Practice Questions

Q90.Assume that each born child is equally likely to be a boy or girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is: (1) 1 (2) 1 12 10 (3) 1 (4) 1 11 17 JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper

Q90.Let 𝐴 and 𝐵 be two non-null events such that 𝐴⊂𝐵. Then, which of the following statements is always correct? (1) 𝑃𝐴| 𝐵≥𝑃( 𝐴) (2) 𝑃𝐴| 𝐵= 𝑃𝐵- 𝑃𝐴 (3) 𝑃𝐴| 𝐵≤ 𝑃( 𝐴) (4) 𝑃𝐴| 𝐵= 1 JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper

Q90.In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is : (1) 400 gain (2) 400 gain 3 9 (3) 400 loss (4) 0 3 JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper

Q90.In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to : (1) 150 (2) 175 65 65 (3) 225 (4) 200 65 65 JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper

Q90.If the probability of hitting a target by a shooter, in any shot is 1 3 , then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than 5 6 , is: (1) 4 (2) 5 (3) 6 (4) 3 JEE Main 2019 (10 Jan Shift 2) JEE Main Previous Year Paper

Q61.Let p, q and r be real numbers (p ≠q, r ≠0), such that the roots of the equation x+p1 + x+q1 = 1r are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to (1) p2 + q2 (2) p2+q2 2 (3) 2(p2 + q2) (4) p2 + q2 + r2

Q61.If λ ∈R is such that the sum of the cubes of the roots of the equation, x2 + (2 −λ)x + (10 −λ) = 0 is minimum, then the magnitude of the difference of the roots of this equation is (1) 20 (2) 2√5 (3) 2√7 (4) 4√2 z ∈C satisfying |z| = 1

Q61.If |z −3 + 2i| ≤4 then the difference between the greatest value and the least value of |z| is (1) √13 (2) 2√13 (3) 8 (4) 4 + √13

Q61.If λ ∈R is such that the sum of the cubes of the roots of the equation x2 + (2 −λ)x + (10 −λ) = 0 is minimum, then the magnitude of the difference of the roots of this equation is : (1) 4√2 (2) 20 (3) 2√5 (4) 2√7

Q61.Let S = {x ∈R : x ≥0 & 2 √x −3 + √x (√x −6) + 6 = 0} . Then S : (1) Contains exactly four elements (2) Is an empty set (3) Contains exactly one element (4) Contains exactly two elements

Q62.The set of all α ∈R, for which w = 1+(1−8α)z1−z is a purely imaginary number, for all and Re z ≠1 , is (1) {0} (2) an empty set (3) {0, 14 , −14 } (4) equal to R

Q62.If tan A and tan B are the roots of the quadratic equation 3x2 −10x −25 = 0 , then the value of 3 sin2(A + B) −10 sin(A + B) cos(A + B) −25 cos2(A + B) is : (1) −25 (2) 10 (3) −10 (4) 25 z ∈C satisfying |z| = 1

Q62.If an angle A of a ΔABC satisfies 5 cos A + 3 = 0, then the roots of the quadratic equation 9x2 + 27x + 20 = 0 are (1) sec A, cot A (2) sec A, tan A (3) tan A, cos A (4) sin A, sec A n = 1 is

Q62.If α, β ∈C are the distinct roots of the equation x2 −x + 1 = 0, then α101 + β107 is equal to (1) 2 (2) −1 (3) 0 (4) 1

Q62.The number of four letter words that can be formed using the letters of the word BARRACK is (1) 144 (2) 120 (3) 264 (4) 270 and Bn = 1 −An . Then, the least odd natural number p

Q63.The least positive integer n for which ( 1−i√31+i√3 ) (1) 2 (2) 5 (3) 6 (4) 3

Q63.From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is: (1) At least 750 but less than 1000 (2) At least 1000 (3) Less than 500 (4) At least 500 but less than 750

Q63.The set of all α ∈R, for which w = 1+(1−8α)z1−z is a purely imaginary number, for all and Re(z) ≠1 , is : (1) {0} (2) {0, 14 , −14 } (3) equal to R (4) an empty set

Q63.Let An = ( 34 ) −( 43 ) 2 + ( 43 ) 3 −… + (−1)n−1( 43 ) n , so that Bn > An , for all n ≥p is (1) 5 (2) 7 (3) 11 (4) 9

Q63. n - digit numbers are formed using only three digits 2,5 and 7 . The smallest value of n for which 900 such distinct numbers can be formed, is (1) 6 (2) 8 (3) 9 (4) 7

Q64.If b is the first term of an infinite G. P whose sum is five, then b lies in the interval. (1) (−∞, −10) (2) (10, ∞) (3) (0, 10) (4) (−10, 0)

Q64. n-digit numbers are formed using only three digits 2, 5 and 7 . The smallest value of n for which 900 such distinct numbers can be formed is : (1) 9 (2) 7 (3) 8 (4) 6

Q64.Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 12 + 2 ⋅22 + 32 + 2 ⋅42 + 52 + 2 ⋅62 + … If B −2A = 100λ, then λ is equal to : (1) 496 (2) 232 (3) 248 (4) 464

Q64.If a, b, c are in A.P. and a2, b2, c2 are in G.P. such that a < b < c and a + b + c = 34 , then the value of a is JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper (1) 1 4 − 3√21 (2) 14 − 4√21 (3) 1 (4) 1 1 − 4 √2 4 − 2√21

Q64.The number of numbers between 2, 000 and 5, 000 that can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is not allowed) and are multiple of 3 is (1) 36 (2) 30 (3) 24 (4) 48