Practice Questions

Q27.In the Bohr's model of hydrogen-like atom the force between the nucleus and the electron is modified as e2 1 F = + β , where β is a constant. For this atom, the radius of the nth orbit in terms of the Bohr 4πε0 ( r2 r3 ) ε0h2 radius = is : (a0 mπe2 ) (1) rn = a0n −β (2) rn = a0n2 + β (3) rn = a0n2 −β (4) rn = a0n + β JEE Main 2013 (23 Apr Online) JEE Main Previous Year Paper

Q27.A copper ball of radius 1 cm and work function 4.47 eV is irradiated with ultraviolet radiation of wavelength 2500 Å . The effect of irradiation results in the emission of electrons from the ball. Further the ball will acquire charge and due to this there will be a finite value of the potential on the ball. The charge acquired by the ball is : (1) 5.5 × 10−13 C (2) 7.5 × 10−13 C (3) 4.5 × 10−12 C (4) 2.5 × 10−11 C

Q28.Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de- Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the nth orbital will therefore be proportional to : JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper (1) n2 (2) n (3) n1/2 (4) n1/4

Q30.Which of the following modulated signal has the best noise-tolerance ? (1) Long-wave (2) Short-wave (3) Medium-wave (4) Amplitude-modulated Q31. 6 litres of an alkene require 27 litres of oxygen at constant temperature and pressure for complete combustion. The alkene is : (1) Ethene (2) Propene (3) 1−Butene (4) 2−Butene

Q3. A satellite moving with velocity v in a force free space collects stationary interplanetary dust at a rate of dM dt = αv where M is the mass (of satellite + dust) at that instant. The instantaneous acceleration of the satellite is (1) −αv22M (2) −αv2M (3) −αv2 (4) −2αv2M

Q4. A projectile moving vertically upwards with a velocity of 200 ms−1 breaks into two equal parts at a height of 490 m. One part starts moving vertically upwards with a velocity of 400 ms−1 . How much time it will take, after the break up with the other part to hit the ground? (1) 2√10 s (2) 5 s (3) 10 s (4) √10 s

Q5. Two bodies A and B of mass m and 2m respectively are placed on a smooth floor. They are connected by a spring of negligible mass. A third body C of mass m is placed on the floor. The body C moves with a velocity v0 along the line joining A and B and collides elastically with A . At a certain time after the collision it is found JEE Main 2012 (12 May Online) JEE Main Previous Year Paper that the instantaneous velocities of A and B are same and the compression of the spring is x0 . The spring constant k will be v0 v20 (2) m (1) m 2x0 x2 0 (3) 2m v0 (4) 2 v0 2 x0 3 m( x0 )

Q6. A circular hole of diameter R is cut from a disc of mass M and radius R; the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre is (1) ( 1532 )MR2 (2) ( 18 )MR2 (3) ( 83 )MR2 (4) ( 1332 )MR2

Q7. A thick-walled hollow sphere has outside radius R0 . It rolls down an incline without slipping and its speed at the bottom is v0 . Now the incline is waxed, so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be 5v0/4 . The radius of gyration of the hollow sphere about an axis through its centre is (1) 3R0/2 (2) 3R0/4 (3) 9R0/16 (4) 3R0

Q8. A wooden wheel of radius R is made of two semicircular parts (see figure); The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than 2πR. To fit the ring on the wheel, it is heated so that its temperature rises by ΔT and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is α, and its Youngs' modulus is Y , the force that one part of the wheel applies on the other part is : (1) 2πSYαΔT (2) SYαΔT (3) πSYαΔT (4) 2SYαΔT

Q8. A large number of droplets, each of radius, r coalesce to form a bigger drop of radius, R. An engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. Velocity of the drop is ( T = surface tension, ρ = density) JEE Main 2012 (19 May Online) JEE Main Previous Year Paper (1) T 1 1/2 (2) 6T 1 1/2 [ ρ ( r −1R )] [ ρ ( r −1R )] (3) 3T 1 1/2 (4) 2T 1 1/2 [ ρ ( r −1R )] [ ρ ( r −1R )]

Q10.Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly: (Assume the gas to be close to ideal gas) (1) 15.4% (2) 9.1% (3) 10.5% (4) 12.5%

Q12. n moles of an ideal gas undergo a process A →B as shown in the figure. Maximum temperature of the gas during the process is (1) 9P0V0 (2) 3P0V0 nR 2nR (3) 9P0V02nR (4) 9P0V04nR

Q14.A uniform tube of length 60.5 cm is held vertically with its lower end dipped in water. A sound source of frequency 500 Hz sends sound waves into the tube. When the length of tube above water is 16 cm and again when it is 50 cm, the tube resonates with the source of sound. Two lowest frequencies (in Hz ), to which tube will resonate when it is taken out of water, are (approximately). (1) 281,562 (2) 281,843 (3) 276,552 (4) 272,544

