Practice Questions

Q90.Three numbers are chosen at random without replacement from {1, 2, 3, … . .8} . The probability that their minimum is 3 , given that their maximum is 6 , is (1) 3 (2) 1 8 5 (3) 41 (4) 25 JEE Main 2012 (Offline) JEE Main Previous Year Paper

Q90.A number n is randomly selected from the set {1, 2, 3, … . , 1000} . The probability that is an integer is ∑ni=1 i (1) 0.331 (2) 0.333 (3) 0.334 (4) 0.332 JEE Main 2012 (12 May Online) JEE Main Previous Year Paper

Q90.A line with positive direction cosines passes through the point P(2, −1, 2) and makes equal angles with the coordinate axes. If the line meets the plane 2x + y + z = 9 at point Q , then the length PQ equals (1) √2 (2) 2 (3) √3 (4) 1 JEE Main 2012 (07 May Online) JEE Main Previous Year Paper

Q1. If a wire is stretched to make it 0.1% longer, its resistance will : (1) increase by 0.2% (2) decrease by 0.2% (3) decrease by 0.05% (4) increases by 0.05%

Q2. An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by : dv = −2.5√v dt where v is the instantaneous speed. The time taken by the object, to come to rest, would be: (1) 2 s (2) 4 s (3) 8 s (4) 1 s

Q3. A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is : (1) π v4g2 (2) π2 v4g2 (3) π v2 (4) π v4g g2

Q4. A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is (1) g (2) 23 g (3) g (4) 3 g 3 2

Q5. A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc: (1) continuously decreases (2) continuously increases (3) first increases and then decreases (4) remains unchanged

Q6. A pulley of radius 2 m is rotated about its axis by a force F = (20t −5t2) Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation made by the pulley before its direction of motion if reversed, is : (1) more than 3 but less than 6 (2) more than 6 but less than 9 (3) more than 9 (4) less than 3

Q7. Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is: (1) −4Gmr (2) −6Gmr (3) −9Gmr (4) zero

Q8. Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly (Surface tension of soap solution = 0.03Nm−1 ): (1) 0.2πmJ (2) 2πmJ (3) 0.4πmJ (4) 4πmJ JEE Main 2011 JEE Main Previous Year Paper

Q9. Water is flowing continuously from a tap having an internal diameter 8 × 10−3 m. The water velocity as it leaves the tap is 0.4 ms−1 . The diameter of the water stream at a distance 2 × 10−1 m below the lap is close to : (1) 7.5 × 10−3 m (2) 9.6 × 10−3 m (3) 3.6 × 10−3 m (4) 5.0 × 10−3 m Q10. 100 g of water is heated from 30∘C to 50∘C. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4148 J/kg/K ): (1) 8.4 kJ (2) 84 kJ (3) 2.1 kJ (4) 4.2 kJ

Q11.A Carnot engine operating between temperatures T1 and T2 has efficiency 16 . When T2 is lowered by 62 K, its efficiency increases to 1 . Then T1 and T2 are, respectively : 3 (1) 372 K and 330 K (2) 330 K and 268 K (3) 310 K and 248 K (4) 372 K and 310 K

Q12.A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats γ . It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by : (1) (γ−1) 2γR Mv2 K (2) γMv22R K (3) (γ−1) 2R Mv2 K (4) 2(γ+1)R(γ−1) Mv2 K

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

Q14.Two particles are executing simple harmonic motion of the same amplitude A and frequency ω along the x- axis. Their mean position is separated by distance X0 (X0 > A). If the maximum separation between them is (X0 + A), the phase difference between their motion is : (1) π (2) π 3 4 (3) π (4) π 6 2

Q15.A mass M , attached to a horizontal spring, executes S.H.M. with amplitude A1 . When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A2 . The ratio of ( A1A2 ) is : (1) M+m (2) M 1/2 M ( M+m ) (3) M+m 1/2 (4) M ( M ) M+m

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

Q17.Two identical charged spheres suspended from a common point by two massless strings of length I are initially a distance d(d << 1) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance x between them, (1) v ∝x−1 (2) v ∝x1/2 (3) v ∝x (4) v ∝x−1/2

Q18.The electrostatic potential inside a charged spherical ball is given by ϕ = αρ2 + b where r is the distance from the centre; a, b are constants. Then the charge density inside ball is (1) −6aε0r (2) −24πaε0r (3) −6aε0 (4) −24πaε0r

Q19.A resistor 'R' and 2μF capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V . Calculate the value of R to make the bulb light up 5 s after the switch has been closed. (log10 2.5 = 0.4) (1) 1.7 × 105Ω (2) 2.7 × 106Ω (3) 3.3 × 107Ω (4) 1.3 × 104Ω

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

Q21.A boat is moving due east in a region where the earth's magnetic field is 5.0 × 10−5NA−1 m−1 due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boat is 1.50 ms−1 , the magnitude of the induced emf in the wire of aerial is : (1) 0.75mV (2) 0.50mV (3) 0.15mV (4) 1mV

Q22.A fully charged capacitor C with initial charge q0 is connected to a coil of self inductance L at t = 0 . The time at which the energy is stored equally between the electric and the magnetic field is : (1) π √LC (2) 2π√LC 4 (3) √LC (4) π√LC

Q23.Let the x −z plane be the boundary between two transparent media. Medium 1 in z ≥0 has a refractive index of √2 and medium 2 with z < 0 has a refractive index of √3 . A ray of light in medium 1 given by the vector →A = 6√3^i + 8√3^j −10^k is incident on the plane of separation. The angle of refraction in medium 2 is (1) 45∘ (2) 60∘ (3) 75∘ (4) 30∘