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Physics

A raindrop with radius \( R = 0.2 \, \text{mm} \) falls from a cloud at a height \( h = 2000 \, \text{m} \) above ground. Assume that the drop is spherical throughout its fall and the force of buoyancy may be neglected, then the terminal speed attained by the raindrop is:
[Density of water \( f_w = 1000 \, \text{kg m}^{-3} \), and Density of air \( f_a = 1.2 \, \text{kg m}^{-3} \), \( g = 10 \, \text{m s}^{-2} \) Coefficient of viscosity of air \( = 1.8 \times 10^{-5} \, \text{N s m}^{-2} \)]

2.

Match List I with List II

Choose the correct answer from the options given below:

3.

Consider the following statements:
A. Atoms of each element emit characteristics spectrum.
B. According to Bohr’s Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.
C. The density of nuclear matter depends on the size of the nucleus.
D. A free neutron is stable but a free proton decay is possible.
E. Radioactivity is an indication of the instability of nuclei.
Choose the correct answer from the options given below:

4.

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from \( 27^\circ \text{C} \) to \( 37^\circ \text{C} \). If the ideal gas is composed of polyatomic molecule that the \( 4 \) vibrational modes, which of the following is true?
[\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \)]

5.

A simple pendulum of '\(m\)',length '\(l\)' and charge '\(+q\)' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be:

6.

Figure A and B show two long straight wires of circular cross-section (\( a \) and \( b \) with \( a < b \)), carrying current \( I \) which is uniformly distributed across the cross-section. The magnitude of magnetic field \( B \) varies with radius \( r \) and can be represented as:

7.

Two Carnot engines A and B operate in series such that engine A absorbs heat at \( T_1 \) and rejects heat to a sink at temperature \( T \). Engine B absorbs half of the heat rejected by Engine A and rejects to the sink at \( T_3 \). When workdone in both the cases is equal, the value of \( T \) is:

8.

The expected graphical representation of the variation of angle of deviation '\( \delta \)' with angle of incidence '\( i \)' in a prism is:

9.

An object of mass \( 0.5 \, \text{kg} \) is executing simple harmonic motion. Its amplitude is \( 5 \, \text{cm} \) and time period \( (T) \) is \( 0.2 \, \text{s} \). What will be the potential energy of the object at an instant \( t = \dfrac{T}{4} \, \text{s} \) starting from mean position. Assume that the initial phase of the oscillation is zero.

10.

A physical quantity ‘\( y \)’ is represented by the formula \( y = m^{2} r^{-4} g^{x} l^{-\dfrac{3}{2}} \). If the percentage errors found in \( y, m, r, l \) and \( g \) are \( 18 \), \( 1 \), \( 0.5 \), \( 4 \) and \( p \) respectively, then find the value of \( x \) and \( p \).

11.

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:

12.

A particle of mass \( M \) originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation \( F = F_{0} \left[ 1 - \left( \dfrac{t -T}{T} \right)^{2} \right] \). Where \( F_{0} \) and \( T \) are constants. The force acts only for the time interval \( 2T \). The velocity \( v \) of the particle after time \( 2T \) is:

13.

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy \( 3 \, \text{eV} \). The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength \( 4000 \, \text{Å} \). What is the maximum kinetic energy of the emitted photoelectron?

14.

Two identical particles of mass \( 1 \, \text{kg} \) each go round a circle of radius \( R \), under the action of their mutual gravitational attraction. The angular speed of each particle is:

15.

Find the truth table for the function \( Y \) of \( A \) and \( B \) represented in the following figure.

16.

What will be the magnitude of electric field at point \( O \) as shown in figure? Each side of the figure is \( l \) and perpendicular to each other?

17.

