Practice Questions

Q26.A neutron moving with a speed 'v' makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which perfactly inelastic collision will take place is : (1) 20.4 eV (2) 10.2 eV (3) 12.1 eV (4) 16.8 eV

Q2. A beaker contains a fluid of density ρ kg , specific heat S kgoCJ and viscosity η . The beaker is filled up to height m3 ˙Q h. To estimate the rate of heat transfer per unit area ( A ) by convection when beaker is put on a hot plate, a Δθ ( inoC ) is the difference in the student proposes that it should depend on η , ( SΔθh ) and ( ρg1 ) when ˙Q temperature between the bottom and top of the fluid. In that situation the correct option for ( A ) is: (1) ( SΔθh )η (2) η( SΔθh )( ρ1g ) ηh (3) ( SΔθηh )( ρg1 ) (4) SΔθ

Q2. A block of mass m = 10 kg rests on a horizontal table. The coefficient of friction between the block and the table is 0. 05. When hit by a bullet of mass 50 g moving with speed v, that gets embedded in it, the block moves and comes to stop after moving a distance of 2 m on the table. If a freely falling object were to acquire speed 10v after being dropped from height H , then neglecting energy losses and taking g = 10 m s−2 , the value of H is close to (1) 0. 2 km . (2) 0. 5 km . (3) 0. 4 km . (4) None of these.

Q3. If electronic charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental quantities, the permeability of vacuum μ0 can be expressed in units of: (1) ( mc2he2 ) (2) ( me2h ) (3) ( me2hc ) (4) ( ce2h )

Q6. From a solid sphere of mass M and radius R, a cube of the maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is: (1) 4MR2 (2) MR2 3√3π 32√2π (3) MR2 (4) 4MR2 16√2π 9√3π

Q7. From a solid sphere of mass M and radius R, a spherical portion of radius ( R2 ) is removed as shown in the figure. Taking gravitational potential V = 0 at r = ∞, the potential at the centre of the cavity thus formed is ( G =gravitational constant) (1) −2GM (2) −GM R 2R (3) −GM (4) −2GM R 3R

Q8. A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to TM . If the Young's modulus of the material of the wire is Y , then 1 is equal to: Y ( g =gravitational acceleration) (1) T 2 A (2) T M 2 A −( TM ) Mg T ) Mg [1 ] [( −1] (3) T M 2 Mg (4) TM 2 A T ) A −( T ) Mg [( −1] [1 ]

Q9. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as V q , where V is the volume of the gas. The value of q is: (γ = CPCv ) (1) γ−1 (2) 3γ+5 2 6 (3) 3γ−5 (4) γ+1 6 2 JEE Main 2015 (04 Apr) JEE Main Previous Year Paper

Q10.Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = UV ∝T 4 and pressure p = 13 ( UV ) . If the shell now undergoes an adiabatic expansion the relation between T and R is: (1) T ∝ 1 (2) T ∝e−R R3 (3) T ∝e−3R (4) T ∝ R1

Q13.A simple harmonic oscillator of angular frequency 2 rad s−1 is acted upon by an external force F = sin t N . If the oscillator is at rest in its equilibrium position at t = 0, its position at later times is proportional to: (1) sin t + 21 cos 2t (2) cost −12 sin 2t (3) sin t −12 sin 2t (4) sin t + 12 sin 2t

Q15.A wire of length L = 20 cm is bent into a semi-circular arc and the two equal halves of the arc are uniformly charged with charges +Q and −Q as shown in the figure. The magnitude of the charge on each half is |Q| = 103ε0 , where ε0 is the permittivity of free the space. The net electric field at the centre O is (1) (25 × 103)ˆi N C−1 (2) (50 × 103)ˆi N C−1 (3) (25 × 103)ˆj N C−1 (4) (50 × 103)ˆj N C−1 → + 30 N C−1 exists in a region of space. If the potential at the origin is taken to

Q20.A wire carrying current I is tied between points P and Q and is in the shape of a circular arc of radius R due to a uniform magnetic field B (perpendicular to the plane of the paper, as shown in the figure) in the vicinity of the wire. If the wire subtends an angle 2θo at the center of the circle (of which it forms an arch) then the tension in the wire is: JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper (1) IBR (2) IBR sinθ0 (3) IBR (4) IBRθ0 2sinθ0 sinθ0

