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JEE Mains | PYQ

A point charge of \( 10\,\mu\text{C} \) is placed at the origin. At what location on the x-axis should a point charge of \( 40\,\mu\text{C} \) be placed so that the net electric field is zero at \( x = 2\,\text{cm} \) on the x-axis?

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is:

Two objects are projected with same velocity ‘\( u \)’ however at different angles \( \alpha \) and \( \beta \) with the horizontal. If \( \alpha + \beta = 90^\circ \), the ratio of horizontal range of the first object to the 2nd object will be:

Match List I with List II.

Choose the correct answer from the options given below:

A wire of length \( 1\,\text{m} \) moving with velocity \( 8\,\text{m/s} \) at right angles to a magnetic field of \( 2\,\text{T} \). The magnitude of induced emf, between the ends of wire will be ______.

For a moving coil galvanometer, the deflection in the coil is \( 0.05 \, \text{rad} \) when a current of \( 10 \, \text{mA} \) is passed through it. If the torsional constant of suspension wire is \( 4.0 \times 10^{-5} \, \text{N m rad}^{-1} \), the magnetic field is \( 0.01 \, \text{T} \) and the number of turns in the coil is \( 200 \), the area of each turn (in \( \text{cm}^2 \)) is:

The distance travelled by a particle is related to time \( t \) as \( x = 4 t^2 \). The velocity of the particle at \( t = 5 \, \text{s} \) is:

A particle executes simple harmonic motion between \( x = -A \) and \( x = +A \). If time taken by particle to go from \( x = 0 \) to \( x = \frac{A}{2} \) is \( 2 \, \text{s} \); then time taken by particle in going from \( x = \frac{A}{2} \) to \( A \) is:

Every planet revolves around the sun in an elliptical orbit:
A. The force acting on a planet is inversely proportional to square of distance from sun.
B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun.
C. The centripetal force acting on the planet is directed away from the sun.
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.
Choose the correct answer from the options given below:

Statement I: When a Si sample is doped with Boron, it becomes P type and when doped by Arsenic it becomes N-type semi-conductor such that P-type has excess holes and N-type has excess electrons.
Statement II: When such P-type and N-type semi-conductors, are fused to make a junction, a current will automatically flow which can be detected with an externally connected ammeter.
In the light of above statements, choose the most appropriate answer from the options given below:

Match List I with List II.

Choose the correct answer from the option given below:

Match List I with List II.

Choose the correct answer from the options given below:

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are:
A. Real
B. Erect
C. Smaller in size than object
D. Laterally inverted
Choose the most appropriate answer from the options given below:

Match List I with List II.

Choose the correct answer from the options given below:

The graph between two temperature scales \( P \) and \( Q \) is shown in the figure, between upper fixed point and lower fixed point there are \( 150 \) equal divisions of scale \( P \) and \( 100 \) divisions on scale \( Q \). The relationship for conversion between the two scales is given by:

The energy levels of an atom is shown in figure.

Which one of these transitions will result in the emission of a photon of wavelength \( 124.1 \, \text{nm} \)?
Given \( ( \, h = 6.62 \times 10^{-34} \, \text{Js} \, ) \).

Given below are two statements:
Statement I: Stopping potential in photoelectric effect does not depend on the power of the light source.
Statement II: For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light.
In the light of above statements, choose the most appropriate answer from the options given below:

Consider a block kept on an inclined plane (inclined at \( 45^\circ \)) as shown in the figure. If the force required to just push it up the incline is \( 2 \) times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane (\( \mu \)) is equal to:

A body of mass \( m \) is taken from earth surface to the height \( h \) equal to twice the radius of earth \( (R_e) \), the increase in potential energy will be: \( (g = \) acceleration due to gravity on the surface of Earth\() \)

A capacitor has capacitance \( 5\,\mu F \) when it’s parallel plates are separated by air medium of thickness \( d \). A slab of material of dielectric constant \( 1.5 \) having area equal to that of plates but thickness \( \dfrac{d}{2} \) is inserted between the plates. Capacitance of the capacitor in the presence of slab will be (in \( \mu F \)) ____.

If a solid sphere of mass \( 5 \, \text{kg} \) and a disc of mass \( 4 \, \text{kg} \) have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be \( \dfrac{x}{7} \). The value of \( x \) is _______.

A train blowing a whistle of frequency \( 320 \, \text{Hz} \) approaches an observer standing on the platform at a speed of \( 66 \, \text{m/s} \). The frequency observed by the observer will be (given speed of sound \( = 330 \, \text{m s}^{-1} \)) ______ \( \text{Hz} \).

A spherical drop of liquid splits into \( 1000 \) identical spherical drops. If \( u_i \) is the surface energy of the original drop and \( u_f \) is the total surface energy of the resulting drops, the (ignoring evaporation), \( \dfrac{u_f}{u_i} = \left( \dfrac{10}{x} \right) \). Then value of \( x \) is ________.

A body of mass \( 1 \, \text{kg} \) collides head on elastically with a stationary body of mass \( 3 \, \text{kg} \). After collision, the smaller body reverses its direction of motion and moves with a speed of \( 2 \, \text{m/s} \). The initial speed of the smaller body before collision is ________ \( \text{ms}^{-1} \).

Two cells are connected between points \( A \) and \( B \) as shown. Cell \( 1 \) has emf of \( 12 \, \text{V} \) and internal resistance of \( 3 \, \Omega \). Cell \( 2 \) has emf of \( 6 \, \text{V} \) and internal resistance of \( 6 \, \Omega \). An external resistor \( R \) of \( 4 \, \Omega \) is connected across \( A \) and \( B \). The current flowing through \( R \) will be ______ \( \text{A} \).

Two long parallel wires carrying currents \( 8 \, \text{A} \) and \( 15 \, \text{A} \) in opposite directions are placed at a distance of \( 7 \, \text{cm} \) from each other. A point \( P \) is at equidistant from both the wires such that the lines joining the point \( P \) to the wires are perpendicular to each other. The magnitude of magnetic field at \( P \) is _____ \( \times 10^{-6} \, \text{T} \). \( \left( \text{Given} : \sqrt{2} = 1.4 \right) \).

A series LCR circuit is connected to an AC source of \( 220 \, \text{V} \), \( 50 \, \text{Hz} \). The circuit contains a resistance \( R = 80 \, \Omega \), an inductor of inductive reactance \( X_L = 70 \, \Omega \) and a capacitor of capacitive reactance \( X_C = 130 \, \Omega \). The power factor of circuit is \( \dfrac{x}{10} \). The value of \( x \) is:

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio \( 3 : 2 \). The ratio of their nuclear sizes will be \( \left( \dfrac{x}{3} \right)^{\tfrac{1}{3}} \). The value of ‘\( x \)’ is:

An object is placed on the principal axis of convex lens of focal length \( 10 \, \text{cm} \) as shown. A plane mirror is placed on the other side of lens at a distance of \( 20 \, \text{cm} \). The image produced by the plane mirror is \( 5 \, \text{cm} \) inside the mirror. The distance of the object from the lens is ______ \( \text{cm} \).