Practice Questions

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.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

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

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

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

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.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

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

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 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 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.Let a1, a2, a3, … an, … ,be in A.P. If a3 + a7 + a11 + a15 = 72, then the sum of its first 17 terms is equal to : (1) 306 (2) 204 (3) 153 (4) 612

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

Q65.The sum ∑10r=1(r2 + 1) × (r!), is equal to: (1) 11 × (11!) (2) 10 × (11! ) (3) (11)! (4) 101 × (10!) 1

Q65.The value of ∑15r=1 r2( 15Cr−115Cr ) (1) 1240 (2) 560 (3) 1085 (4) 680 JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper

Q65.If the sum of the first ten terms of the series (1 35 ) 2 + (2 25 ) 2 + (3 15 ) 2 + 42 + (4 45 ) 2 + … . , 5 is equal to (1) 100 (2) 99 (3) 102 (4) 101 n , x, y ≠0, is 28, then the sum of the coefficients

Q66.If the coefficients of x−2 and x−4 , in the expansion of 3 18 + 1 1 , (x > 0) , are m and n respectively, then (x 2x 3 ) m is equal to n (1) 27 (2) 182 (3) 54 (4) 54

Q66.For x ∈R, x ≠−1, if (1 + x)2016 + x(1 + x)2015 + x2(1 + x)2014 + … + x2016 = 2016 aixi , then a17 is ∑ i=0 equal to (1) 2017! (2) 2016! 17!2000! 17!1999! (3) 2016! (4) 2017! 16! 2000!

Q66.If the number of terms in the expansion of (1 −2x + y24 ) of all the terms in this expansion is (1) 243 (2) 729 (3) 64 (4) 2187