Practice Questions

Q89.If the line 𝑥- 2 = 𝑦+ 1 = 𝑧- 1 intersects the plane 2𝑥+ 3𝑦- 𝑧+ 13 = 0 at a point 𝑃 and the plane 3 2 -1 3𝑥+ 𝑦+ 4𝑧= 16 at a point 𝑄, then 𝑃𝑄 is equal to JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper (1) 2√7 (2) 14 (3) 2√14 (4) √14

Q89.The perpendicular distance from the origin to the plane containing the two lines, x + 3 2 = y −5 2 = z +7 5 and x − 1 1 = y −4 4 = z +7 4 , is (1) 11√6 (2) 11 √6 (3) 11 (4) 6√11

Q89.The plane passing through the point (4, −1, 2) and parallel to the lines x+23 = y−2−1 = z+12 and x−2 1 = y−32 = z−43 also passes through the point (1) (1, 1, −1) (2) (−1, − 1, −1) (3) (−1, −1, 1) (4) (1, 1, 1)

Q89.If a point 𝑅4, 𝑦, 𝑧 lies on the line segment joining the points 𝑃2, - 3,4 and 𝑄8,0, 10, then the distance of 𝑅 from the origin is (1) 2√21 (2) √53 (3) 6 (4) 2√14 JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper

Q89.The direction ratios of normal to the plane through the points (0,-1,0) and (0,0,1) and making an angle π with 4 the plane y −z + 5 = 0 are; 2,-1,1 2, √2 −√2 √2, 1, −1 2√3, 1, −1 (1) option 1 and 2 (2) option 2 and 3 (3) option 3 and 4 (4) all the options

Q89.A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs 12 when the throw results in the sum of 9 , and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is: (1) 1 loss (2) 1 gain 2 2 (3) 2 gain (4) 1 loss 4

Q89.Let P be the plane, which contains the line of intersection of the planes, x + y + z −6 = 0 and 2x + 3y + z + 5 = 0 and it is perpendicular to the xy-plane. Then the distance of the point (0, 0, 256) from P is equal to: JEE Main 2019 (09 Apr Shift 2) JEE Main Previous Year Paper (1) 205√5 units (2) 17 units √5 (3) 11 units (4) 63√5 units √5

Q90.A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then ( standardmeandeviationof X of X ) is equal to: (1) 4 (2) 4√3 (3) 3√2 (4) 4√3 3 JEE Main 2019 (11 Jan Shift 2) JEE Main Previous Year Paper

Q90.An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered 1, 2, 3, … , 9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is (1) 13 (2) 19 36 72 (3) 15 (4) 19 72 36 JEE Main 2019 (10 Jan Shift 1) JEE Main Previous Year Paper

Q90.An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is: (1) 21 (2) 26 49 49 (3) 32 (4) 27 49 49 JEE Main 2019 (09 Jan Shift 2) JEE Main Previous Year Paper

Q90.Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let 𝑋 denote the random variable of number of aces obtained in the two drawn cards. Then 𝑃𝑋= 1 + 𝑃𝑋= 2 equals: 24 52 (1) (2) 169 169 49 25 (3) (4) 169 169 JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper

Q90.Let a random variable 𝑋 has a binomial distribution with mean 8 and variance 4. If 𝑃𝑋≤2 = 𝑘 then the 216, value of 𝑘 is equal to (1) 121 (2) 1 (3) 17 (4) 137 JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper

Q90.In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is : (1) 400 gain (2) 400 gain 3 9 (3) 400 loss (4) 0 3 JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper

Q90.Two newspapers A and B are published in a city. It is known that 25% of the city population reads A and 20% reads B while 8% reads both A and B. Further, 30% of those who read A but not B look into advertisements and 40% of those who read B but not A also look into advertisements, while 50% of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisements is: (1) 13.5 (2) 12.8 (3) 13.9 (4) 13 JEE Main 2019 (09 Apr Shift 2) JEE Main Previous Year Paper

Q90.For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is 4 5 , then the probability that he is unable to solve less than two problems is (1) 201 5 ( 51 ) 49 (2) 16425 ( 51 ) 48 (3) 316 25 ( 54 ) 48 (4) 545 ( 54 ) 49 JEE Main 2019 (12 Apr Shift 2) JEE Main Previous Year Paper

Q90.Two integers are selected at random from the set {1, 2, … , 11} . Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is : (1) 7 (2) 1 10 2 (3) 2 (4) 3 5 5 JEE Main 2019 (11 Jan Shift 1) JEE Main Previous Year Paper

Q90.The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is: (1) 2 (2) 4 (3) 5 (4) 3 JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper

Q90.If the probability of hitting a target by a shooter, in any shot is 1 3 , then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than 5 6 , is: (1) 4 (2) 5 (3) 6 (4) 3 JEE Main 2019 (10 Jan Shift 2) JEE Main Previous Year Paper

Q1. Let A = + and B = − . The magnitude of a coplanar vector C such that (ˆi ˆj) (2ˆi ˆj) → → → → → → A . C = B. C = A . B is given by: (1) √912 (2) √209 (3) √59 (4) √109

Q1. The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c. Which of the following correctly gives the Planck length? (1) G2hc (2) Gh 21 ( c3 ) (3) G 12 h2c (4) G (h2c3

Q2. An automobile, travelling at 40 km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 80 km/h, the minimum stopping distance, in metres, is (assume no skidding) (1) 75 m (2) 160 m (3) 100 m (4) 150 m

Q2. All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up. (1) (2) (3) (4)

Q2. The velocity time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in 15 s and (ii) the time at which the car will catch up with the scooter are, respectively. (1) 112. 5 m and 22. 5 s (2) 337. 5 m and 25 s (3) 225. 5 m and 10 s (4) 112. 5 m and 15 s

Q3. A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of 30∘ . The external force required to take the same body up the plane with the same acceleration will be: (g = 10 m/s2) (1) 4 N (2) 14 N (3) 6 N (4) 20 N

Q3. A body of mass m starts moving from rest along x−axis so that its velocity varies as v = a√s where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t second after the start of the motion is (1) 8 ma4t2 (2) 14 ma4t2 (3) 4 ma4t2 (4) 18 ma4t2