Practice Questions

Q90.If A and B are any two events such that P(A) = 25 and P(A ∩B) = 203 , then the conditional probability, P(A|(A′ ∪B′)), where A′ denotes the complement of A , is equal to : (1) 11 (2) 5 20 17 (3) 8 (4) 1 17 4 JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper

Q90.An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is (1) 496 (2) 192 729 729 (3) 240 (4) 256 729 729 JEE Main 2016 (10 Apr Online) JEE Main Previous Year Paper

Q90.Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is not true? (1) E1 and E3 are independent (2) E1, E2 and E3 are independent (3) E1 and E2 are independent (4) E2 and E3 are independent JEE Main 2016 (03 Apr) JEE Main Previous Year Paper

Q61.Let α and β be the roots of equation x2 −6x −2 = 0 . If an = αn −βn, ∀ n ≥1, then the value of a10−2a8 is 2a9 equal to (1) −3 (2) 6 (3) −6 (4) 3 is

Q61.The largest value of r, for which the region represented by the set {ω ∈C||ω −4 −i| ≤r} is contained in the region represented by the set {z ∈C||z −1| ≤|z + i|}, is equal to : (1) 2√2 (2) 32 √2 (3) √17 (4) 52 √2

Q62.A complex number z is said to be unimodular if |z| = 1 . Let z1 and z2 are complex numbers such that z1−2z2 2−z1 z 2 unimodular and z2 is not unimodular, then the point z1 lies on a (1) circle of radius √2 (2) straight line parallel to x-axis (3) straight line parallel to y-axis (4) circle of radius 2

Q62.If the two roots of the equation, (a −1) (x4 + x2 + 1) + (a + 1)(x2 + x + 1) 2 = 0 are real and distinct, then the set of all values of a is equal to (1) (0, 12 ) (2) (−12 , 0) ∪(0, 12 ) (3) (−∞, −2) ∪(2, ∞) (4) (−12 , 0)

Q62.If 2 + 3i is one of the roots of the equation 2x3 −9x2 + kx −13 = 0, k ∈R, then the real root of this equation (where i2 = −1) : (1) Exists and is equal to 1 (2) Does not exist 2 (3) Exists and is equal to 1 (4) Exists and is equal to −12

Q63.If z is a non-real complex number, then the minimum value of Im z5 is (Where Im z = Imaginary part of z ) (Im z)5 JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper (1) −2 (2) −4 (3) −5 (4) −1

Q63.The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman is (1) 1960 (2) 15! (3) (15!)2 (4) 14!

Q63.The number of integers greater than 6000 that can be formed, using the digits 3, 5, 6, 7 and 8 , without repetition is (1) 72 (2) 216 (3) 192 (4) 120

Q64.Let A = {x1, x2, … , x7} and B = {y1, y2, y3} be two sets containing seven and three distinct elements respectively. Then the total number of functions f : A →B that are onto, if there exist exactly three elements x in A such that f(x) = y2, is equal to: (1) 12 ⋅7 C2 (2) 16 ⋅7 C3 (3) 14 ⋅ 7C3 (4) 14 ⋅7 C2

Q64.The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0) is JEE Main 2015 (04 Apr) JEE Main Previous Year Paper (1) 780 (2) 901 (3) 861 (4) 820

Q64.The value of ∑30r=16(r + 2)(r −3) is equal to: (1) 7775 (2) 7785 (3) 7780 (4) 7770

Q65.If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is: (1) 12 (2) 10 (3) 6 (4) 9

Q65.Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is (1) 510 (2) 219 (3) 256 (4) 275

Q65.Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is : (1) 26. 5 (2) 29. 5 (3) 28 (4) 31

Q66.The sum of first 9 terms of the series 131 + 13+231+3 + 13+23+331+3+5 +. . . is (1) 192 (2) 71 (3) 96 (4) 142

Q66.The sum of the 3rd and the 4th terms of a G. P. is 60 and the product of its first three terms is 1000. If the first term of this G. P. is positive, then its 7th term is: (1) 320 (2) 640 (3) 2430 (4) 7290 5 1 k

Q66.If the coefficient of the three successive terms in the binomial expansion of (1 + x)n are in the ratio 1 : 7 : 42, then the first of these terms in the expansion is (1) 9th (2) 6th (3) 8th (4) 7th

Q67.In a ΔABC , ab = 2 + √3, and ∠C = 60°. Then the ordered pair (∠A, ∠B) is equal to: (1) (105°, 15°) (2) (15°, 105°) (3) (45°, 75°) (4) (75°, 45°)

Q67.If = 3 , then k is equal to: ∑ n(n+1)(n+2)(n+3) n=1 (1) 33655 (2) 10517 (3) 19 (4) 1 112 6 is

Q67.If m is the A. M. of two distinct real numbers I and n (I, n > 1) and G1, G2 and G3 are three geometric means between I and n, then G41 + 2G42 + G43 equals (1) 4l2m2 n2 (2) 4 l2mn (3) 4 lm2 n (4) 4lmn2

Q68.The sum of coefficients of integral powers of x in the binomial expansion of (1 −2√x) 50 is (1) 2 1 (250 + 1) (2) 12 (350 + 1) (3) 1 2 (350) (4) 12 (350 −1)

Q68.Let L be the line passing through the point P(1, 2) such that its intercepted segment between the co-ordinate axes is bisected at P . If L1 is the line perpendicular to L and passing through the point (−2, 1), then the point of intersection of L and L1 is (1) ( 53 , 2310 ) (2) ( 45 , 125 ) (3) ( 2011 , 2910 ) (4) ( 103 , 175 )