The planet Mars has two moons, if one of them has a period \( 7 \) hours, \( 30 \) minutes and an orbital radius of \( 9.0 \times 10^3 \, \text{km} \). Find the mass of Mars.
\( \left\{ \begin{aligned} \\ \text{Given} \\ \frac{4\pi^2}{G} &= 6 \times 10^{11} \,\text{N}^{-1}\,\text{m}^{-2}\,\text{kg}^2 \end{aligned} \right. \)

18.

A \( 100 \, \Omega \) resistance, a \( 0.1 \, \mu \text{F} \) capacitor and an inductor are connected in series across a \( 250 \, \text{V} \) supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is \( 60 \, \text{Hz} \).

19.

The resistance of a conductor \( 15^\circ \text{C} \) is \( 16 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 20 \, \Omega \). What will be the temperature coefficient of resistance of the conductor?

20.

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 \( E_{\text{mech}} = 8 \, \text{J} \), the incorrect statement for this system is:

[where K.E. = kinetic energy]

21.

1.A swimmer wants to cross a river from point A to point B. Line AB makes an angle of \( 30^\circ \) with flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle \( \theta \) with the line AB should be ______\( ^\circ \), so that the swimmer reaches point B.

22.

The \( K_\alpha \) X-ray of molybdenum has wavelength \( 0.071 \, \text{nm} \). If the energy of a molybdenum atom with a K electron knocked out is \( 27.5 \, \text{keV} \), the energy of this atom when an L electron is knocked out will be ______ \( \text{keV} \). (Round off to the nearest integer)
[\( h = 4.14 \times 10^{-15} \, \text{eVs} \), \( c = 3 \times 10^{8} \, \text{ms}^{-1} \)]

23.

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is ______ \( \text{mm} \).
[Refractive index of air = \( 1.0003 \), wavelength of yellow light in vacuum = \( 6000 \, \mathring{A} \)]

24.

For the circuit shown, the value of current at time \( t = 3.2 \, \text{s} \) will be _____ \( \text{A} \).

25.

A small block slides down from the top of hemisphere of radius \( R = 3 \, \text{m} \) shown in the figure. The height ‘\( h \)’ at which the block will lose contact with the surface of the sphere is ________ \( \text{m} \).
(Assume there is no friction between the block and the hemisphere)

26.

A particle executes simple harmonic motion represented by displacement function as \( x(t) = A \sin(\omega t + \phi) \). If the position and velocity of the particle at \( t = 0 \, \text{s} \) are \( 2 \, \text{cm} \) and \( 2\omega \, \text{cm s}^{-1} \) respectively, then its amplitude is \( x\sqrt{2} \, \text{cm} \) where the value of \( x \) is __________.

27.

In the given figure the magnetic flux through the loop increases according to the relation \( \phi_{B}(t) = 10 t^{2} + 20 t \), where \( \phi_{B} \) is in milliwebers and \( t \) is in seconds. The magnitude of current through \( R = 2 \, \Omega \) resistor at \( t = 5 \, \text{s} \) is __________ \( \text{mA} \).

28.

In the given figure, two wheels \( P \) and \( Q \) are connected by a belt \( B \). The radius of \( P \) is three times as that of \( Q \). In case of same rotational kinetic energy, the ratio of rotational inertias \( \left( \dfrac{I_{1}}{I_{2}} \right) \) will be \( x : 1 \). The value of \( x \) will be ________.

29.

The water is filled upto height of \( 12 \, \text{m} \) in a tank having vertical sidewalls. A hole is made in one of the walls at a depth ‘\( h \)’ below the water level. The value of ‘\( h \)’ for which the emerging stream of water strikes the ground at the maximum range is _______ \( \text{m} \).

30.

The maximum amplitude for an amplitude modulated wave is found to be \( 12 \, \text{V} \) while the minimum amplitude is found to be \( 3 \, \text{V} \). The modulation index is \( 0.6x \) where \( x \) is __________.

JEE Main 2021 27th July Evening Shift

Physics Chemistry Mathematics

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Find the truth table for the function \( Y \) of \( A \) and \( B \) represented in the following figure.

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