Practice Questions

Q13.An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section 8.0 × 10−3 m2 . Initially the gas is at 300 K and occupies a volume of 2.4 × 10−3 m3 and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is 1.0 × 105 N/m2 . The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper of the heater. The heat capacity of the heater coil is also negligible). (1) 300 K (2) 800 K (3) 500 K (4) 1000 K k r2 k is the spring m − 4 m2 ) where

Q13.The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to (ln 5 = 1.601, ln 2 = 0.693). (1) 231 s (2) 142 s (3) 208 s (4) 161 s

Q14.A particle moves with simple harmonic motion in a straight line. In first τ s, after starting from rest it travels a distance a, and in next τ s it travels 2a, in same direction, then : (1) Amplitude of motion is 3a (2) Time period of oscillations is 8τ (3) Amplitude of motion is 4a (4) Time period of oscillations is 6τ

Q15.A source of sound A emitting waves of frequency 1800 Hz is falling towards ground with a terminal speed v. The observer B on the ground directly beneath the source receives waves of frequency 2150 Hz. The source A receives waves, reflected from ground of frequency nearly: (Speed of sound = 343 m/s ) (1) 2150 Hz (2) 2500 Hz (3) 1800 Hz (4) 2400 Hz

Q17.The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose relative permittivity varies linearly from ϵ1 at one plate to ϵ2 at the other. The capacitance of the capacitor is JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper (1) ϵ0(∈2−∈1)A (2) ϵ0(∈2+∈1)A [d ln(∈2/∈1)] 2d (3) ϵ0(∈1+∈2)A (4) ϵ0A d [dln(∈2/∈1)]

Q20.A conductor lies along the z-axis at −1.5 ≤z < 1.5 m and carries a fixed current of 10.0 A in −ˆaz direction → (see figure). For a field B = 3.0 × 10−4 e−0.2x ˆay T, find the power required to move the conductor at constant speed to x = 2.0 m, y = 0 m in 5 × 10−3 s. Assume parallel motion along the x-axis. (1) 1.57 W (2) 2.97 W (3) 14.85 W (4) 29.7 W

Q24.The focal lengths of objective lens and eye lens of a Galilean Telescope are respectively 30 cm and 3.0 cm. Telescope produces virtual, erect image of an object situated far away from it at least distance of distinct vision from the eye lens. In this condition the Magnifying Power of the Galilean Telescope should be : (1) +8. 8 (2) −11. 2 (3) +11. 2 (4) −8. 8 JEE Main 2014 (09 Apr Online) JEE Main Previous Year Paper

Q25.Interference pattern is observed at ' P ' due to superimposition of two rays coming out from a source ' S ' as shown in the figure. The value of ' l ' for which maxima is obtained at ' P ' is: ( R is perfect reflecting surface) (1) 1 = 2nλ (2) 1 = (2n−1)λ √3−1 2(√3−1 ) (2n−1)λ 1 = (3) 1 = (2n−1λ)√3 √3−1 4(2−√3 ) (4)

Q25.Using monochromatic light of wavelength λ, an experimentalist sets up the Young's double slit experiment in three ways as shown. If she observes that y = β′ , the wavelength of light used is : (1) 520 nm (2) 580 nm (3) 540 nm (4) 560 nm

Q27.The radiation corresponding to 3 →2 transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of 3 × 10−4 T. If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to : (1) 1.8 eV (2) 1.1 eV (3) 0.8 eV (4) 1.6 eV

Q27.A photon of wavelength λ is scattered from an electron, which was at rest. The wavelength shift Δλ is three times of λ and the angle of scattering θ is 60∘ . The angle at which the electron recoiled is ϕ. The value of tan ϕ JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper is : (electron speed is much smaller than the speed of light) (1) 0.16 (2) 0.22 (3) 0.25 (4) 0.28

Q27.A beam of light has two wavelengths of 4972Å and 6216Å with a total intensity of 3.6 × 10−3 Wm−2 equally distributed among the two wavelengths. The beam falls normally on an area of 1 cm2 of a clean metallic surface of work function 2.3eV. Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photoelectrons liberated in 2 s is approximately: (1) 6 × 1011 (2) 9 × 1011 (3) 11 × 1011 (4) 15 × 1011

