Practice Questions

Q79.If the mirror image of the point (1, 3, 5) with respect to the plane 4x −5y + 2z = 8 is (α, β, γ), then 5(α + β + γ) equals : (1) 43 (2) 47 (3) 41 (4) 39

Q79.The equation of the plane passing through the point 1, 2, - 3 and perpendicular to the planes 3𝑥+ 𝑦- 2𝑧= 5 and 2𝑥- 5𝑦- 𝑧= 7, is (1) 11𝑥+ 𝑦+ 17𝑧+ 38 = 0 (2) 3𝑥- 10𝑦- 2𝑧+ 11 = 0 (3) 6𝑥- 5𝑦+ 2𝑧+ 10 = 0 (4) 6𝑥- 5𝑦- 2𝑧- 2 = 0

Q79.Let →a and b be two vectors such that 2→a+ 3b = 3→a+ b and the angle between →a and b is 60°. If 8→a → vector, then b is equal to : (1) 8 (2) 4 (3) 6 (4) 5

Q79.Let the plane passing through the point (−1, 0, −2) and perpendicular to each of the planes 2x + y −z = 2 and x −y −z = 3 be ax + by + cz + 8 = 0. Then the value of a + b + c is equal to: (1) 3 (2) 8 (3) 5 (4) 4

Q79.The differential equation satisfied by the system of parabolas y2 = 4a(x + a) is (1) dy 2 dy (2) dy 2 dy −y = 0 + y = 0 y( dx ) −2x( dx ) y( dx ) −2x( dx ) + −y = 0 + −y = 0 (4) y( dxdy ) 2x( dxdy ) (3) y( dxdy ) 2 2x( dxdy )

Q79.A plane P contains the line x + 2y + 3 z + 1 = 0 = x −y −z −6, and is perpendicular to the plane −2x + y + z + 8 = 0. Then which of the following points lies on P? (1) (2, −1, 1) (2) (0, 1, 1) (3) (−1, 1, 2) (4) (1, 0, 1)

Q79.Let →a = 2ˆi + ˆj −2ˆk and b = ˆi + ˆj. If →cis a vector such that →a⋅→c= →c, →c−→a = 2√2 and the angle between π , then the value of is: and →cis × × 6 (→a → → b) (→a b) ×→c (1) 2 (2) 4 3 (3) 3 (4) 32

Q79.Let P be the plane passing through the point (1, 2, 3) and the line of intersection of the planes = 6. Then which of the following points does NOT lie on P ? →r⋅(ˆi + ˆj + 4ˆk) = 16 & →r⋅(−ˆi + ˆj + ˆk) JEE Main 2021 (26 Aug Shift 2) JEE Main Previous Year Paper (1) (4, 2, 2) (2) (6, −6, 2) (3) (−8, 8, 6) (4) (3, 3, 2)

Q79.The coefficients a, b and c of the quadratic equation, ax2 + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is: (1) 1 (2) 1 72 36 (3) 1 (4) 5 54 216

Q79.The angle between the straight lines, whose direction cosines l, m, n are given by the equations 2l + 2 m −n = 0 and mn + nl+ lm= 0, is: (1) π (2) π 3 2 (3) cos−1( 89 ) (4) π −cos−1( 94 )

Q79.Equation of a plane at a distance √221 planes x −y −z −1 = 0 and 2x + y −3 z + 4 = 0, is (1) −x + 2y + 2z −3 = 0 (2) 3x −4z + 3 = 0 (3) 3x −1y −5z + 2 = 0 (4) 4x −y −5z + 2 = 0

Q79.If the shortest distance between the straight lines 3(x −1) = 6(y −2) = 2(z −1) and 4(x −2) = 2(y −λ) = (z −3), λ ∈R is 1 , then the integral value of λ is equal to: √38 (1) 3 (2) 2 (3) 5 (4) −1

Q79.Let the acute angle bisector of the two planes 𝑥- 2𝑦- 2𝑧+ 1 = 0 and 2𝑥- 3𝑦- 6𝑧+ 1 = 0 be the plane 𝑃. Then which of the following points lies on 𝑃 ? 1 (1) ( 0, 2, - 4 ) (2) -2, 0, - 2 (3) ( 4, 0, - 2 ) (4) 3, 1, - 1 2

Q79.In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is : (1) 14 (2) 7 45 45 (3) 8 (4) 28 45 45

Q80.Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be 21 and probability of occurrence of 0 at the odd place be 31 . Then the probability that 10 is followed by 01 is equal to : (1) 1 (2) 1 18 3 (3) 1 (4) 1 6 9

Q80.A student appeared in an examination consisting of 8 true-false type questions. The student guesses the answers with equal probability. The smallest value of n, so that the probability of guessing at least n correct answers is less than 1 , is : 2 (1) 5 (2) 6 (3) 3 (4) 4

Q80.An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is: (1) 1 (2) 5 32 16 3 1 (3) (4) 16 2

Q80.Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is: (1) 5 (2) 1 8 8 (3) 5 (4) 1 16

Q80.A fair die is tossed until six is obtained on it. Let X be the number of required tosses, then the conditional probability P(X ⩾5 ∣X > 2) is : (1) 25 (2) 5 36 6 (3) 11 (4) 125 36 216

Q80.A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is : (1) 3 (2) 52 4 867 (3) 39 (4) 22 50 425 ¯

Q80.Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0. 4096 and 0. 2048 respectively. Then the probability of getting exactly 3 successes is equal to : (1) 32 (2) 80 625 243 (3) 40 (4) 128 243 625

Q80.A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is (1) 15 (2) 15 213 214 (3) 15 (4) 15 212 28

Q80.Two dices are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is: (1) 4 (2) 17 9 36 (3) 5 (4) 1 12 2

Q80.Let A denote the event that a 6 -digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3 . Then probability of event A is equal to : (1) 9 (2) 4 56 9 (3) 3 (4) 11 7 27

Q80.When a certain biased die is rolled, a particular face occurs with probability 16 −x and its opposite face occurs with probability 61 + x. All other faces occur with probability 16 . Note that opposite faces sum to 7 in any die. If 0 < x < 61 , and the probability of obtaining total sum = 7, when such a die is rolled twice, is 9613 , then the value of x is JEE Main 2021 (27 Aug Shift 1) JEE Main Previous Year Paper (1) 161 (2) 121 (3) 81 (4) 19 Z is the set of ∈R : x −2 > B = C = ∈R : x −4