JEE Main 2022 June 24 Shift 1 Paper & Solutions - JEE MCQ

Identify the pair of physical quantities which have different dimensions.

A projectile is projected with velocity of 25 m/s at an angle θ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of θ will be
[use g = 10 m/s²]

A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms^-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 ms^-2]

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

A vertical electric field of magnitude 4.9 × 10⁵ N/C prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be (Given g = 9.8 m/s²)

A particle experiences a variable force in a horizontal x-y plane. Assume distance in meters and force in newton. If the particle moves from point (1, 2) to point (2, 3) in the x-y plane; then kinetic energy changes by

The approximate height from the surface of earth at which the weight of the body becomes 1/3 of its weight on the surface of earth is
[Radius of earth R = 6400 km and √3 = 1.732]

A resistance of 40 Ω is connected to a source of alternating current rated 220 V, 50 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:
y₁ = 5 sin 2π(x - vt) cm
y₂ = 3 sin 2π(x - vt + 1.5) cm
These waves simultaneously pass 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 × 10^-2 Am^-1 at a point, what will be the approximate magnitude of electric field intensity at that point?
(Given: Permeability of free space  speed of light in vacuum c = 3 × 10⁸ ms^-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 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 MeV per nucleon. The energy Q released per fission will be:

A baseband signal of 3.5 MHz frequency is modulated with a carrier signal of 3.5 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°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 30π cm² separated by 1 mm. A material of dielectric strength 3.6 × 107 Vm-1 is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is 7 × 10^-6 C, the value of dielectric constant of the material is:
[Use  Nm² C^-2]

he 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 r/2 from the centre is:

Two metallic blocks M₁ and M₂ of the same area of cross-section are connected to each other (as shown in the figure). If the thermal conductivity of M₂ is K, then the thermal conductivity of M₁ will be:
[Assume steady state heat conduction]

0.056 kg of Nitrogen is enclosed in a vessel at a temperature of 127°C. The amount of heat required to double the speed of its molecules is ___ k cal. (Take R = 2 cal mol^–1 K^–1)(In Integers)

Two identical thin biconvex lenses of focal length 15 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 ___ cm.(In Integers)

A transistor is used in common-emitter mode in an amplifier circuit. When a signal of 10 mV is added to the base-emitter voltage, the base current changes by 10 μA and the collector current changes by 1.5 mA. The load resistance is 5 kΩ. The voltage gain of the transistor will be ___.(In Integers)

As shown in the figure, an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is √a/πA. The value of a is ___.(In Integers)

Sodium light of wavelengths 650 nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm. The distance between the slit and the screen is 2.0 m. The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is _____ × 10^-5 m. (In Integers)

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is v₁. When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes v₂. If v₂ = xv₁, the value of x will be ________. (In Integers)

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

A ball of mass 100 g is dropped from a height h = 10 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 h/2. The spring constant is ______ Nm^-1. (Use g = 10 ms^-2)(In Integers)

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

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