Practice Questions

Q8. A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11kms−1 , the escape velocity from the surface of the planet would be (1) 1.1kms−1 (2) 11kms−1 (3) 110kms−1 (4) 0.11kms−1

Q9. This question contains Statement −1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement - I: For a mass M kept at the centre of a cube of side ' a ', the flux of gravitational field passing through its sides is 4π GM. and Statement - II If the direction of a field due to a point source is radial and its dependence on the distance ' r ' for the source is given as 1/r2 , its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface (1) Statement −1 is false, Statement −2 is true. (2) Statement −1 is true, Statement −2 is true; Statement −2 is correct explanation for Statement-1. (3) Statement −1 is true, Statement −2 is true; (4) Statement −1 is true, Statement −2 is False. Statement −2 is not a correct explanation for Statement-1.

Q10.A spherical solid ball of volume V is made of a material of density ρ1 . It is falling through a liquid of density ρ2 (ρ2 < ρ1). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., Fviscous = −kv2(k > 0). The terminal speed of the ball is (1) (2) Vgρ1 k √Vg(ρ1−ρ2)k (3) gρ1 (4) Vg(ρ1−ρ2) k √V k

Q11.A jar filled with two non mixing liquids 1 and 2 having densities ρ1 and ρ2 respectively. A solid ball, made of a material of density ρ3 , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which JEE Main 2008 JEE Main Previous Year Paper of the following is true for ρ1, ρ2 and ρ3 ? (1) ρ3 < ρ1 < ρ2 (2) ρ1 < ρ3 < ρ2 (3) ρ1 < ρ2 < ρ3 (4) ρ1 < ρ3 < ρ2

Q12.A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution. Which of the following shows the relative nature of the liquid columns in the two tubes? (1) (2) (3) (4)

Q13.An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V1 and contains ideal gas at pressure P1 and temperature T1 . The other chamber has volume V2 and contains ideal gas at pressure P2 and temperature T2 . If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be (1) T1T2(P1V1+P2V2) (2) P1V1T1+P2V2T2 P1V1T2+P2V2T1 P1V1+P2V2 (3) P1V1T2+P2V2T1 (4) T1T2(P1V1+P2V2) P1V1+P2V2 P1V1T1+P2V2T2

Q14.While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be xcm for the second resonance. Then JEE Main 2008 JEE Main Previous Year Paper (1) 18 > x (2) x > 54 (3) 54 > x > 36 (4) 36 > x > 18

Q15.The speed of sound in oxygen (O2) at a certain temperature is 460 ms−1 . The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal) (1) 460 ms−1 (2) 500 ms−1 (3) 650 ms−1 (4) None of these

Q16.A wave travelling along the x-axis is described by the equation y(x, t) = 0.005 cos(αx −βt). If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then α and β in appropriate units are (1) α = 25.00π, β = π (2) α = 0.08π , 2.0π (3) α = 0.04π , β = 1.0π (4) α = 12.50π, β = 2.0π

Q17.A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range 0 ≤r < ∞, where r is the distance from the centre of the shell? (1) (2) (3) (4)

Q18.A parallel plate capacitor with air between the plates has a capacitance of 9pF. The separation between its plates is ' d '. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k1 = 3 and thickness d3 while the other one has dielectric constant k2 = 6 and thickness 23d . Capacitance of the capacitor is now (1) 1.8pF (2) 45pF (3) 40.5pF (4) 20.25pF

Q19.Paragraph: Consider a block of conducting material of resistivity ' ρ ' shown in the figure. Current 'l' enters at 'A' and leaves from ' D '. We apply superposition principle to find voltage ' ΔV ' developed between ' B ' and ' JEE Main 2008 JEE Main Previous Year Paper C '. The calculation is done in the following steps: (i) Take current 'l' entering from 'A' and assume it to spread over a hemispherical surface in the block. (ii) Calculate field E(r) at distance ' r ' from A by using Ohm's law E = ρj, where j is the current per unit area at ' r '. (iii) From the ' r ' dependence of E(r), obtain the potential V (r) at r. (iv) Repeat (i), (ii) and (iii) for current 'l' leaving ' D ' and superpose results for ' A ' and ' D '. Question: ΔV measured between B and C is ρl ρl (1) ρl (2) ρl πa − π(a+b) a − (a+b) ρl ρl (3) ρl (4) 2πa − 2π(a+b) 2π(a−b)

Q20.Paragraph: Consider a block of conducting material of resistivity ' ρ ' shown in the figure. Current 'l' enters at 'A' and leaves from ' D '. We apply superposition principle to find voltage ' ΔV ' developed between ' B ' and ' C '. The calculation is done in the following steps: (i) Take current 'l' entering from 'A' and assume it to spread over a hemispherical surface in the block. (ii) Calculate field E(r) at distance ' r ' from A by using Ohm's law E = ρj, where j is the current per unit area at ' r '. (iii) From the ' r ' dependence of E(r), obtain the potential V (r) at r. (iv) Repeat (i), (ii) and (iii) for current 'l' leaving ' D ' and superpose results for ' A ' and ' D '. Question: For current entering at A , the electric field at a distance ' r ' from A is (1) ρl (2) ρl 8πr2 r2 (3) ρl (4) ρl 2πr2 4πr2

Q21.A 5 V battery with internal resistance 2Ω and a 2 V battery with internal resistance 1Ω are connected to a 10Ω resistor as shown in the figure. The current in the 10Ω resistor is JEE Main 2008 JEE Main Previous Year Paper (1) 0.27AP2 to P1 (2) 0.03AP1 to P2 (3) 0.03AP2 to P1 (4) 0.27 APP1 to P2

Q22.Relative permittivity and permeability of a material are εr and μr , respectively. Which of the following values of these quantities are allowed for a diamagnetic material? (1) εr = 0.5, μr = 1.5 (2) εr = 1.5, μr = 0.5 (3) εr = 0.5, μr = 0.5 (4) εr = 1.5, μr = 1.5

Q23.A horizontal overhead power line is at a height of 4 m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is (μ0 = 4π × 10−7 T m A−1) (1) 2.5 × 10−7 T southward (2) 5 × 10−6 T northward (3) 5 × 10−6 T southward (4) 2.5 × 10−7 northward

Q24.Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area A = 10 cm2 and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is (μ0 = 4π × 10−7TmA−1) (1) 2.4π × 10−5H (2) 4.8π × 10−4H (3) 4.8π × 10−5H (4) 2.4π × 10−4H

Q25.A student measures the focal length of convex lens by putting an object pin at a distance 'u' from the lens and measuring the distance ' v ' of the image pin. The graph between ' u ' and ' v ' plotted by the student should look like (1) (2) (3) (4)

Q26.An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distance are measured by (1) a vernier scale provided on the microscope (2) a standard laboratory scale (3) a meter scale provided on the microscope (4) a screw gauage provided on the microscope

Q27.Paragraph: Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere JEE Main 2008 JEE Main Previous Year Paper constructively (see in figure). Question: Electrons accelerated by potential V are diffracted from a crystal. If d = 1Å and i = 30∘, V should be about (h = 6.6 × 10−34Js, me = 9.1 × 10−31 kg, e = 1.6 × 10−19C) (1) 2000 V (2) 50 V (3) 500 V (4) 1000 V

Q28.Paragraph: Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see in figure). Question: If a strong diffraction peak is observed when electrons are incident at an angle 'i' from the normal to the crystal planes with distance ' d ' between them (see figure), de Broglie wavelength λdB of electrons can be calculated by the relationship ( n is an integer) (1) d sin i = nλdB (2) 2d cos i = nλdB (3) 2d sin i = nλdB (4) d cos i = nλdB

Q29.Paragraph: Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere JEE Main 2008 JEE Main Previous Year Paper constructively (see in figure). Question: In an experiment, electrons are made to pass through a narrow slit of width 'd' comparable to their de Broglie wavelength. They are detected on a screen at a distance ' D ' from the slit (see figure). Which of the following graph can be expected to represent the number of electrons ' N ' detected as a function of the detector position ' y ' (y = 0 corresponds to the middle of the slit)? (1) (2) (3) (4)

Q30.Suppose an electron is attracted towards the origin by a force k/r where ' k ' is a constant and ' r ' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be ' rn ' and the kinetic energy of the electron to be Tn . Then which of the following is true? (1) Tn ∝1/n2, rn ∝n2 (2) Tn independent of n, rn ∝n (3) Tn ∝1/n, rn ∝n (4) Tn ∝1/n, rn ∝n2 JEE Main 2008 JEE Main Previous Year Paper

Q31.This question contains Statement −1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement - I: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. and Statement - II For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei it decrease with increasing Z . (1) Statement −1 is false, Statement −2 is true. (2) Statement - 1is true, Statement −2 is true; Statement −2 is correct explanation for Statement-1. (3) Statement −1 is true, Statement −2 is true; (4) Statement −1 is true, Statement −2 is False. Statement −2 is not a correct explanation for Statement-1.

Q32.A working transistor with its three legs marked P, Q and R is tested using a multimeter. No conduction is found between P and Q . By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q , some resistance is seen on the multimeter. Which of the following is true for the transistor? (1) It is an npn transistor with R as base (2) It is a pnp transistor with R as collector (3) It is a pnp transistor with R as emitter (4) It is an npn transistor with R as collector