given: \( R = 8.3 \, \text{J mol}\,\text{K} \), \( \ln 2 = 0.6931 \)]

A body rotating with an angular speed of \( 600 \, \text{rpm} \) is uniformly accelerated to \( 1800 \, \text{rpm} \) in \( 10 \, \text{s} \). The number of rotations made in the process is \( \_\_\_\_\_\_ \).

For the forward biased diode characteristics shown in the figure, the dynamic resistance at \( I_D = 3 \, \text{mA} \) will be \( \_\_\_\_\_\_ \, \Omega \).

A body of mass '\( m \)' is launched up on a rough inclined plane making an angle of \( 30^\circ \) with the horizontal. The coefficient of friction between the body and plane is \( \dfrac{\sqrt{x}}{5} \) if the time of ascent is half of the time of descent. The value of \( x \) is \( \_\_\_\_\_\_ \).

A zener diode having zener voltage \( 8 \, \text{V} \) and power dissipation rating of \( 0.5 \, \text{W} \) is connected across a potential divider arranged with maximum potential drop across zener diode is as shown in the diagram. The value of protective resistance \( R_P \) is ________ \( \Omega \).

Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is \( \dfrac{\sqrt{x}}{2} \). Then, the value of \( x \) is __________.

A certain metallic surface is illuminated by monochromatic radiation of wavelength \( \lambda \). The stopping potential for photoelectric current for this radiation is \( 3V_0 \). If the same surface is illuminated with a radiation of wavelength \( 2\lambda \), the stopping potential is \( V_0 \). The threshold wavelength of this surface for photoelectric effect is __________ \( \lambda \).

A series LCR circuit of \( R = 5 \Omega \), \( L = 20 \, \text{mH} \) and \( C = 0.5 \, \mu \text{F} \) is connected across an AC supply of \( 250 \, \text{V} \), having variable frequency. The power dissipated at resonance condition is ______________ \( \times 10^{2} \, \text{W} \) .

In the given figure switches \( S_{1} \) and \( S_{2} \) are in open condition. The resistance across \( ab \) when the switches \( S_{1} \) and \( S_{2} \) are closed is __________ \( \Omega \).

A radioactive substance decays to \( \left( \dfrac{1}{16} \right)^{\text{th}} \) of its initial activity in \( 80 \, \text{days} \). The half life of the radioactive substance expressed in days is __________ .

JEE Main 2021 20th July Evening Shift

Physics Chemistry Mathematics

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Two vectors \( \vec{P} \) and \( \vec{Q} \) have equal magnitudes. If the magnitude of \( \vec{P} + \vec{Q} \) is \( n \) times the magnitude of \( \vec{P} - \vec{Q} \), then angle between \( \vec{P} \) and \( \vec{Q} \) is: