Practice Questions

Q10.A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 104N. When the tension is changed to T, the velocity changed to 2v . The value of T is close to: (1) 2.50 × 104N (2) 5.15 × 103 N (3) 30.5 × 104 N (4) 10.2 × 102 N

Q10.Three charged particles A , B and C with charges −4q, 2q and −2q are present on the circumference of a circle of radius d. The charged particles A, C and centre O of the circle formed an equilateral triangle as shown JEE Main 2020 (08 Jan Shift 1) JEE Main Previous Year Paper in the figure. The electric field at the point O is (1) √3q (2) 2√3q πε0d2 πε0d2 (3) √3q (4) 3√3q 4πε0d2 4πε0d2 →

Q10.Assume that the displacement (s) of air is proportional to the pressure difference (Δp) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air (ρ) and the frequency (f). If Δp~10 Pa, n~300 m/s, p~1 kg/m3 f~1000Hz, then s will be of the order of (take the multiplicative constant to be 1 ) (1) 1003 mm (2) 10 mm (3) 101 mm (4) 1 mm

Q11.A two point charges 4q and –q are fixed on the x -axis at x = −d2 and x = d2 , respectively. If the third point charge ‘ q ’ is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will: JEE Main 2020 (04 Sep Shift 1) JEE Main Previous Year Paper (1) Increase by 3q2 (2) Increase by 2q2 4π∈0d 3π∈0d (3) decrease by q2 (4) decrease by 4q2 4π∈0d 3π∈0d

Q11.Two identical strings X and Z made of same material have tension TX and TZ in then if their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio TX/TZ is : (1) 2. 25 (2) 0. 44 (3) 1. 25 (4) 1. 5

Q11.An electric dipole of moment →p = (−ˆi −3ˆj 2ˆk) to this dipole at→r= +ˆi + 3ˆj + 5ˆk (note that →r∙→p = 0 ) is parallel to: (1) (+ˆi −3ˆj −2ˆk) (2) (−ˆi + 3ˆj −2ˆk) + (3) (+ˆi + 3ˆj −2ˆk) (4) (−ˆi −3ˆj 2ˆk)

Q11.In the circuit shown, charge on the 5μF capacitor is : (1) 18. 00μC (2) 10. 90μC (3) 16. 36μC (4) 5. 45μC

Q11.A potentiometer wire PQ of 1m length is connected to a standard cell E1 . Another cell E2 of emf 1. 02 V is connected with a resistance ' r' and switch S (as shown in figure). With switch S open, the null position is obtained at a distance of 49 cm from Q. The potential gradient in the potentiometer wire is : (1) 0. 02 V/ cm (2) 0. 01 V/ cm (3) 0. 03 V/ cm (4) 0. 04 V/ cm JEE Main 2020 (02 Sep Shift 2) JEE Main Previous Year Paper

Q11.Two identical electric point dipoles have dipole have dipole moments →p1 = pˆi and →p2 = −pˆi and are held on the x-axis at distance ' a ' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is ' m', their speed when they are infinitely far apart is : (1) P 1 (2) P 1 a √ πε0 ma a √ 2πε0 ma (3) P 2 (4) P 3 a √ πε0 ma a √ 2πε0 ma

Q11.The current I1 (in A ) flowing through 1Ω resistor in the following circuit is: (1) 0.4 (2) 0.5 (3) 0.2 (4) 0.25

Q11.In a resonance tube experiment when the tube is filled with water up to a height of 17. 0 cm , from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of 24. 5 cm . If the velocity of sound in air is 330 m s−1, the tuning fork frequency is : (1) 2200 Hz (2) 550 Hz (3) 1100 Hz (4) 3300 Hz

Q11.Model a torch battery of length l to be made up of a thin cylindrical bar of radius a and a concentric thin cylindrical shell of radius b filled in between with an electrolyte of resistivity ρ (see figure). If the battery is connected to a resistance of value R, the maximum Joule heating in R will take place for : JEE Main 2020 (03 Sep Shift 1) JEE Main Previous Year Paper (1) R = 2πℓ(ρ ab ) (2) R = 2πℓln(ρ ba ) (3) R = πℓIn(ρ ab ) (4) R = 2ρπℓln( ba )

