Practice Questions

Q86.The area (in sq. units) of the parallelogram whose diagonals are along the vectors 8ˆi −6ˆj and 3ˆi + 4ˆj −12ˆk, is: (1) 20 (2) 65 (3) 52 (4) 26

Q86.If the vector b = 3ˆj + 4ˆk is written as the sum of a vector b1 , parallel to →a = ˆi + ˆj and a vector b2, → → perpendicular to →a, then b1 × b2 is equal to : JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper (1) 6ˆi −6ˆj + 29 ˆk (2) −3ˆi + 3ˆj −9ˆk (3) −6ˆi + 6ˆj −92 ˆk (4) 3ˆi −3ˆj + 9ˆk

Q87.If the line, x−3 1 = y+2−1 = z+λ−2 lies in the plane, 2x −4y + 3z = 2 , then the shortest distance between this line and the line, x−1 12 = 9y = 4z is (1) 1 (2) 2 (3) 3 (4) 0

Q87.If the image of the point 𝑃1, - 2, 3 in the plane, 2𝑥+ 3𝑦- 4𝑧+ 22 = 0 measured parallel to the line, 𝑥 𝑦 𝑧 = = is 𝑄, then 𝑃𝑄 is equal to: 1 4 5 (1) 3√5 (2) 2√42 (3) √42 (4) 6√5

Q87.The coordinates of the foot of the perpendicular from the point (1, −2, 1) on the plane containing the lines x+1 6 = y−17 = z−38 and x−13 = y−25 = z−37 , is: (1) (2, −4, 2) (2) (1, 1, 1) (3) (0, 0, 0) (4) (−1, 2, −1) = 2, is,

Q88.The line of intersection of the planes →r ⋅(3ˆi −ˆj + ˆk) = 1 and →r ⋅(ˆi + 4ˆj −2ˆk) (1) x−613 y−513 z (2) x−47 y z+ 57 2 = 7 = −13 2 = −7 = 13 y z−57 (3) x−613 y−513 z (4) x−47 2 = −7 = −13 −2 = 7 = 13

Q88.The distance of the point 1, 3, - 7 from the plane passing through the point 1, - 1, - 1 , having normal 𝑥- 1 𝑦+ 2 𝑧- 4 𝑥- 2 𝑦+ 1 𝑧+ 7 perpendicular to both the lines = = and = = , is: 1 -2 3 2 -1 -1 (1) 20 (2) 10 √74 √83 (3) 5 (4) 10 √83 √74 JEE Main 2017 (02 Apr) JEE Main Previous Year Paper

Q88.If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B & C , then the locus of the centroid of ΔABC is (1) 1 + 1 + 1 = 1 (2) x2 y2 z2 x2 1 + y21 + z21 = 3 (3) 1 + 1 + 1 = 9 (4) 1 + 1 + 1 = 91 x2 y2 z2 x2 y2 z2

Q89.An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is: JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper (1) 127 (2) 63 128 64 (3) 255 (4) 1 256 2

Q89.For three events, 𝐴, 𝐵 and 𝐶, 𝑃(Exactly one of 𝐴 or 𝐵 occurs) = 𝑃(Exactly one of 𝐵 or 𝐶 occurs) 1 1 = 𝑃(Exactly one of 𝐶 or 𝐴 occurs) = and 𝑃(All the three events occur simultaneously) = . 4 16 Then the probability that at least one of the events occurs, is: (1) 7 (2) 7 32 16 7 3 (3) (4) 64 16

Q89. From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one women. Then the probability for these committees to have more women than men, is : (1) 3 (2) 2 11 23 (3) 1 (4) 21 11 220

Q90.Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are 4 3 , 12 and 58 respectively, then the probability that the target is hit by P or Q but not by R is: (1) 3964 (2) 2164 (3) 9 (4) 15 64 64 JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper

Q90.Let E & F be two independent events. The probability that E & F happen is 121 and the probability that neither E nor F happens is 1 , then a value of P(E) is: 2 P(F) (1) 4 (2) 1 3 3 (3) 3 (4) 5 2 12 JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper

Q90.If two different numbers are taken from the set 0, 1, 2, 3, . . . . . , 10; then the probability that their sum as well as absolute difference are both multiple of 4, is: (1) 6 (2) 12 55 55 (3) 14 (4) 7 45 55 JEE Main 2017 (02 Apr) JEE Main Previous Year Paper

Q61.The sum of all real values of x satisfying the equation (x2 −5x + 5) x2+4x−60 = 1 is (1) 6 (2) 5 (3) 3 (4) −4

Q61.If x is a solution of the equation √2x + 1 − √2x −1 = 1, (x ≥12 ) , then √4x2 −1 is equal to : (1) 3 (2) 1 4 2 (3) 2√2 (4) 2 JEE Main 2016 (10 Apr Online) JEE Main Previous Year Paper

Q61.If the equations x2 + bx −1 = 0 and x2 + x + b = 0 have a common root different from −1, then |b| is equal to : (1) 2 (2) 3 (3) √3 (4) √2

Q62.Let z = 1 + ai , be a complex number, a > 0, such that z3 is a real number. Then, the sum 1 + z + z2 + … . +z11 is equal to : (1) 1365 √3i (2) −1365 √3i (3) −1250 √3i (4) 1250 √3i

Q62.A value of θ for which 2+3i sin θ is purely imaginary, is 1−2i sin θ (1) sin−1( √34 ) (2) sin−1( √31 ) (3) π (4) π 3 6

Q62.The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there 2√2 units in the south-west wards direction. Then its new position in the Argand plane is at the point represented by : (1) 1 + i (2) 2 + 2i (3) −2 −2i (4) −1 −i

Q63.If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is (1) 52nd (2) 58th (3) 46th (4) 59th

Q63.If n+2C6 = 11, then n satisfies the equation: n−2P2 (1) n2 + n −110 = 0 (2) n2 + 2n −80 = 0 (3) n2 + 3n −108 = 0 (4) n2 + 5n −84 = 0

Q63.If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all such words is : (1) 110 (2) 59 (3) 11! (4) 56 (2!)3

Q64.Let x, y, z be positive real numbers such that x + y + z = 12 and x3y4z5 = (0 .1)(600)3. Then x3 + y3 + z3 is equal to (1) 342 (2) 216 (3) 258 (4) 270 is equal to:

Q64.If the 2nd, 5th and 9th terms of a non-constant arithmetic progression are in geometric progression, then the common ratio of this geometric progression is (1) 1 (2) 74 (3) 8 (4) 4 5 3 is 16 m , then m