Practice Questions

Q14.A velocity selector consists of electric field 𝐸= 𝐸 ^k and magnetic field 𝐵= 𝐵 ^j with 𝐵= 12 mT. The value 𝐸 required for an electron of energy 728eV moving along the positive x-axis to pass undeflected is (Given, mass of electron = 9 . 1 × 10-31 kg) (1) 192 kV m-1 (2) 192 mV m-1 (3) 9600 kV m-1 (4) 16 kV m-1

Q14.A metal surface is illuminated by a radiation of wavelength 4500 A . The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of 90° with the magnetic field. If it starts revolving in a circular path of radius 2 mm, the work function of the metal is approximately (1) 1. 36 eV (2) 1. 69 eV (3) 2. 78 eV (4) 2. 23 eV

Q14.A coil of inductance 1 H and resistance 100 Ω is connected to a battery of 6 V . Determine approximately : (a) The time elapsed before the current acquires half of its steady-state value (b) The energy stored in the magnetic field associated with the coil at an instant 15 ms after the circuit is switched on. (Given ln 2 = 0. 693, e −32 = 0. 25) (1) t = 10 ms; U = 2 mJ (2) t = 10 ms; U = 1 mJ (3) t = 7 ms; U = 1 mJ (4) t = 7 ms; U = 2 mJ

Q14.A series LCR circuit has L = 0. 01 H, R = 10 Ω and C = 1 μF and it is connected to ac voltage of amplitude (Vm) 50 V . At frequency 60% lower than resonant frequency, the amplitude of current will be approximately (1) 466 mA (2) 312 mA (3) 238 mA (4) 196 mA

Q14.A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be (Assume the coil to be short circuited.) (1) Doubled (2) The same (3) Quadrupled (4) Halved

Q15.If Electric field intensity of a uniform plane electro magnetic wave is given as E = −301. 6 sin(kz −ωt)ˆax + 452. 4 sin(kz −ωt)ˆay V m−1. Then, magnetic intensity H of this wave in A m−1 will be [Given : Speed of light in vacuum c = 3 × 108 m s−1 , Permeability of vacuum μ0 = 4π × 10−7 N A−2 ] (1) +0. 8 sin(kz −ωt)ˆay + 0. 8 sin(kz −ωt)ˆax (2) +1. 0 × 10−6 sin(kz −ωt)ˆay + 1. 5 × 10−6(kz −ωt)ˆax (3) −0. 8 sin(kz −ωt)ˆay −1. 2 sin(kz −ωt)ˆax (4) −1. 0 × 10−6 sin(kz −ωt)ˆay −1. 5 × 10−6 sin(kz −ωt)ˆa λ, then this phenomenon is called as

Q15.Two long parallel conductors S1 and S2 are separated by a distance 10 cm and carrying currents of 4 A and 2 A respectively. The conductors are placed along x-axis in X −Y plane. There is a point P located between the conductors (as shown in figure). + m s−1 ; where ˆi & A charge particle of 3π coulomb is passing through the point P with velocity →v= (2ˆi 3ˆj) ˆj represents unit vector along x & yaxis respectively. The force acting on the charge particle is 4π × + N. The value of x is 10−5(−xˆi 2ˆj) (1) 2 (2) 1 (3) 3 (4) −3

Q17.For an object placed at a distance 2. 4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm from the lens. A glass plate of refractive index 1. 5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen? (1) 0. 8 m (2) 3. 2 m (3) 1. 2 m (4) 5. 6 m

Q21.In an experiment of determine the Young's modulus of wire of a length exactly 1 m, the extension in the length of the wire is measured as 0. 4 mm with an uncertainty of ±0. 02 mm when a load of 1 kg is applied. The JEE Main 2022 (26 Jul Shift 1) JEE Main Previous Year Paper diameter of the wire is measured as 0. 4 mm with an uncertainty of ±0. 01 mm. The error in the measurement of Young's modulus (ΔY) is found to be x × 1010 N m−2 . The value of x is _____ .

Q21.A pendulum of length 2 m consists of a wooden bob of mass 50 g . A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed v and the bob just completes the 3 vertical circle. The value of v is _____ m s−1 (if g = 10 m s−2 ). JEE Main 2022 (27 Jun Shift 1) JEE Main Previous Year Paper

Q22.A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be 1 √xgh m s−1 . The value of x (rounded off to the nearest integer) is _____. 2

Q22.A small spherical ball of radius 0. 1 mm and density 104 kg m−3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it JEE Main 2022 (29 Jun Shift 2) JEE Main Previous Year Paper continue to fall with same constant velocity inside water, then the value of h will be ____ m. (Given g = 10 m s−2 , viscosity of water = 1. 0 × 10−5 N‐s m−2 ).

Q25.An observer is riding on a bicycle and moving towards a hill at 18 km h-1. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is 640 Hz and velocity of the sound in air is 320 m s-1, the beat frequency between the two sounds heard by observer will be _____ Hz.

Q26.The potential energy of a particle of mass 4 kg in motion along the x-axis is given by U = 4(1 −cos 4x) J. The time period of the particle for small oscillation (sin θ ≃θ) ( Kπ ) s. The value of K is _____ .

Q27.In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be √x2 . The value of x is _____ .

Q27.A ray of light is incident at an angle of incidence 60° on the glass slab of refractive index √3. After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is 4√3 cm . The thickness of the glass slab is _____ cm .

Q28.A convex lens of focal length 20 cm is placed in front of convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is _____ cm.

Q29.In a hydrogen spectrum λ be the wavelength of first transition line of Lyman series. The wavelength difference will be " aλ" between the wavelength of 3rd transition line of Paschen series and that of 2nd transition line of Balmer Series where a = _____.

Q29.An object ' O' is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the figure. The object starts moving towards the mirror at a speed 2 cm s−1 . The position of the image from the mirror after 10 s will be at _____ cm.

Q29.The X −Y plane be taken as the boundary between two transparent media M1 and M2 . M1 in Z ≥0 has a refractive index of √2 and M2 with Z < 0 has a refractive index of √3. A ray of light travelling in M1 along → the direction given by the vector A = 4√3i −3√3j −5ˆk, is incident on the plane of separation. The value of difference between the angle of incident in M1 and the angle of refraction in M2 will be _____ degree.

Q29.An AC source is connected to an inductance of 100 mH , a capacitance of 100 μF and a resistance of 120 Ω as shown in figure. The time in which the resistance having a thermal capacity 2 J ∘C−1 will get heated by 16°C is _____ s.

Q29.A Zener of breakdown voltage VZ = 8 V and maximum Zener current, IZM = 10 mA is subjected to an input voltage Vi = 10 V with series resistance R = 100 Ω . In the given circuit RL represents the variable load resistance. The ratio of maximum and minimum value of RL is _____ .

Q30.The current in a coil of self inductance 𝐿= 2 . 0 H is increasing according to the law 𝑖= 2sin𝑡2. Find the amount of energy spent (in J) during the period when the current changes from 0 to 2 A.

Q30.A modulating signal 2sin6 . 28 × 106𝑡 is added to the carrier signal 4sin12 . 56 × 109𝑡 for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will be _____ MHz.

Q32.Bonding in which of the following diatomic molecule(s) become(s) stronger, on the basis of MO Theory, by removal of an electron? (A) NO (B) N2 (C) O2 (D) C2 (E) B2 Choose the most appropriate answer from the options given below : (1) A, B, C only (2) B, C, E only (3) A, C only (4) D only JEE Main 2022 (25 Jun Shift 1) JEE Main Previous Year Paper