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JEE Mains | PYQ

The ratio of de-Broglie wavelength of an \( \alpha \) particle and a proton accelerated from rest by the same potential is \( \dfrac{1}{\sqrt{m}} \), the value of \( m \) is:

The equation of a circle is given by \( x^{2}+y^{2}=a^{2} \), where \( a \) is the radius. If the equation is modified to change the origin other than \( (0,0) \), then find out the correct dimensions of \( A \) and \( B \) in a new equation: \( (x-At)^{2}+\left(y-\dfrac{t}{B}\right)^{2}=a^{2} \). The dimension of \( t \) \( [T^{-1}] \).

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

For the given logic gates combination, the correct truth table will be:

A fully loaded boeing aircraft has a mass of \( 5.4 \times 10^{5}\ \text{kg} \). Its total wing area is \( 500\ \text{m}^{2} \). It is in level flight with a speed of \( 1080\ \text{km/h} \). If the density of air \( \rho \) is \( 1.2\ \text{kg m}^{-3} \), the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be: \( (g = 10\ \text{m/s}^{2}) \)

Heat energy of \( 184 \, \text{kJ} \) is given to i.e. of mass \( 600 \, \text{g} \) at \( -12^\circ \text{C} \). Specific heat of ice is \( 2222.3 \, \text{J} \, \text{kg}^{-1} \, {}^\circ\text{C}^{-1} \) and latent heat of ice in \( 336 \, \text{kJ} / \text{kg}^{-1} \).

(A) Final temperature of system will be \( 0^\circ \text{C} \).
(B) Final temperature of the system will be greater than \( 0^\circ \text{C} \).
(C) The final system will have a mixture of ice and water in the ratio of \( 5:1 \).
(D) The final system will have a mixture of ice and water in the ratio of \( 1:5 \).

The electric current in a circular coil of four turns produces a magnetic induction \( 32 \, \text{T} \) at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be:

point charge \( 2 \times 10^{-2} \, \text{C} \) is moved from P to S in a uniform electric field of \( 30 \, \text{N} \, \text{C}^{-1} \) directed along positive x-axis. If coordinates of P and S are \( (1, \, 2, \, 0) \, \text{m} \) and \( (0, \, 0, \, 0) \, \text{m} \) respectively, the work done by electric field will be:

The time taken by an object to down \( 45^\circ \) rough inclined plane is \( n \) times as it takes to slide down a perfectly smooth \( 45^\circ \) incline plane. The coefficient of kinetic friction between the object and the in line plane is:

A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best option)

Given below are two statements:
Statement I : Electromagnetic waves are not defected by electric and magnetic field.
Statement II : The amplitude of electric field and the magnetic field in electromagnetic waves are released to each other as \( E_{0} = \sqrt{\frac{\mu_{0}}{\varepsilon_{0}}} \, B_{0} \).
In the light of the above statement, choose the correct answer from options given below:

Substance A has atomic mass number \( 16 \) and half life of \( 1 \, \text{day} .\) Another substance B has atomic mass number \( 32 \) and half life of \( \frac{1}{2} \, \text{day} .\) If both A and B simultaneously start undergo radio activity at the same time with initial mass \( 320 \, \text{g} \) each, how many total atoms of A and B combined would be left after \( 2 \, \text{days} .\)

A force acts for \( 20 \, \text{s} \) on a body of mass \( 20 \, \text{kg} \), starting from rest, after which the fore ceases and then body describes \( 50 \, \text{m} \) in the next \( 10 \, \text{s} .\) The value of force will be:

A square loop of area \( 25 \, \text{cm}^2 \) has a resistance of \( 10 \, \Omega .\) The loop is placed in uniform magnetic field of magnitude \( 40.0 \, \text{T} .\) The plane of loop is perpendicular to the magnetic filed. The work done in pulling the loop out of the magnetic field slowly and uniformly in \( 1.0 \, \text{sec} \), will be:

With the help potentiometer, we can determine the value of emf of given cell. The sensitivity of the potentiometer is:
(A) Directly proportional to the length of the potentiometer wire.
(B) Directly proportional to the potential gradient of the wire.
(C) Inversely proportional to the potential gradient of the wire.
(D) Inversely proportional to the length of the potentiometer wire.
Choose the correct option for the above statements

The time period of a satellite of earth is \( 24 \, \text{hours} .\) If the separation between the earth and the satellite is decreased to only fourth of the previous value, then its new time period will become.

