Practice Questions

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

Q28.A system of four gates is set up as shown. The 'truth table' corresponding to this system is : (1) (2) (3) (4)

Q28.In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n −1). If n >> 1, the frequency of radiation emitted is proportional to : (1) 1 (2) 1 n3/2 n3 (3) 1 (4) 1 n n2

Q29.The half-life of a radioactive element A is the same as the mean-life of another radioactive element B. Initially both substances have the same number of atoms, then : (1) A and B decay at the same rate always. (2) A and B decay at the same rate initially. (3) A will decay at a faster rate than B. (4) B will decay at a faster rate than A .

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

Q30.If a carrier wave c(t) = A sin ωct is amplitude modulated by a modulator signal m(t) = A sin ωmt then the equation of modulated signal [Cm(t)] and its modulation index are respectively (1) Cm(t) = A (1 + sin ωmt) sin ωct and 2 (2) Cm(t) = A (1 + sin ωmt) sin ωmt and 1 (3) Cm(t) = A (1 + sin ωmt) sin ωct and 1 (4) Cm(t) = A (1 + sin ωct) sin ωmt and 2

Q30.Correct set up to verify Ohm's law is : (1) (2) (3) (4)

Q30.Figure shows a circuit in which three identical diodes are used. Each diode has forward resistance of 20Ω and infinite backward resistance. Resistors R1 = R2 = R3 = 50Ω. Battery voltage is 6 V . The current through R3 is : (1) 50 mA (2) 100 mA (3) 60 mA (4) 25 mA

Q1. Given that K = energy, V = velocity, T = time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension? (1) [KV −2 T−2] (2) [K 2V 2T −2] (3) [K 2V −2T −2] (4) [KV 2T 2]

Q1. Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is (1) 6% (2) zero (3) 1% (4) 3%

Q1. A student measured the diameter of a wire using a screw gauge with the least count 0.001 cm and listed the measurements. The measured value should be recorded as (1) 5.3200 cm (2) 5.3 cm (3) 5.32 cm (4) 5.320 cm

Q1. The electrical resistance R of a conductor of length l and area of cross section a is given by R = ρla where ' ρ ' is the electrical resistivity. What is the dimensional formula for electrical conductivity ' σ ' which is reciprocal of resistivity? (1) [M −1L−3T 3A2] (2) [ML−3T −3A2] (3) [ML3T −3A−2] (4) [M −2L3T 2A−1]

Q1. The amount of heat produced in an electric circuit depends upon the current (I), resistance (R) and time (t). If the error made in the measurements of the above quantities are 2%, 1% and 1% respectively then the maximum possible error in the total heat produced will be (1) 1% (2) 2% (3) 6% (4) 3%

Q2. A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity u and the guard's room passes with velocity v. The middle wagon of the train passes the pole with a velocity. (1) u+v (2) 1 √u2 + v2 2 2 2 ) (3) √uv (4) √( u2+v2

Q2. A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be (1) 20√2 m (2) 10 m (3) 10√2 m (4) 20 m

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

Q3. Sand is being dropped on a conveyer belt at the rate of 2 kg per second. The force necessary to keep the belt moving with a constant speed of 3 ms−1 will be (1) 12 N (2) 6 N (3) zero (4) 18 N

Q3. A car of mass 1000 kg is moving at a speed of 30 m/s . Brakes are applied to bring the car to rest. If the net retarding force is 5000 N , the car comes to stop after travelling d m in t s . Then (1) d = 150, t = 5 (2) d = 120, t = 8 (3) d = 180, t = 6 (4) d = 90, t = 6

Q3. An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is 1/3 . If the line joining the centre of the hemispherical surface to the insect makes an angle α with the vertical, the maximum possible value of α so that the insect does not slip is given by (1) cot α = 3 (2) sec α = 3 (3) cosec α = 3 (4) cos α = 3

Q4. A block of weight W rests on a horizontal floor with coefficient of static friction μ. It is desired to make the block move by applying minimum amount of force. The angle θ from the horizontal at which the force should be applied and magnitude of the force F are respectively. μW (1) θ = tan−1(μ), F = F = √1+μ2 μW (2) θ = tan−1 ( μ1 ), √1+μ2 F = 1+μμW (3) θ = 0, F = μW (4) θ = tan−1 ( 1+μμ ),

Q4. An engine pumps water continuously through a hose. Water leaves the hose with velocity v and m is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface is (1) mv3 (2) mv2 (3) 1 mv2 (4) 1 mv3 2 2

Q5. Two point masses of mass m1 = fM and m2 = (1 −f)M(f < 1) are in outer space (far from gravitational influence of other objects) at a distance R from each other. They move in circular orbits about their centre of mass with angular velocities ω1 for m1 and ω2 for m2 . In that case (1) (1 −f)ω1 = fω (2) ω1 = ω2 and independent of f (3) fω1 = (1 −f)ω2 (4) ω1 = ω2 and depend on f

Q5. A particle gets displaced by Δ¯r = (2^i + 3^j + 4^k)m under the action of a force →F = (7^i + 4^j + 3^k). The change in its kinetic energy is (1) 38 J (2) 70 J (3) 52.5 J (4) 126 J

Q5. The force →F = F^i on a particle of mass 2 kg, moving along the x-axis is given in the figure as a function of its position x. The particle is moving with a velocity of 5 m/s along the x-axis at x = 0. What is the kinetic energy of the particle at x = 8 m? (1) 34 J (2) 34.5 J (3) 4.5 J (4) 29.4 J

Q5. Two cars of masses m1 and m2 are moving in circles of radii r1 and r2 , respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is (1) m1r1 : m2r2 (2) m1 : m2 (3) r1 : r2 (4) 1 : 1