Practice Questions

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.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

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

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.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.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.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.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

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 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

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]

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

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

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. 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

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

Q4. A body of mass 𝑚= 10−2 kg is moving in a medium and experiences a frictional force 𝐹= −𝑘𝑣2 . Its initial 1 speed is 𝑣0 = 10 m s−1 . After 10 s its kinetic energy is 8𝑚𝑣02, then value of 𝑘 will be:- (1) 10−1 kg m-1 s-1 (2) 10−3 kg m-1 (3) 10−3 kg 𝑠-1 (4) 10−4 kg m-1

Q5. Two particles A and B of equal mass M are moving with the same speed v as shown in figure. They collide completely inelastic and move as a single particle C . The angle θ that the path of C makes with the X -axis is JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper given by- (1) tan θ = √3− √2 (2) tan θ = 1− √2 1− √2 √2 (1+ √3) (3) tan θ = 1− √3 (4) tan θ = √3+ √2 1+ √2 1− √2

Q6. A circular hole of radius R is made in a thin uniform disc having mass and radius R, as shown in figure. The 4 moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is- (1) 219MR2 (2) 237MR2 256 512 (3) 197MR2 (4) 19MR2 256 512

Q6. In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct? (1) Every object that is weighed using this balance (2) Left arm is shorter than the right arm appears lighter than its actual weight (3) Both the arms are of same length (4) Left arm is longer than the right arm

Q6. A slender uniform rod of mass 𝑀 and length 𝑙 is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle 𝜃 with the vertical is: (1) 2𝑔 (2) 3𝑔 3𝑙cos⁡𝜃 2𝑙sin𝜃 (3) 2𝑔 (4) 3𝑔 3𝑙sin⁡𝜃 2𝑙cos⁡𝜃

Q7. If the Earth has no rotational motion, the weight of a person on the equator is W . Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3 W . The radius 4 of the Earth is 6400 km and g = 10 m s−2 (1) 0.63 × 10−3 rad s−1 (2) 0.28 × 10−3 rad s−1 (3) 1.1 × 10−3 rad s−1 (4) 0.83 × 10−3 rad s−1

Q8. A man grows into a giant such that his linear dimensions increase by a factor of 9 . Assuming that his density remains same, the stress in the leg will change by a factor of: 1 (1) (2) 9 81 (3) 1 (4) 81 9