The modulation index for an A.M. wave having maximum and minimum peak-to-peak voltages of \( 14 \, \text{mV} \) and \( 6 \, \text{mV} \) respectively is:

For the given figures, choose the correct options:

At \( 300\,\text{K} \), the rms speed of oxygen molecules is \( \sqrt{\frac{\alpha+5}{\alpha}} \) times to that of its average speed in the gas. Then, the value of \( \alpha \) will be: (used \( \pi=\frac{22}{7} \))

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are \( 2.8 \) (medium \( -1 \)) and \( 6.8 \) (medium \( -2 \)), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be \( \tan^{-1}\!\left(\left(1+\frac{10}{\theta}\right)^{\frac{1}{2}}\right) \) the value of \( \theta \) is _______. (Given for dielectric media, \( \mu_r=1 \))

An inductor of inductance \( 2\,\mu\text{H} \) is connected in series with a resistance, a variable capacitor and an AC source of frequency \( 7\,\text{kHz} \). The value of capacitance for which maximum current is drawn into the circuit is \( \frac{1}{x}\,\text{F} \), where the value of \( x \) is _______. (Take \( \pi=\frac{22}{7} \))

A metal block of base area \( 0.20\,\text{m}^{2} \) is placed on a table, as shown in figure. A liquid film of thickness \( 0.22\,\text{mm} \) is inserted between the block and the table. The block is pushed by a horizontal force of \( 0.1\,\text{N} \) and moves with a constant speed. If the viscosity of the liquid is \( 5.0\times 10^{-3}\,\text{Pl} \), the speed of block is ______ \( \times 10^{-3}\,\text{m/s} \).

A car is moving on a circular path of radius \( 600\,\text{m} \) such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of \( 54\,\text{km/hr} \) \( t(1-e^{-\pi/2})\,\text{s} \). The value of \( t \) is __________.

When two resistances \( R_1 \) and \( R_2 \) connected in series and introduction into the left gap of a meter bridge and a resistance of \( 10 \, \Omega \) is introduced into the right gap, a null point is found at \( 60 \, \text{cm} \) from left side. When \( R_1 \) and \( R_2 \) are connected in parallel and introduced into the left gap, a resistance of \( 3 \, \Omega \) is introduced into the right-gap to get null point at \( 40 \, \text{cm} \) from left end. The product of \( R_1 R_2 \) is _____ \( \Omega^2 \).

A particle of mass \( 250 \, \text{g} \) executes a simple harmonic motion under a periodic force \( F = (-25 x) \, \text{N} \). The particle attains a maximum speed of \( 4 \, \text{m} \, /\text{s}^{} \) during its oscillation. The amplitude of the motion is ______ cm.

A particle of mass \( 100 \, \text{g} \) is projected at time \( t = 0 \) with a speed \( 20 \, \text{m} \, \text{s}^{-1} \) at an angle \( 45^\circ \) to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time \( t = 2 \, \text{s} \) is found to be \( \sqrt{K} \, \text{kg} \, \text{m}^2 / \text{s} \). The value of \( K \) is ________. (Take \( g = 10 \, \text{m} \, \text{s}^{-2} \)).

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as \( 5.25 \, \text{mm} \) and apparent thickness of the glass slab as \( 5.00 \, \text{mm} \). Travelling microscope has \( 20 \) divisions in one \( \text{cm} \) on main scale and \( 50 \) divisions on vernier scale is equal to \( 49 \) divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is \( \dfrac{x}{10} \times 10^{-3} \), where \( x \) is __________.

For a charged spherical ball, electrostatic potential inside the ball varies with \( r \) as \( V = 2ar^2 + b \).
Here, \( a \) and \( b \) are constant; \( r \) is the distance from the centre. The volume charge density inside the ball is \( -\lambda a \varepsilon \). The value of \( \lambda \) is _____________.
\( \varepsilon \) = permittivity of the medium.

A null point is found at \( 200 \, \text{cm} \) is potentiometer when cell in secondary circuit is shunted by \( 5\,\Omega \). When a resistance of \( 15\,\Omega \) is used for shunting, null point moves to \( 300 \, \text{cm} \). The internal resistance of the cell is __________ \( \Omega \).