Q1. From the following, the quantity (constructed from the basic constants of nature), that has the dimensions, as well as correct order of magnitude, vis-a-vis typical atomic size, is: (1) e2 (2) 4πε0e2 4πε0mc2 me2 (3) me2 (4) 4πε0mc2 4πε0b2 e2

Q2. The maximum range of a bullet fired from a toy pistol mounted on a car at rest is R0 = 40 m. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity v = 20 m/s on a horizontal surface? (g = 10 m/s2) (1) 30∘ (2) 60∘ (3) 75∘ (4) 45∘

Q4. A projectile of mass M is fired so that the horizontal range is 4 km . At the highest point the projectile explodes in two parts of masses M/4 and 3M/4 respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is : (1) 16 km (2) 1 km (3) 10 km (4) 2 km

Q5. A tennis ball (treated as hollow spherical shell) starting from O rolls down a hill. At point A the ball becomes air borne leaving at an angle of 30∘ with the horizontal. The ball strikes the ground at B. What is the value of JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper the distance AB ? (Moment of inertia of a spherical shell of mass m and radius R about its diameter = 23 mR2 ) (1) 1.87 m (2) 2.08 m (3) 1.57 m (4) 1.77 m

Q5. The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point, P, located as shown, would be (nearly) : JEE Main 2013 (09 Apr Online) JEE Main Previous Year Paper (1) 5 GM (2) 8 GM 6 x2 9 x2 (3) 7 GM (4) 6 GM 8 x2 7 x2

Q9. A thin tube sealed at both ends is 100 cm long. It lies horizontally, the middle 20 cm containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced ? (Given : cross-section of the tube can be assumed to be uniform) (1) 2.95 cm (2) 5.18 cm (3) 8.65 cm (4) 0.0 cm

Q11.An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M . The piston and the cylinder have equal cross-sectional area A . When the piston is in equilibrium, the volume of the gas is V0 and its pressure is M0 . The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency [Assume the system is in space.] 0 1 (1) (2) . 0 . 2π 1 √MVAγP 0 2π √A2γPMV 0 (3) 1 AγP 0 (4) 1 V 0MP 0 . 2π V 0M 2π A2γ

Q13.A and B are two sources generating sound waves. A listener is situated at C. The frequency of the source at A is 500 Hz. A, now, moves towards C with a speed 4 m/s. The number of beats heard at C is 6 . When A moves away from C with speed 4 m/s, the number of beats heard at C is 18 . The speed of sound is 340 m/s . The frequency of the source at B is : (1) 500 Hz (2) 506 Hz (3) 512 Hz (4) 494 Hz

Q17.A letter ′A′ is constructed of a uniform wire with resistance 1.0Ω per cm, The sides of the letter are 20 cm and the cross piece in the middle is 10 cm long. The apex angle is 60 . The resistance between the ends of the legs is close to: (1) 50.0Ω (2) 10Ω (3) 36.7Ω (4) 26.7Ω

Q18.One of the two small circular coils, (none of them having any self - inductance) is suspended with a V-shaped copper wire, with plane horizontal. The other coil is placed just below the first one with plane horizontal. Both the coils are connected in series with a dc supply. The coils are found to attract each other with a force. Which one of the following statements is incorrect? (1) Both the coils carry currents in the same (2) Coils will attract each other, even if the supply is direction. an ac source. (3) Force is proportional to d−1 (4) Force is proportional to d−2

Q20.A circular loop of radius 0. 3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2. 0 A flows through the smaller loop, then the flux linked with a bigger loop is: (1) 3 .3 ×10−11 weber (2) 6 .6 ×10−9 weber (3) 9 .1 ×10−11 weber (4) 6 × 10−11 weber

Q23.A thin glass plate of thickness is 2500 λ ( λ is wavelength of light used) and refractive index μ = 1.5 is inserted 3 between one of the slits and the screen in Young's double slit experiment. At a point on the screen equidistant from the slits, the ratio of the intensities before and after the introduction of the glass plate is : (1) 2 : 1 (2) 1 : 4 (3) 4 : 1 (4) 4 : 3

Q25.A ray of light of intensity I is incident on a parallel glass slab at point A as shown in diagram. It undergoes partial reflection and refraction. At each reflection, 25% of incident energy is reflected. The rays AB and A′B′ undergo interference. The ratio of Imax and Imin is : (1) 49 : 1 (2) 7 : 1 (3) 4 : 1 (4) 8 : 1