Q15.This question has statement 1 and statement 2 . Of the four choices given after the statements, choose the one that best describes the two statements. An insulating solid sphere of radius R has a uniformly positive charge density ρ. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero. Statement 1: When a charge q is taken from the centre to the surface of the sphere, its potential energy changes by qp Statement 2 : The electric field at a distance r(r < R) from the centre of the sphere is 3ε0 ρr 3ε0 (1) Statement 1 is true, Statement 2 is true, (2) Statement 1 is true, Statement 2 is false Statement 2 is not the correct explanation for statement 1. (3) Statement 1 is false, Statement 2 is true (4) Statement 1 is true, Statement 2 is the correct explanation for statement 1 JEE Main 2012 (Offline) JEE Main Previous Year Paper

Q18.A charge Q is uniformly distributed over the surface of non conducting disc of radius R. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity ω. As a result of this rotation a magnetic field of induction B is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure (1) (2) (3) (4)

Q18.Two circuits (a) and (b) have charged capacitors of capacitance C, 2C and 3C with open switches. Charges on each of the capacitor are as shown in the figures. On closing the switches Circuit (a) Circuit (b) (1) No charge flows in (a) but charge flows from R (2) Charges flow from L to R in both (a) and (b) to L in (b) (3) Charges flow from R to L in (a) and from L to R (4) No charge flows in (a) but charge flows from L in (b) to R in (b)

Q20.A coil of self inductance L is connected at one end of two rails as shown in figure. A connector of length l, mass m can slide freely over the two parallel rails. The entire set up is placed in a magnetic field of induction B going into the page. At an instant t = 0 an initial velocity v0 is imparted to it and as a result of that it starts JEE Main 2012 (19 May Online) JEE Main Previous Year Paper moving along x-axis. The displacement of the connector is represented by the figure. (1) (2) (3) (4)

Q20.The circuit in figure consists of wires at the top and bottom and identical springs as the left and right sides. The wire at the bottom has a mass of 10 g and is 5 cm long. The wire is hanging as shown in the figure. The springs stretch 0.5 cm under the weight of the wire and the circuit has a total resistance of 12Ω. When the lower wire JEE Main 2012 (12 May Online) JEE Main Previous Year Paper is subjected to a static magnetic field, the springs, stretch an additional 0.3 cm. The magnetic field is (1) 0.6 T and directed out of page (2) 1.2 T and directed into the plane of page (3) 0.6 T and directed into the plane of page (4) 1.2 T and directed out of page

Q26.A diatomic molecule is made of two masses m1 and m2 which are separated by a distance r. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by ( n is an integer) (1) (m1+m2)2n2h2 (2) n2h2 2m21m22r2 2(m1+m2)r2 (3) 2n2h2 (4) (m1+m2)n2h2 (m1+m2)r2 2m1m2r2 JEE Main 2012 (Offline) JEE Main Previous Year Paper

Q28.A sample originally contained 1020 radioactive atoms, which emit α-particles. The ratio of α particles emitted in the third year to that emitted during the second year is 0.3. How many α particles were emitted in the first year? JEE Main 2012 (07 May Online) JEE Main Previous Year Paper (1) 3 × 1018 (2) 3 × 1019 (3) 5 × 1018 (4) 7 × 1019

Q13.Three perfect gases at absolute temperatures T1, T2 and T3 are mixed. The masses of molecules are m1 , m2 and m3 and the number of molecules are n1, n2 and n3 respectively. Assuming no loss of energy, the final temperature of the mixture is : 2 2 +n3T 32 (1) n1T1+n2T2+n3T3 (2) n1T1+n2T n1+n2+n3 n1T1+n2T2+n3T3 1 (3) n21T 2 +n22T 22 +n23T 32 (4) (T1+T2+T3) n1T1+n2T2+n3T3 3

Q16.The transverse displacement y(x, t) of a wave on a string is given by y(x, t) = e−(ax2+bt2+2√abxt) . This represents a (1) (2) standing wave of frequency √b wave moving in −x direction with speed √ba (3) standing wave of frequency 1 (4) wave moving in +x direction with √ab √b JEE Main 2011 JEE Main Previous Year Paper

Q20.A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius R. The magnitude of the magnetic induction along its axis is (1) μ0I (2) μ0I 2π2R 2πR (3) μ0I (4) μ0l 4π2R π2R

Q15.Let there be a spherically symmetric charge distribution with charge density varying as ρ(r) = ρ0 ( 54 −rR ) upto r = R, and ρ(r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance r(r < R) from the origin is given by (1) 4πρ0r 3ε0 ( 53 −rR ) (2) 4ε0ρ0r ( 53 −rR ) (3) 4ρ0r 3ε0 ( 54 −rR ) (4) 3ε0ρ0r ( 54 −rR ) JEE Main 2010 JEE Main Previous Year Paper