Practice Questions

Q88.Statement 1: The shortest distance between the lines x 2 = −1y = 2z and x−14 = y−1−2 = z−14 is √2. Statement 2: The shortest distance between two parallel lines is the perpendicular distance from any point on one of the lines to the other line. (1) Statement 1 is true, Statement 2 is false. (2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1. (3) Statement 1 is false, Statement 2 is true. (4) Statement 1 is true, Statement 2 is true, , Statement 2 is not a correct explanation for Statement 1.

Q89.The coordinates of the foot perpendicular from the point (1, 0, 0) to the line x −1 y + 1 z + 10 = = are 2 −3 8 (1) (2, −3, 8) (2) (1, −1, −10) (3) (5, −8, −4) (4) (3, −4, −2) ∑ni=1 i2

Q89.The values of a for which the two points (1, a, 1) and (−3, 0, a) lie on the opposite sides of the plane 3x + 4y −12z + 13 = 0, satisfy JEE Main 2012 (07 May Online) JEE Main Previous Year Paper (1) 0 < a < 31 (2) −1 < a < 0 (3) a < −1 or a < 13 (4) a = 0

Q89.The equation of a plane containing the line x+1 −3 = y−32 = z+21 and the point (0, 7, −7) is (1) x + y + z = 0 (2) x + 2y + z = 21 (3) 3x −2y + 5z + 35 = 0 (4) 3x + 2y + 5z + 21 = 0

Q89.If →a = ^i −2^j + 3^k,→b = 2^i + 3^j −^k and →c = r^i + ^j + (2r −1^k are three vectors such that →c is parallel to the plane of →a and →b, then r is equal to (1) 1 (2) −1 (3) 0 (4) 2

Q89.If the lines x−1 2 = y+13 = z−14 and x−31 = y−k2 = 1z intersect, then k is equal to (1) −1 (2) 29 (3) 9 (4) 0 2

Q90.If six students, including two particular students A and B, stand in a row, then the probability that A and B are separated with one student in between them is (1) 8 (2) 4 15 15 (3) 2 (4) 1 15 15 JEE Main 2012 (19 May Online) 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.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 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

Q90.There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the urn and there after a ball is drawn at random from the urn, then the probability that it is white is (1) 1 (2) 2 4 3 (3) 1 (4) 1 5 3 JEE Main 2012 (26 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

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

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

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

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