Q11.Concentric metallic hollow spheres of radii R and 4R hold charges Q1 and Q2 respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) −V(4R) is: (1) Q2 (2) 3Q2 4πε0R 4πε0R (3) 3Q1 (4) 3Q1 16πε0R 4πε0R

Q11.For the given input voltage waveform Vin (t), the output voltage waveform V0(t), across the capacitor is correctly depicted by : (1) (2) (3) (4) towards a large screen placed in the

Q11.A wire of length L and mass per unit length 6.0 × 10−3 kg m−1 is put under tension of 540 N. Two consecutive frequencies that it resonates at are: 420 Hz and 490 Hz. Then L in meters is : (1) 2.1m (2) 1.1m (3) 8.1m (4) 5.1m

Q11.The driver of bus approaching a big wall notices that the frequency of his bus's horn changes from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is 330 ms–1 : (1) 91 kmh−1 (2) 81 kmh−1 (3) 61 kmh−1 (4) 71 kmh−1

Q11.Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1 (on S1 ) and E2 (on S2 ) on their surfaces are such that E1 = R1 . Then the ratio V1 (on S1 ) /V2 (on S2 ) of the E2 R2 electrostatic potentials on each sphere is: (1) R1 (2) R1 2 R2 ( R2 ) (3) 3 ( R2R1 ) (4) ( R1R2 )

Q11.In a building there are 15 bulbs of 45W , 15 bulbs of 100W, 15 small fans of 10W and 2 heaters of 1kW . The voltage of electric main supply is 220V . The minimum fuse capacity (rated value) of the building will be: (1) 5A (2) 25A (3) 15A (4) 20A

Q11.In finding the electric field using Gauss law the formula E = qenc is applicable. In the formula ε0 is ε0|A| permittivity of free space, A is the area of Gaussian surface and qenc is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation? (1) Only when the Gaussian surface is an (2) Only when the Gaussian surface is an → equipotential surface equipotential surface and E is constant on the surface. → (3) (4) For any choice of Gaussian surface. Only when E = constant on the surface.

Q12.The figure shows a region of length ' 𝓁 ' with a uniform magnetic field of 0. 3 T in it and a proton entering the region with velocity 4 × 105 m s−1 making an angle 60° with the field. If the proton completes 10 revolution by the time it cross the region shown, ' 𝓁 ' is close to (mass of proton = 1. 67 × 10−27 kg, charge of the proton = 1. 6 × 10−19 C) (1) 0. 11 m (2) 0. 88 m (3) 0. 44 m (4) 0. 22 m

Q12.A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and released, it starts JEE Main 2020 (09 Jan Shift 2) JEE Main Previous Year Paper performing simple harmonic motion of time period T. The mass of the loop is m then: (1) 2iB T = √2miB (2) T = √πm (3) iB T = √2πmiB (4) T = √πm

Q12.In the given circuit diagram, a wire is joining points B and D. The current in this wire is: (1) 0.4A (2) 2A (3) 4A (4) zero JEE Main 2020 (09 Jan Shift 1) JEE Main Previous Year Paper

Q12.Consider the force F on a charge ' q' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F , if ' q' is placed at distance r from the centre of the shell? (1) F = 1 Qq for r < R (2) 1 qQ > F > 0 for r < R 4π∈0 R2 4π∈0 R2 (3) F = 1 Qq for r > R (4) F = 1 Qq for all r 4π∈0 r2 4π∈0 r2 JEE Main 2020 (06 Sep Shift 2) JEE Main Previous Year Paper

Q12.A parallel plate capacitor has plate of length l, width w and separation of plates is d. It is connected to a battery of emf V . A dielectric slab of the same thickness d and of dielectric constant K = 4 is being inserted between the plates of the capacitor. At what length of the slab inside plates, will the energy stored in the capacitor be two times the initial energy stored? (1) 2l (2) l 3 3 (3) l (4) l 4 2

Q12.A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q . If it acquires a speed ν when it has fallen through a vertical height y (see figure), then (assume the remaining portion to be spherical) (1) v2 = y[ 4πϵ0R2ymqQ + g] (2) v2 = y[ 4πϵ0R(R+y)mqQ + g] (3) v2 = 2y[ 4πϵ0(R+y)3mQqR + g] (4) v2 = 2y[ 4πε0R(R+y)mqQ + g] JEE Main 2020 (05 Sep Shift 1) JEE Main Previous Year Paper