Practice Questions

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.A perpendicular is drawn from a point on the line = = to the plane 𝑥+ 𝑦+ 𝑧= 3 such that the 2 -1 1 foot of the perpendicular 𝑄 also lies on the plane 𝑥- 𝑦+ 𝑧= 3. Then the coordinates of 𝑄 are (1) 2, 0, 1 (2) – 1, 0, 4 (3) 4, 0, – 1 (4) 1, 0, 2

Q89.In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is : (1) 1 (2) 5 6 6 (3) 1 (4) 2 3 3

Q89.On which of the following lines lies the point of intersection of the line, x−4 2 = 2 = z−31 and the plane, x + y + z = 2? y−5 (1) x−4 1 = 1 = z−5−1 (2) x−11 = y−32 = z+4−5 (3) x−2 2 = y−32 = z+33 (4) x+33 = 4−y3 = z+1−2

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

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.The equation of a plane containing the line of intersection of the planes 2𝑥- 𝑦- 4 = 0 and 𝑦+ 2𝑧- 4 = 0 and passing through the point 1,1, 0 is JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper (1) 𝑥- 3𝑦- 2𝑧= - 2 (2) 𝑥+ 3𝑦+ 𝑧= 4 (3) 𝑥- 𝑦- 𝑧= 0 (4) 2𝑥- 𝑧= 2

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 equation of the line passing through -4, 3, 1, parallel to the plane 𝑥+ 2𝑦- 𝑧- 5 = 0 and intersecting the 𝑥 + 1 𝑦- 3 𝑧- 2 line = = is -3 2 -1 𝑥+ 4 𝑦- 3 𝑧- 1 𝑥+ 4 𝑦- 3 𝑧- 1 (1) = = (2) = = 3 -1 1 1 1 3 (3) 𝑥+ 4 = 𝑦- 3 = 𝑧- 1 (4) 𝑥- 4 = 𝑦+ 3 = 𝑧+ 1 -1 1 1 2 1 4

Q89.If the line, x−1 2 = y+13 = z−24 meets the plane, x + 2y + 3z = 15 at a point P, then the distance of P from the origin is, (1) 2√5 (2) 92 (3) √5 (4) 7 2 2

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.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.Let S = {1, 2, … . . , 20}. A subset B of S is said to be "nice", if the sum of the elements of B is 203 . Than the probability that a randomly chosen subset of S is "nice" is : JEE Main 2019 (11 Jan Shift 2) JEE Main Previous Year Paper (1) 7 (2) 5 220 220 (3) 4 (4) None of the above 220

Q89.If Q(0, −1, −3) is the image of the point P in the plane 3x −y + 4z = 2 and R is the point (3, −1, −2), then the area (in sq. units) of ΔPQR is (1) √91 (2) √91 4 2 (3) 2√13 (4) √65 2 JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper

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

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.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.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.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.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.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.Assume that each born child is equally likely to be a boy or girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is: (1) 1 (2) 1 12 10 (3) 1 (4) 1 11 17 JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper

Q90.In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to : (1) 150 (2) 175 65 65 (3) 225 (4) 200 65 65 JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper

Q90.Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is: (1) 8 (2) 6 (3) 5 (4) 7 JEE Main 2019 (10 Apr 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