Practice Questions

Q14.A conducting loop of radius cm is placed perpendicular to a uniform magnetic field of 0 . 5 T. The √𝜋 magnetic field is decreased to zero in 0 . 5 s at a steady rate. The induced emf in the circular loop at 0 . 25 s is: (1) emf = 1mV (2) emf = 10mV (3) emf = 100mV (4) emf = 5mV

Q14.The displacement equations of two interfering waves are given by y1 = 10 sin (ωt + π3 ) cm, cm respectively. The amplitude of the resultant wave is _____ cm. y2 = 5[sin (ωt) + √3 cos ωt]

Q14.In the given circuit, the current I through the battery will be (1) 2. 5 A (2) 1 A (3) 2 A (4) 1. 5 A

Q14.A person observes two moving trains, A reaching the station and B leaving the station with equal speed of 30 m s−1 . If both trains emit sounds with frequency 300 Hz, (Speed of sound : 330 m s−1 ) approximate difference of frequencies heard by the person will be : (1) 33 Hz (2) 55 Hz (3) 80 Hz (4) 10 Hz

Q14.The free space inside a current carrying toroid is filled with a material of susceptibility 2 × 10-2. The percentage increase in the value of magnetic field inside the toroid will be (1) 0 . 2% (2) 0 . 1% (3) 2% (4) 1%

Q14.Match the List-I with List-II. List I List II A AC generator I Presence of both L and C B Transformer II Electromagnetic Induction C Resonance phenomenon to occur III Quality factor D Sharpness of resonance IV Mutual Inductance Choose the correct answer from the options given below: (1) A-IV, B-II, C-I, D-III (2) A-II, B-I, C-III, D-IV (3) A-II, B-IV, C-I, D-III (4) A-IV, B-III, C-I, D-II

Q14.The energy of an electromagnetic wave contained in a small volume oscillates with (1) Double the frequency of the wave (2) The frequency of the wave (3) Half the frequency of the wave (4) Zero frequency

Q14.A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be (1) 1 : 1 (2) 1 : 3 (3) 2 : 1 (4) 1 : 4

Q14.Given below are two statements: Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor. Statement II: An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non- zero power factor. In the light of above statements, choose the correct answer from the options given below: (1) Statement I is false but statement II is true (2) Statement I is true but statement II is false (3) Both Statement I and Statement II are false (4) Both Statement I and Statement II are true

Q14.A particle executes simple harmonic motion between x = –A and x = +A. If time taken by particle to go from x = 0 to A2 is 2 s; then time taken by particle in going from x = A2 to A is: (1) 3 s (2) 2 s (3) 1. 5 s (4) 4 s

Q14.The velocity of a particle executing SHM varies with displacement ( x) as 4v2 = 50–x2 . The time period of oscillations is x 7 s. The value of x is ______. [Take π = 227 ]

Q14.A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental of 180 Hz will be _____ cm

Q15.Two charges of each magnitude 0. 01 C and separated by a distance of 0. 4 mm constitute an electric dipole. If → → the dipole is placed in an uniform electric field E of 10 dyne ⋅C−1 making 30∘ angle with E, the magnitude of torque acting on dipole is: (1) 4. 0 × 10−10 N m (2) 1. 0 × 10−8 N m (3) 1. 5 × 10−9 N m (4) 2. 0 × 10−10 N m

Q15.If V is the gravitational potential due to sphere of uniform density on its surface, then its value at the centre of sphere will be: (1) 4 V (2) V 3 2 (3) V (4) 3V 2

Q15.If →𝐸 and →𝐾 represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by: (𝜔- angular frequency) 1 → → → → (1) 𝐾× 𝐸 (2) 𝜔𝐸× 𝐾 𝜔 (3) 𝜔→𝐾× →𝐸 (4) →𝐾× →𝐸

Q15.A 12 V battery connected to a coil of resistance 6 Ω through a switch, drives a constant current in the circuit. The switch is opened in 1 ms. The emf induced across the coil is 20 V. The inductance of the coil is : (1) 10 mH (2) 8 mH (3) 5 mH (4) 12 mH

Q15. As per the given graph, choose the correct representation for curve 𝐴 and curve 𝐵 {Where 𝑋𝐶= Reactance of pure capacitive circuit connected with A.C. source 𝑋𝐿= Reactance of pure inductive circuit connected with A.C. source 𝑅= Impedance of pure resistive circuit connected with A.C. source 𝑍= Impedance of the 𝐿𝐶𝑅 series circuit } (1) 𝐴= 𝑋𝐶, 𝐵= 𝑅 (2) 𝐴= 𝑋𝐿, 𝐵= 𝑅 (3) 𝐴= 𝑋𝐿, 𝐵= 𝑍 (4) 𝐴= 𝑋𝐶, 𝐵= 𝑋𝐿

Q15.The electric potential at the centre of two concentric half rings of radii R1 and R2 , having same linear charge density λ is . (1) 2λ (2) λ ∈0 2∈0 (3) λ (4) λ 4∈0 ∈0

Q15.A monochromatic light wave with wavelength 𝜆1 and frequency 𝜈1 in air enters another medium. If the angle of incidence and angle of refraction at the interface are 45° and 30° respectively, then the wavelength 𝜆2 and frequency 𝜈2 of the refracted wave are: (1) 𝜆2 = √2𝜆1, 𝜈2 = 𝜈1 (2) 𝜆2 = 𝜆1, 𝜈2 = 1 √2𝜈1 (3) 𝜆2 = 𝜆1, 𝜈2 = √2𝜈1 (4) 𝜆2 = 1 𝜈2 = 𝜈1 √2𝜆1,

Q15.The ratio of intensities at two points P and Q on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are π and π respectively are 3 2, (1) 2 : 3 (2) 1 : 3 (3) 3 : 1 (4) 3 : 2

Q15.For a certain organ pipe, the first three resonance frequencies are in the ratio of 1 : 3 : 5 respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is 324 m s–1 the length of the organ pipe is _____ m .

Q15.A cubical volume is bounded by the surfaces x = 0, x = a, y = 0, y = a, z = 0, z = a . The electric field in → the region is given by E = E0xˆi. Where E0 = 4 × 104 NC−1 m−1 . If a = 2 cm , the charge contained in the cubical volume is Q × 10–14 C . The value of Q is ______. (Take ϵ0 = 9 × 10−12 C2 N−1m−2 )

Q15.Given below are two statements: Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface JEE Main 2023 (13 Apr Shift 2) JEE Main Previous Year Paper Statement II : Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light In the light of above statements, choose the correct answer from the options given below (1) Statement I is false but Statement II is true (2) Statement I is true but Statement II is false (3) Both Statement I and Statement II are true (4) Both Statement I and Statement II are false

Q15.As shown in the figure, a point charge Q is placed at the centre of conducting spherical shell of inner radius a and outer radius b. The electric field due to charge Q in three different regions I, II and III is given by : (I : r < a, II : a < r < b, III : r > b) (1) EI = 0, EII = 0, EIII ≠0 (2) EI ≠0, EII = 0, EIII ≠0 (3) EI ≠0, EII = 0, EIII = 0 (4) EI = 0, EII = 0, EIII = 0

Q15.Given below are two statements: Statement I: Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an 𝐴𝐶 source, when resonance occurs. Statement II: Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage. In the light of the above statements, choose the correct answer from the options given below: (1) Statement I is false but Statement II is true (2) Both Statement I and Statement II are true (3) Statement I is true but Statement II is false (4) Both Statement I and Statement II are false