JEE MainsJEE AdvanceBITSAT

JEE Mains | PYQ

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): In an uniform magnetic field, speed and energy remains the same for a moving charged particle.
Reason (R): Moving charged particle experiences magnetic force perpendicular to its direction of motion.

Two identical cells each of emf \( 1.5 \, \text{V} \) are connected in parallel across a parallel combination of two resistors each of resistance \( 20 \, \Omega \). A voltmeter connected in the circuit measures \( 1.2 \, \text{V} \). The internal resistance of each cell is:

Identify the pair of physical quantities which have different dimensions:

A projectile is projected with velocity of \( 25 \, \text{m/s} \) at an angle \( \theta \) with the horizontal. After \( t \) seconds its inclination with horizontal becomes zero. If \( R \) represents horizontal range of the projectile, the value of \( \theta \) will be: [use \( g = 10 \, \text{m/s}^{2} \)]

A block of mass \( 10 \, \text{kg} \) starts sliding on a surface with an initial velocity of \( 9.8 \, \text{m s}^{-1} \). The coefficient of friction between the surface and block is \( 0.5 \). The distance covered by the block before coming to rest is:[use \( g = 9.8 \, \text{m s}^{-2} \)]

A boy ties a stone of mass \( 100 \, \text{g} \) to the end of a \( 2 \, \text{m} \) long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of \( 80 \, \text{N} \). If the maximum speed with which the stone can revolve is \( \frac{K}{\pi} \, \text{rev.}/\text{min} \). The value of \( K \) is : (Assume the string is massless and unstretchable)

A vertical electric field of magnitude \( 4.9 \times 10^{5} \, \text{N}/\text{C} \) just prevents a water droplet of a mass \( 0.1 \, \text{g} \) from falling. The value of charge on the droplet will be: (Given \( g = 9.8 \, \text{m}/\text{s}^{2} \))

A particle experiences a variable force \( \vec{F} = \left( 4x \, \hat{i} + 3y^{2} \, \hat{j} \right) \) in a horizontal \( x\text{-}y \) plane. Assume distance in meters and force is newton. If the particle moves from point \( (1, 2) \) to point \( (2, 3) \) in the \( x\text{-}y \) plane, then Kinetic Energy changes by:

The approximate height from the surface of earth at which the weight of the body becomes \( \frac{1}{3} \) of its weight on the surface of earth is: [Radius of earth \( R = 6400 \, \text{km} \) and \( \sqrt{3} = 1.732 \)]

A resistance of \( 40 \, \Omega \) is connected to a source of alternating current rated \( 220 \, \text{V} \), \( 50 \, \text{Hz} \). Find the time taken by the current to change from its maximum value to the rms value:

The equations of two waves are given by: \( y_{1} = 5 \sin 2\pi(x - vt) \, \text{cm} \) ; \( y_{2} = 3 \sin 2\pi(x - vt + 1.5) \, \text{cm} \) These waves are simultaneously passing through a string. The amplitude of the resulting wave is:

A plane electromagnetic wave travels in a medium of relative permeability \( 1.61 \) and relative permittivity \( 6.44 \). If magnitude of magnetic intensity is \( 4.5 \times 10^{-2} \, \mathrm{A \, m^{-1}} \) at a point, what will be the approximate magnitude of electric field intensity at the point?
(Given: Permeability of free space \( \mu_{0} = 4 \pi \times 10^{-7} \, \mathrm{N \, A^{-2}} \) , speed of light in vacuum \( c = 3 \times 10^{8} \, \mathrm{m \, s^{-1}} \) )

Choose the correct option from the following options given below:

Nucleus A is having mass number \( 220 \) and its binding energy per nucleon is \( 5.6 \, \mathrm{MeV} \). It splits in two fragments 'B' and 'C' of mass numbers \( 105 \) and \( 115 \). The binding energy of nucleons in 'B' and 'C' is \( 6.4 \, \mathrm{MeV} \) per nucleon. The energy \( Q \) released per fission will be:

A baseband signal of \( 3.5 \, \mathrm{MHz} \) frequency is modulated with a carrier signal of \( 3.5 \, \mathrm{GHz} \) frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal?

