Practice Questions

Q88.If L1 is the line of intersection of the planes 2x −2y + 3z −2 = 0, x −y + z + 1 = 0 and L2 is the line of intersection of the planes x + 2y −z −3 = 0, 3x −y + 2z −1 = 0, then the distance of the origin from the plane, containing the lines L1 and L2 is (1) 1 (2) 1 √2 4√2 (3) 1 (4) 1 3√2 2√2

Q88.If the angle between the lines x 2 = 2y = 1z and 5−x−2 = 7y−14P = z−34 is cos−1( 32 ), then P is equal to (1) 2 (2) 7 7 2 (3) −47 (4) −74

Q88.An angle between the lines whose direction cosines are given by the equations, l + 3m + 5n = 0 and 5lm −2mn + 6nl = 0, is (1) cos−1 ( 81 ) (2) cos−1 ( 61 ) (3) cos−1 ( 31 ) (4) cos−1 ( 41 )

Q88.A variable plane passes through a fixed point (3, 2, 1) and meets x, y and z-axes at A, B & C respectively. A plane is drawn parallel to the yz– plane through A , a second plane is drawn parallel to the zx− plane through B and a third plane is drawn parallel to the xy- plane through C . Then the locus of the point of intersection of these three planes, is (1) x 3 + 2y + 1z = 1 (2) x1 + 1y + 1z = 116 (3) x + y + z = 6 (4) x3 + 2y + 1z = 1

Q88.A variable plane passes through a fixed point ( 3 , 2, 1) and meets x, y and z axes at A, B and C respectively. A plane is drawn parallel to yz - plane through A , a second plane is drawn parallel zx plane through B and a third plane is drawn parallel to xy - plane through C . Then the locus of the point of intersection of these three planes, is (1) (x + y + z = 6) (2) x3 + 2y + 1z = 1 (3) x 3 + 2y + 1z = 1 (4) x1 + 1y + 1z = 116

Q89.The length of the projection of the line segment joining the points (5, −1, 4) and (4, −1, 3) on the plane, x + y + z = 7 is (1) √23 (2) √32 (3) 2 (4) 1 3 3

Q89.A plane bisects the line segment joining the points (1, 2, 3) and (−3, 4, 5) at right angles. Then this plane also passes through the point. (1) (−3, 2, 1) (2) (3, 2, 1) (3) (1, 2, −3) (4) (−1, 2, 3) JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper

Q89.An angle between the plane, x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z −1 = 0 and 5x + 8y + 2z + 14 = 0 , is (1) cos−1 3 (2) cos−1 17 ( √17 ) (√3 ) 3 (4) (3) sin−1 sin−1 17 ( √17 ) (√3 )

Q89.An angle between the plane x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z −1 = 0 and 5x + 8y + 2z + 14 = 0 is 3 ) √17 17 (1) cos−1(√3 ) (2) cos−1( 17 (3) sin−1( √173 ) (4) sin−1(√3 )

Q89.Two different families A and B are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is 1 , then the number of children in each family is 12 (1) 6 (2) 5 (3) 3 (4) 4 ¯

Q90.A box ' A ' contanis 2 white, 3 red and 2 black balls. Another box ' B′ contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box ' B′ is (1) 7 (2) 9 16 32 (3) 87 (4) 169 JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper

Q90.A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its color is observed and this ball along with two additional balls of the same color are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is: (1) 3 (2) 3 4 10 (3) 2 (4) 1 5 5 JEE Main 2018 (08 Apr) JEE Main Previous Year Paper

Q90.A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, and the probability of winning the game by both the players is equal, then the value of ' p ' is (1) 1 (2) 1 3 5 (3) 1 (4) 2 4 5 JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper

Q90.A box A contains 2 white, 3 red and 2 black balls. Another box B contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement from a randomly, selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box B is : (1) 7 (2) 9 8 16 (3) 7 (4) 9 16 32 JEE Main 2018 (15 Apr) JEE Main Previous Year Paper

Q90.Let A, B and C be three events, which are pair-wise independent and E denotes the complement of an event is equal to¯E . If P(A ∩B ∩C) = 0 and P(C) > 0, then P[(A ∩B) C] ¯¯¯(1) P(A) −P(B) (2) P(A) −P(B) + P(A) +¯¯¯(3) P(A) P(B) (4) P(B) JEE Main 2018 (16 Apr Online) JEE Main Previous Year Paper

Q1. The following observations were taken for determining surface tension 𝑇 of water by capillary method: diameter of capillary, 𝐷= 1.25 × 10-2 m rise of water, ℎ= 1.45 × 10-2 m 𝑟ℎ𝑔 Using 𝑔= 9.80 m s-2 and the simplified relation 𝑇= × 103 N m-1 the possible error in surface tension 2 is closest to: (1) 10% (2) 0 . 15% (3) 1 . 5% (4) 2 . 4%

Q1. Time (T), velocity (C) and angular momentum (h) are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be: (1) [M] = [T−1C−2h] (2) [M] = [T−1C2h] (3) [M] = [T−1C−2h−1] (4) [M] = [TC−2 h]

Q1. A physical quantity P is described by the relation P = a 21 b2 c3d−4 . If the relative errors in the measurement of a , b , c and d respectively, are 2% , 1% , 3% and 5%. Then the relative error in P will be: (1) 12% (2) 8% (3) 25% (4) 32%

Q2. A body is thrown vertically upwards. Which one of the following graphs correctly represents the velocity𝑣 vs time 𝑡? (1) (2) (3) (4)

Q2. A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m s−2 and the car has acceleration 4 m s−2 . The car will catch up with the bus after time : (1) √120 s (2) 15 s (3) √110 s (4) 10√2 s

Q2. Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity? (1) (2) (3) (4)

Q3. A conical pendulum of length l makes an angle θ = 45° with respect to Z−axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O . The speed of the pendulum, in its circular path, will be - (Take g = 10 m s−2) (1) 0.2 m s−1 (2) 0.4 m s−1 (3) 2 m s−1 (4) 4 m s−1

Q3. A time dependent force 𝐹= 6𝑡 acts on a particle of mass 1 kg. If the particle starts from the rest, the work done by the force during the first 1 sec will be: (1) 18 J (2) 4.5 J (3) 22 J (4) 9 J

Q3. An object is dropped from a height h from the ground. Every time it hits the ground it loses 50% of its kinetic energy. The total distance covered as t →∞ is: (1) 3h (2) ∞ (3) 5 h (4) 8 h 3 3

Q4. A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is: (1) 2 Mg (2) 2 Mg 2m+M 2M+m (3) 2 mg (4) 2 mg 2M+m 2m+M