Practice Questions

Q27.An electromagnetic wave of frequency 5GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2 . Its velocity in this medium is _______ × 107 m s-1.

Q27.The total charge enclosed in an incremental volume of 2 × 10−9 m3 located at the origin is nC, if electric flux density of its field is found as D = e−x sin yˆi −e−x cosyˆj + 2zˆk C m−2

Q27.The value of aluminium susceptibility is 2 . 2 × 10-5. The percentage increase in the magnetic field if space 𝑥 within a current carrying toroid is filled with aluminium is 104. Then the value of 𝑥 is

Q27.Two small spheres each of mass 10 mg are suspended from a point by threads 0. 5 m long. They are equally charged and repel each other to a distance of 0. 20 m. The charge on each of the sphere is 21a × 10−8 C. The value of a will be ___.[Given g = 10 m s−2 ]

Q27.A cylindrical wire of radius 0. 5 mm and conductivity 5 × 107 S m−1 is subjected to an electric field of 10 mV m−1. The expected value of current in the wire will be x3π mA. The value of x is _________.

Q27.A parallel plate capacitor has plate area 100 m2 and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10 . The resultant capacitance of the system is x pF. The value of ε0 = 8. 85 × 10−12 F m−1 . The value of x to the nearest integer is ______.

Q27.Cross-section view of a prism is the equilateral triangle 𝐴𝐵𝐶 shown in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from 𝑃 (midpoint of 𝐵𝐶) to 𝐴 is ___________ × 10-10 s . (Given, speed of light in vacuum √3 = 3 × 108 m s-1 and cos30° = ) 2

Q27.In the given circuit of potentiometer, the potential difference E across AB( 10 m length) is larger than E1 and E2 as well. For key K1 (closed), the jockey is adjusted to touch the wire at point J1 so that there is no deflection in the galvanometer. Now the first battery (E1) is replaced by second battery (E2) for working by making K1 open and K2 closed. The galvanometer gives then null deflection at J2 . The value of E1E2 is a2 , where a =_______ .

Q27.A 2μF capacitor C1 is first charged to a potential difference of 10 V using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor C2 of 8μF. The charge in C2 on equilibrium condition is μC. (Round off to the Nearest Integer)

Q27.In the given figure the magnetic flux through the loop increases according to the relation ϕB(t) = 10t2 + 20t , where ϕB is in milliwebers and t is in seconds. The magnitude of current through R = 2 Ω resistor at t = 5 s is _____ mA.

Q27.A certain metallic surface is illuminated by monochromatic radiation of wavelength λ . The stopping potential for photoelectric current for this radiation is 3 V 0. If the same surface is illuminated with a radiation of wavelength 2λ, the stopping potential is V0. The threshold wavelength of this surface for photoelectric effect is___________ λ.

Q27.A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12 V between its plates. The charging battery is now disconnected and a porcelain plate with k = 7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of _______ pJ. (Assume no friction)

Q27.A closed organ pipe of length L and an open organ pipe contain gases of densities ρ1 and ρ2 respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is x , where x is _______. 3 L√ρ1ρ2 (Round off to the Nearest Integer)

Q27.From the given data, the amount of energy required to break the nucleus of aluminium 2713Al is __________ x × 10−3 J Mass of neutron = 1. 00866 u Mass of proton = 1. 00726 u Mass of Aluminium nucleus = 27. 18846 u (Assume 1 u corresponds to x J of energy) (Round off to the nearest integer) of its initial value in 30 years. The half-life of

Q27.The frequency of a car horn encountered a change from 400 Hz to 500 Hz . When the car approaches a vertical wall. If the speed of sound is 330 m s−1 . Then the speed of car is ___ km h−1 .

Q27.A circular coil of radius 8. 0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s−1 in a uniform horizontal magnetic field of 3. 0 × 10−2 T . The maximum emf induced in the coil will be _______ ×10−2 volt (rounded off to the nearest integer).

Q27.In a series LCR resonant circuit, the quality factor is measured as 100 . If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be _______

Q27.A point source of light S , placed at a distance 60 cm infront of the centre of a plane mirror of width 50 cm, hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance 1. 2 m from it (see in the figure). The distance between the extreme points where he can see the image of the light source in the mirror is__ cm

Q28.Seawater at a frequency f = 9 × 102 Hz , has permittivity ε = 80ε0 and resistivity ρ = 0. 25 Ω m . Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source V (t) = V0 sin(2πft). Then the conduction current density becomes 10x times the displacement current density after time t = 8001 s. The value of x is _______ (Given : 1 = 9 × 109 N m2 4πε0 C−2)

Q28.A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t = 0, then the energy stored in the coil JEE Main 2021 (25 Feb Shift 1) JEE Main Previous Year Paper after 4 s in J ,

Q28.In an electric circuit, a call of certain emf provides a potential difference of 1. 25 V across a load resistance of 5 Ω. However, it provides a potential difference of 1 V across a load resistance of 2 Ω.The emf of the cell is given by x V. Then the value of x is . 10 = √3) suffers minimum deviation. It is found that the angle of

Q28.Two identical conducting spheres with negligible volume have 2. 1 nC and −0. 1 nC charges, respectively. They are brought into contact and then separated by a distance of 0. 5 m. The electrostatic force acting between the spheres is ___ ×10−9 N . [Given : 4πε0 = 9×1091 SI unit]

Q28.A radioactive substance decays to ( 161 )th of its initial activity in 80 days. The half life of the radioactive substance expressed in days is ________.

Q28.In an LCR series circuit, an inductor 30 mH and a resistor 1 Ω are connected to an AC source of angular frequency 300 rad s−1. The value of capacitance for which the current leads the voltage by 45° is 1 × 10−3 F . Then the value of x is x

Q28.A plane electromagnetic wave with a frequency of 30 MHz travels in free space. At a particular point in space and time, the electric field is 6 V m−1 . The magnetic field at this point will be x × 10−8 T. The value of x is,