Q23.An electromagnetic wave travelling in the x− direction has frequency of 2 × 1014 H z and electric field amplitude of 27 V m–1 oscillates in Y −direction. From the options given below, which one describes the magnetic field for this wave? (1) → (2) → B(x, t) = × 10−8 B(x, t) = × sin[2π(1.5 × 10−8 x −2 × 1014 (9 T)ˆj (9 10−8T)ˆi sin[1.5 × 10−6 x −2 × 1014t] → → (3) (4) B B −2 × −2 × (x, t) = (9 × (x, t) = (3 × 10−8T)ˆj sin 2π[( 1.5×10−8x ) 1014t] 10−8T)^ksin2π[( 1.5×10−6x ) 1014t]

Q23.For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor C ′ , when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor C ′ , must have been connected in: (1) Parallel with C and has a magnitude 1−ω2LC (2) Series with C and has a magnitude 1−ω2LC ω2L ω2L (3) Series with C and has a magnitude C (4) Parallel with C and has a magnitude C (ω2LC−1) (ω2LC−1)

Q25.Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is μ , a ray, incident at an angle θ , on the face AB would get transmitted through the face AC of the prism JEE Main 2015 (04 Apr) JEE Main Previous Year Paper provided: sin + θ > (1) θ < cos−1[μ (A sin−1( μ1 ))] (2) sin−1[μ sin(A −sin−1( μ1 ))] sin θ > + (3) θ < sin−1[μ (A −sin−1( μ1 ))] (4) cos−1[μ sin(A sin−1( μ1 ))]

Q28.If one were to apply the Bohr model to a particle of mass ′m′ and charge ′q′ moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the nth level will be: (1) n( hqBπm ) (2) n( 4πmhqB ) (3) n( 2πmhqB ) (4) n( 8πmhqB )

Q6. From a sphere of mass M and radius R, a smaller sphere of radius R2 is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two sphere is: (1) 41GM2 (2) 41GM2 3600R2 450R2 (3) 59GM2 (4) GM2 450R2 225R2 JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper

Q8. There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d1 and d2 are filled in the tube. Each liquid subtends 90o angle at centre. Radius joining their interface makes an angle α with vertical. Ratio d1 is : d2 (1) 1+sinα (2) 1+cosα 1−sinα 1−cosα (3) 1+tanα (4) 1+sinα 1−tanα 1−cosα

Q9. A cylindrical vessel of cross-section A contains water to a height h. There is a hole in the bottom of radius ' a '. The time in which it will be emptied is: (1) 2 A (2) √2 A πa2 √hg πa2 √hg (3) 2√2 A (4) A g πa2 √h g √2πa2 √h

Q9. A large number of liquid drops each of radius r coalesce to form a single drop of the radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given surface tension of the liquid T , density ρ ) ( 1r −1R ) (1) √2Tρ ( 1r −1R ) (2) √6Tρ ( 1r −1R ) (3) √4Tρ ( 1r −1R ) (4) √Tρ

Q10.The equation of state for a gas is given by PV = nRT + αV , where n is the number of moles and α is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are T0 and P0 respectively. The work done by the gas when its temperature doubles isobarically will be : (1) P0 T0 ln 2 (2) P0T0RP0+α (3) P0T0R (4) P0 T0R P0−α

Q10.Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in volume of contained air and S change in total surface area, T is the surface tension and P atmospheric pressure, then which of the following relation is correct? (1) 4PV + 3ST = 0 (2) 3PV + 4ST = 0 (3) 2PV + 3ST = 0 (4) 3PV + 2ST = 0

Q11.A black coloured solid sphere of radius R and mass M is inside a cavity with a vacuum inside. The walls of the cavity are maintained at temperature T0 . The initial temperature of the sphere is 3T0 . If the specific heat of the material of the sphere varies as αT 3 per unit mass with the temperature T of the sphere, where α is a constant, then the time taken for the sphere to cool down to temperature 2T0 will be ( σ is Stefan Boltzmann constant) (1) 16πR2σ Mα ln( 32 ) (2) 16πR2σMα ln( 163 ) (3) 4πR2σ Mα ln( 23 ) (4) 4πR2σMα ln( 163 )

Q12.Two bodies of masses 1 kg and 4 kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25 rad s−1 , and amplitude 1. 6 cm while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take g = 10 m s−2 ). (1) 20 N (2) 60 N (3) 40 N (4) 10 N

Q12.Three rods of Copper, Brass and Steel are welded together to form a Y-shaped structure. Area of cross-section of each rod is 4 cm2 . End of copper rod is maintained at 100°C. Where as ends of brass and steel are kept at JEE Main 2014 (06 Apr) JEE Main Previous Year Paper 0°C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0. 92, 0. 26 and 0. 12 CGS units respectively. Rate of heat flow through copper rod is : (1) 1. 2 Cal /s (2) 2. 4 Cal /s (3) 4. 8 Cal /s (4) 6. 0 Cal /s