A Carnot engine whose heat sinks at \( 27^\circ \mathrm{C} \), has an efficiency of \( 25\% \). By how many degrees should the temperature of the source be changed to increase the efficiency by \( 100\% \) of the original efficiency?

A parallel plate capacitor is formed by two plates each of area \( 30\pi \, \mathrm{cm^{2}} \) separated by \( 1 \, \mathrm{mm} \). A material of dielectric strength \( 3.6 \times 10^{7} \, \mathrm{V \, m^{-1}} \) is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is \( 7 \times 10^{-6} \, \mathrm{C} \), the value of dielectric constant of the material is:
[Use \( \dfrac{1}{4\pi \varepsilon_{0}} = 9 \times 10^{9} \, \mathrm{N \, m^{2} \, C^{-2}} \) ]

The magnetic field at the centre of a circular coil of radius \( r \), due to current \( I \) flowing through it, is \( B \). The magnetic field at a point along the axis at a distance \( \frac{r}{2} \) from the centre

Two metallic blocks \( M_1 \) and \( M_2 \) of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of \( M_2 \) is \( K \) then the thermal conductivity of \( M_1 \) will be: [Assume steady state heat conduction]

\( 0.056 \, \text{kg} \) of Nitrogen is enclosed in a vessel at a temperature of \( 127^\circ \text{C} \). The amount of heat required to double the speed of its molecules is ________ \( \text{k cal} \).
(Take \( R = 2 \, \text{cal mol}^{-1}\,\text{K}^{-1} \))

Two identical thin biconvex lenses of focal length \( 15 \, \text{cm} \) and refractive index \( 1.5 \) are in contact with each other. The space between the lenses is filled with a liquid of refractive index \( 1.25 \). The focal length of the combination is ________ \( \text{cm} \).

A transistor is used in common-emitter mode in an amplifier circuit. When a signal of \( 10 \, \text{mV} \) is added to the base-emitter voltage, the base current changes by \( 10 \, \mu\text{A} \) and the collector current changes by \( 1.5 \, \text{mA} \). The load resistance is \( 5 \, \text{k}\Omega \). The voltage gain of the transistor will be ________.

As shown in the figure an inductor of inductance \( 200 \, \text{mH} \) is connected to an AC source of emf \( 220 \, \text{V} \) and frequency \( 50 \, \text{Hz} \). The instantaneous voltage of the source is \( 0 \, \text{V} \) when the peak value of current is \( \frac{\sqrt{a}}{\pi} \, \text{A} \). The value of \( a \) is ________.

Sodium light of wavelengths \( 650 \, \text{nm} \) and \( 655 \, \text{nm} \) is used to study diffraction at a single slit of aperture \( 0.5 \, \text{mm} \). The distance between the slit and the screen is \( 2.0 \, \text{m} \). The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is _________ \( \times 10^{-5} \, \text{m} \).

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is \( v_{1} \). When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes \( v_{2} \). If \( v_{2} = x \, v_{1} \), the value of \( x \) will be ______________.

From the top of a tower, a ball is thrown vertically upward which reaches the ground in \( 6 \, \text{s} \). A second ball thrown vertically downward from the same position with the same speed reaches the ground in \( 1.5 \, \text{s} \). A third ball released, from the rest from the same location, will reach the ground in _________ \( \text{s} \).

A ball of mass \( 100 \, \text{g} \) is dropped from a height \( h = 10 \, \text{cm} \) on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance \( \frac{h}{2} \). The spring constant is ______________ \( \text{N m}^{-1} \). (Use \( g = 10 \, \text{m s}^{-2} \))

In a potentiometer arrangement, a cell gives a balancing point at \( 75 \, \text{cm} \) length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf's of two cells respectively is \( 3:2 \), the difference in the balancing length of the potentiometer wire in above two cases will be ________ \( \text{cm} \).

A metre scale is balanced on a knife edge at its centre. When two coins, each of mass \( 10 \, \text{g} \) are put one on the top of the other at the \( 10.0 \, \text{cm} \) mark the scale is found to be balanced at \( 40.0 \, \text{cm} \) mark. The mass of the metre scale is found to be \( x \times 10^{-2} \, \text{kg} \). The value of \( x \) is __________.