Practice Questions

Q90.A box A contains 2 white, 3 red and 2 black balls. Another box B contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement from a randomly, selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box B is : (1) 7 (2) 9 8 16 (3) 7 (4) 9 16 32 JEE Main 2018 (15 Apr) JEE Main Previous Year Paper

Q90.A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its color is observed and this ball along with two additional balls of the same color are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is: (1) 3 (2) 3 4 10 (3) 2 (4) 1 5 5 JEE Main 2018 (08 Apr) JEE Main Previous Year Paper

Q90.Let A, B and C be three events, which are pair-wise independent and E denotes the complement of an event is equal to¯E . If P(A ∩B ∩C) = 0 and P(C) > 0, then P[(A ∩B) C] ¯¯¯(1) P(A) −P(B) (2) P(A) −P(B) + P(A) +¯¯¯(3) P(A) P(B) (4) P(B) JEE Main 2018 (16 Apr Online) JEE Main Previous Year Paper

Q90.A box ' A ' contanis 2 white, 3 red and 2 black balls. Another box ' B′ contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box ' B′ is (1) 7 (2) 9 16 32 (3) 87 (4) 169 JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper

Q61.Let p(x) be a quadratic polynomial such that p(0) = 1. If p(x) leaves remainder 4 when divided by x −1 and it leaves remainder 6 when divided by x + 1 then: (1) p(−2) = 19 (2) p(2) = 19 (3) p(−2) = 11 (4) p(2) = 11

Q61.If, for a positive integer 𝑛, the quadratic equation, 𝑥𝑥+ 1 + 𝑥+ 1𝑥+ 2 + . .. + 𝑥+ 𝑛-¯ 1𝑥+ 𝑛= 10𝑛 has two consecutive integral solutions, then 𝑛 is equal to: (1) 12 (2) 9 (3) 10 (4) 11 JEE Main 2017 (02 Apr) JEE Main Previous Year Paper

Q62.Let z ∈C, the set of complex numbers. Then the equation, 2|z + 3i| −|z −i| = 0 represents: (1) A circle with radius 8 (2) An ellipse with length of minor axis 16 3 9 (3) An ellipse with length of major axis 16 (4) A circle with diameter 10 3 3

Q62.The equation Im( iz−2z−i ) + 1 = 0, z ∈C, z ≠i represents a part of a circle having radius equal to : (1) 1 (2) 2 (3) 3 (4) 1 4 2

Q62.Let 𝜔 be a complex number such that 2𝜔+ 1 = 𝑧 where 𝑧= √-3 . If 1 1 1 1 -𝜔2 - 1 𝜔2 = 3𝑘, 1 𝜔2 𝜔7 Then 𝑘 can be equal to: (1) – 𝑧 (2) 1 𝑧 (3) -1 (4) 1

Q63.If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is: (1) 47th (2) 45th (3) 46th (4) 44th

Q63.The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B1 and a particular girl G1 never sit adjacent to each other, is: (1) 7! (2) 5 × 6! (3) 6 × 6! (4) 5 × 7!

Q63.A man 𝑋 has 7 friends, 4 of them are ladies and 3 are men. His wife 𝑌 also has 7 friends, 3 of them are ladies and 4 are men. Assume 𝑋 and 𝑌 have no common friends. Then the total number of ways in which 𝑋 and 𝑌 together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of 𝑋 and 𝑌 are in this party is: (1) 485 (2) 468 (3) 469 (4) 484

Q64. If three positive numbers a , b and c are in A.P. such that abc = 8, then the minimum possible value of b is: (1) 4 23 (2) 2 (3) 4 31 (4) 4

Q64.If the arithmetic mean of two numbers a and b, a > b > 0 , is five times their geometric mean, then a+ba−b is equal to: (1) 7√3 (2) 3√2 12 4 (3) √6 (4) 5√6 2 12

Q64.For any three positive real numbers 𝑎, 𝑏 and 𝑐. If 925𝑎2 + 𝑏2 + 25𝑐2 - 3𝑎𝑐= 15𝑏3𝑎+ 𝑐. Then (1) 𝑏, 𝑐 and 𝑎 are in G.P. (2) 𝑏, 𝑐 and 𝑎 are in A.P. (3) 𝑎, 𝑏 and 𝑐 are in A.P. (4) 𝑎, 𝑏 and 𝑐 are in G.P.

Q65.Let Sn = 131 + 13+231+2 + 13+23+331+2+3 + … + 13+23+…n31+2+…,+n . If 100 Sn = n, then n is equal to: (1) 200 (2) 199 (3) 99 (4) 19 10 x+1 x−1

Q65.The value of 21𝐶1-10𝐶1 + 21𝐶2-10𝐶2 + 21𝐶3-10𝐶3 + 21𝐶4-10𝐶4 + … + 21𝐶10-10𝐶10 is (1) 221 - 211 (2) 221 - 210 (3) 220 - 29 (4) 220 - 210

Q65.If the sum of the first n terms of the series √3 + √75 + √243 + √507 + … is 435√3, then n equals: (1) 13 (2) 15 (3) 29 (4) 18

Q66.If 5tan2⁡𝑥- cos2⁡𝑥= 2cos⁡ 2𝑥+ 9, then the value of cos⁡4𝑥 is 3 1 (1) - (2) 5 3 2 7 (3) (4) - 9 9

Q66.If (27)999 is divided by 7, then the remainder is (1) 3 (2) 1 (3) 6 (4) 2

Q66.The coefficient of x−5 in the binomial expansion of ( x 32 −x 31 +1 − x−x 21 ) where x ≠0,1 is (1) −1 (2) 4 (3) 1 (4) −4

Q67.The locus of the point of intersection of the straight lines, tx −2y −3t = 0 and x −2ty + 3 = 0 (t ∈R), is: (1) A hyperbola with the length of conjugate axis 3 (2) A hyperbola with eccentricity √5 (3) An ellipse with the length of major axis 6 (4) An ellipse with eccentricity 2 √5

Q67.The lengths of two adjacent sides of a cyclic quadrilateral are 2 units and 5 units and the angle between them is 60o . If the area of the quadrilateral is 4√3 sq. units, then the perimeter of the quadrilateral is (1) 12.5 units (2) 13 units (3) 13.2 units (4) 12 units

Q67.Let 𝑘 be an integer such that the triangle with vertices 𝑘, - 3𝑘, 5, 𝑘 and -𝑘, 2 has area 28 sq. units. Then the orthocenter of this triangle is at the point: (1) 2, - 1 (2) 1, 3 2 4 3 1 (3) 1, - (4) 2, 4 2

Q68.If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the center and subtend angles cos−1( 71 ) and sec−1(7) at the center respectively, then the distance between these chords is: (1) 8 (2) 16 √7 7 (3) 4 (4) 8 √7 7