JEE MainsJEE AdvanceBITSAT

JEE Mains | PYQ

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as \( 10\,\mathrm{V} \) and \( 5\,\mathrm{A} \), respectively. The least counts of voltmeter and ammeter are \( 500\,\mathrm{mV} \) and \( 200\,\mathrm{mA} \), respectively. The estimated error in the resistance measurement is __________ \( \Omega \) .

A mass of \( 1 \, \text{kg} \) is kept on an inclined plane with \( 30^\circ \) inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of \( 4 \, \text{m/s} \). The work done by the frictional force in time \( 2 \, \text{s} \) is __________ \( \text{J} \). (Take \( g=10 \, \text{m/s}^2 \))

The velocity \( (v) \) versus time \( (t) \) plot of a particle is shown in the figure, for a time interval of \( 40\,\mathrm{s} \). The total distance travelled by the particle and the average velocity during this period are, respectively ________.

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first \( 2 \, \text{s} \) it rotates through an angle \( \theta_1 \) and in the next \( 2 \, \text{s} \) it rotates through an angle \( \theta_2 \). The ratio \( \frac{\theta_2}{\theta_1} \) is ______________ .

An object of uniform density rolls up the curved path with the velocity \( v_0 \) as shown in the figure. If the maximum height attained by an object is \( \frac{7 v_0^2}{10 g} \) (\( g \) = acceleration due to gravity, the object is a ______________ .

A body of mass \( m \) is taken from the surface of earth to a height equal to twice the radius of earth \( (R_e) \). The increase in potential energy will be ____________ . (\( g \) is acceleration due to gravity at the surface of earth)

Eight mercury drops, each of radius \( r \), coalesce to form a bigger drop. The surface energy released in this process is _____________________ . (\( S \) is the surface tension of mercury).

An ideal gas at pressure \( P \) and temperature \( T \) is expanding such that \( P T^3 = \text{constant} \). The coefficient of volume expansion of the gas is ____________ .

Match List – I with List – II.

Choose the correct answer from the options given below:

A metal rod of length \( L \) rotates about one end at origin with a uniform angular velocity \( \omega \). The magnetic field radially falls off as \( B(r)=B_0 e^{-\lambda r} \), \( \lambda \) being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is:

Under steady state condition the potential difference across the capacitor in the circuit is ________ \( \text{V} \).

A particle of charge \( q \) and mass \( m \) is projected from origin with an initial velocity \( \vec{v}=\left(\dfrac{v_0}{\sqrt{2}}\hat{x}+\dfrac{v_0}{\sqrt{2}}\hat{y}\right) \).
There exists a uniform magnetic field \( \vec{B}=B_0\hat{z} \) and a space varying electric field \( \vec{E}=E_0 e^{-\lambda x}\,\hat{x} \) within the region \( 0\le x\le L \). After travelling a distance such that x-coordinate has changed from \( x=0 \) to \( x=L \), the change in the kinetic energy is ____________ .

Given below are two statements one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The electromagnetic wave exerts pressure on the surface on which they are allowed to fall.
Reason (R): There is no mass associated with the electromagnetic waves.
In the light of the above statements, choose the correct answer from the options given below:

A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses?

An object \( AB \) is placed \( 15 \, \text{cm} \) on the left of a convex lens \( P \) of focal length \( 10 \, \text{cm} \). Another convex lens \( Q \) is now placed \( 15 \, \text{cm} \) right of lens \( P \). If the focal length of lens \( Q \) is \( 15 \, \text{cm} \), the final image is ____________ .

The maximum intensity in a Young’s double slit experiment is \( I_0 \). Distance between the slits \( (d) \) is \( 5\lambda \), where \( \lambda \) is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at \( D = 10d \) is ________________ .

An electron is travelling with a velocity \( v \) in free space and when it enters a medium, its velocity is reduced by \( 20\% \). The de Broglie wavelength of electron in the medium is \( \alpha \lambda_0 \), where \( \lambda_0 \) is its de Broglie wavelength in free space. The value of \( \alpha \) is ________________ .

Assuming the experimental mass of \( ^{12}_{6}\mathrm{C} \) as \( 12\,u \), the mass defect of \( ^{12}_{6}\mathrm{C} \) atom is ____________ \( \text{MeV}/c^2 \).
(Mass of proton \( = 1.00727\,u \). mass of neutron \( = 1.0866\,u \), \( 1\,u = 931.5\, \text{MeV}/c^2 \) and \( c \) is the speed of the light in vacuum).

In a semiconductor p-n diode, the doping concentrations on p-side and n-side are \( 10^{15} \) \( \text{atoms}/\text{cm}^3 \) and \( 10^{18} \) \( \text{atoms}/\text{cm}^3 \), respectively. Which one of the following statements is true?

A copper wire of length \( 3 \, \text{m} \) is stretched by \( 3 \, \text{mm} \) by applying an external force. The volume of the wire is \( 600 \times 10^{-6} \, \text{m}^3 \). The elastic potential energy stored in the wire in stretched condition would be ____________ \( \text{J} \).
(Given Young modules of copper\( = 1.1 \times 10^{11}\,\mathrm{N/m^2}\)

The heat extracted out of \( x \) gram of water initially at \( 50^\circ \text{C} \) to cool it down to \( 0^\circ \text{C} \) is sufficient to evaporate \( (1000 - x) \) gram of water also initially at \( 50^\circ \text{C} \). The value of \( x \) (closest integer) is ____________ .
(Take latent heat of water \( 2256 \, \text{kJ/kg} \cdot \text{K} \), specific heat capacity of water \( 4200 \, \text{J/kg} \cdot \text{K} \))

A series LCR circuit with \( R = 20 \, \Omega \), \( L = 1.6 \, \text{H} \) and \( C = 40 \, \mu \text{F} \) is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is ______________ \( \Omega \).

When an external resistance of \( 5 \, \Omega \) is connected across terminals of a cell, a current of \( 0.25 \, \text{A} \) flows through it. When the \( 5 \, \Omega \) resistor is replaced by a \( 2 \, \Omega \) resistor, a current of \( 0.5 \, \text{A} \) flows through it. The internal resistance of the cell is ___________ \( \Omega \).

A circular loop of radius \( 20 \, \text{cm} \) and resistance \( 2 \, \Omega \) is placed in a time varying magnetic field \( \vec{B} = (2t^{2} + 2t + 3)\,\text{T} \). At \( t = 0 \), for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at \( t = 3 \, \text{s} \) is \( \dfrac{\alpha}{50} \, \text{A} \). The value of \( \alpha \) is ____________. (Take \( \pi = \dfrac{22}{7} \))