Practice Questions

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.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 P be a plane lx + my + nz = 0 containing the line, 1−x1 = y+42 = z+23 . If plane segment AB joining points A(−3, −6, 1) and B(2, 4, −3) in ratio k : 1 then the value of k is equal to : (1) 1. 5 (2) 3 (3) 2 (4) 4

Q79.Let a, b ∈R. If the mirror image of the point P(a, 6, 9) with respect to the line x−37 = y−25 = z−1−9 is (20, b, −a −9), then |a + b| is equal to: (1) 86 (2) 90 (3) 84 (4) 88

Q79.The distance of the point ( - 1, 2, - 2 ) from the line of intersection of the planes 2𝑥+ 3𝑦+ 2𝑧= 0 and 𝑥- 2𝑦+ 𝑧= 0 is : 1 √42 (1) (2) √2 2 5 √34 (3) (4) 2 2

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.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.If →a = 2, →b = 5 and →a×→b = 8, then →a⋅→b is equal to: (1) 6 (2) 4 (3) 3 (4) 5

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.Let the foot of perpendicular from a point 𝑃( 1, 2, - 1 ) to the straight line 𝐿: 𝑥 = 𝑦 = 𝑧 be 𝑁. Let a line be 1 0 -1 drawn from 𝑃 parallel to the plane 𝑥+ 𝑦+ 2𝑧= 0 which meets 𝐿 at point 𝑄. If 𝛼 is the acute angle between the lines 𝑃𝑁 and 𝑃𝑄, then cos𝛼 is equal to . 1 √3 (1) (2) √5 2 1 1 (3) (4) √3 2√3

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.Consider the line L given by the equation x−3 2 = y−11 = z−21 . Let Q be the mirror image of the point (2, 3, −1) with respect to L. Let a plane P be such that it passes through Q, and the line L is perpendicular to P. Then which of the following points is on the plane P? (1) (−1, 1, 2) (2) (1, 1, 1) (3) (1, 1, 2) (4) (1, 2, 2)

Q79.If the equation of plane passing through the mirror image of a point (2, 3, 1) with respect to line x+1 2 = y−31 = z+2−1 and containing the line x−23 = 1−y2 = z+11 is αx + βy + γz = 24 then α + β + γ is equal to: (1) 20 (2) 19 (3) 18 (4) 21

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.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

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 equation of the plane which contains the y-axis and passes through the point (1, 2, 3) is: (1) x + 3z = 10 (2) x + 3z = 0 (3) 3x + z = 6 (4) 3x −z = 0

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.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 9 distinct balls be distributed among 4 boxes, 𝐵1, 𝐵2, 𝐵3 and 𝐵4. If the probability that 𝐵3 contains 9 exactly 3 balls is 𝑘3 then 𝑘 lies in the set : 4 (1) {𝑥∈𝑅: | 𝑥- 3 | < 1} (2) {𝑥∈𝑅: | 𝑥- 2 | ≤1} (3) {𝑥∈𝑅: | 𝑥- 1 | < 1} (4) {𝑥∈𝑅: | 𝑥- 5 | ≤1}

Q80.Let A be a set of all 4 -digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is: (1) 1 (2) 122 5 297 (3) 97 (4) 2 297 9

Q80.Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 × 2 matrices. The probability that such formed matrices have all different entries and are non-singular, is: (1) 45 (2) 23 162 81 (3) 22 (4) 43 81 162

Q80.Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P (exactly one of A, B occurs) = 59 , is: (1) 4 (2) 1 9 5 (3) 5 (4) 2 12 9

Q80.A seven digit number is formed using digits 3, 3, 4, 4, 4, 5, 5 . The probability, that number so formed is divisible by 2 , is (1) 4 (2) 3 7 7 (3) 1 (4) 6 7 7