Practice Questions

Q89.Equation of the line of the shortest distance between the lines x 1 = −1 = 1z and x−10 = y+1−2 = 1z is JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper (1) −2 x = 1y = 2z (2) x1 = −1y = −2z y+1 (3) x−1 1 = −1 = −2z (4) x−11 = y+1−1 = 1z

Q89.The angle between the lines whose direction cosines satisfy the equations l + m + n = 0 and l2 = m2 + n2 is (1) π (2) π 6 2 (3) π (4) π 3 4 = 14 , where A stands for¯¯¯

Q89.A line in the 3 -dimensional space makes an angle θ(0 < θ ≤π2 ) with both the X and Y −axes. Then, the set of all values of θ is in the interval : (1) ( π3 , π2 ] (2) (0, π4 ] (3) [ π4 , π2 ] (4) [ π6 , π3 ]

Q89.A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that x ∈A is: (1) 1 (2) 64 2 127 (3) 63 (4) 31 128 128

Q89.If the distance between planes, 4x −2y −4z + 1 = 0 and 4x −2y −4z + d = 0 is 7 , then d is: (1) 41 or −42 (2) 42 or −43 (3) −41 or 43 (4) −42 or 44

Q90.If X has a binomial distribution, B(n, p) with parameters n and p such that P(X = 2) = P(X = 3), then E(X), the mean of variable X, is (1) 2 −p (2) 3 −p (3) p (4) p 2 3 JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper

Q90.Let A and E be any two events with positive probabilities Statement I: P(E/A) ≥P(A/E)P(E). Statement II: P(A/E) ≥P(A ∩E). (1) Both the statements are false (2) Both the statements are true (3) Statement - I is false, Statement - II is true (4) Statement - I is true, Statement - II is false JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper

Q90.Let A and B be two events such that P(A ∪B) = 16 , P(A ∩B) = 41 and P(A) the complement of the event A . Then the events A and B are (1) Independent but not equally likely. (2) Independent and equally likely. (3) Mutually exclusive and independent. (4) Equally likely but not independent. JEE Main 2014 (06 Apr) JEE Main Previous Year Paper

Q90.A number x is chosen at random from the set {1, 2, 3, 4, … . , 100}. Define the event: A = the chosen number x satisfies (x−10)(x−50) ≥0 Then P(A) is: (x−30) (1) 0.71 (2) 0.70 (3) 0.51 (4) 0.20 JEE Main 2014 (12 Apr Online) JEE Main Previous Year Paper

Q90.If A and B are two events such that P(A ∪B) = P(A ∩B), then the incorrect statement amongst the following statements is : (1) P(A) + P(B) = 1 (2) P(A ∩B′) = 0 (3) A & B are equally likely (4) P(A′ ∩B) = 0 JEE Main 2014 (09 Apr Online) JEE Main Previous Year Paper

Q61.The real number k for which the equation, 2x3 + 3x + k = 0 has two distinct real roots in [0, 1] belongs to (1) lies between −1 and 0. (2) does not exist. (3) lies between 1 and 2 . (4) lies between 2 and 3 .

Q61.If α and β are roots of the equation x2 + px + 3p4 = 0 , such that |α −β| = √10 , then p belongs to the set : (1) {2, −5} (2) {−3, 2} (3) {−2, 5} (4) {3, −5}

Q61.The values of ' a ' for which one root of the equation x2 −(a + 1)x + a2 + a −8 = 0 exceeds 2 and the other is lesser than 2 , are given by : (1) 3 < a < 10 (2) a ≥10 (3) −2 < a < 3 (4) a ≤−2 JEE Main 2013 (09 Apr Online) JEE Main Previous Year Paper

Q61.If p and q are non-zero real numbers and α3 + β3 = −p, αβ = q , then a quadratic equation whose roots are α2 β2 β , α is : (1) px2 −qx + p2 = 0 (2) qx2 + px + q2 = 0 (3) px2 + qx + p2 = 0 (4) qx2 −px + q2 = 0

Q61.The least integral value α of x such that x−5 > 0, satisfies : x2+5x−14 (1) α2 + 3α −4 = 0 (2) α2 −5α + 4 = 0 (3) α2 −7α + 6 = 0 (4) α2 + 5α −6 = 0 , where z is any non-zero complex number. The set A = {a : |z| = 1 and z ≠±1} is equal

Q62.If the equations x2 + 2x + 3 = 0 and ax2 + bx + c = 0, a, b, c ∈R, have a common root, then a : b : c is: (1) 1 : 3 : 2 (2) 3 : 1 : 2 (3) 1 : 2 : 3 (4) 3 : 2 : 1 JEE Main 2013 (07 Apr) JEE Main Previous Year Paper (given z ≠−1)

Q62.Let a = Im ( 1+z22iz ) to: (1) (−1, 1) (2) [−1, 1] (3) [0, 1) (4) (−1, 0]

Q62.Let z satisfy |z| = 1 and z = 1 −¯z. Statement 1 : z is a real number. Statement 2 : Principal argument of z is π3 (1) Statement 1 is true Statement 2 is true; Statement (2) Statement 1 is false; Statement 2 is true 2 is a correct explanation for Statement 1 . (3) Statement 1 is true, Statement 2 is false. (4) Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 . JEE Main 2013 (25 Apr Online) JEE Main Previous Year Paper Q63.5 - digit numbers are to be formed using 2, 3, 5, 7 , 9 without repeating the digits. If p be the number of such numbers that exceed 20000 and q be the number of those that lie between 30000 and 90000 , then p : q is: (1) 6 : 5 (2) 3 : 2 (3) 4 : 3 (4) 5 : 3

Q62.If a complex number z statisfies the equation x + √2|z + 1| + i = 0 , then |z| is equal to : (1) 2 (2) √3 (3) √5 (4) 1

Q62.If Z1 ≠0 and Z2 be two complex numbers such that Z2 is a purely imaginary number, then 2Z1+3Z2 is equal Z1 2Z1−3Z2 to: (1) 2 (2) 5 (3) 3 (4) 1

Q63.If z is a complex number of unit modulus and argument θ, then arg ( 1+1+z−z ) can be equal to (1) θ (2) π −θ (3) −θ (4) π2 −θ

Q63.A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is : (1) 40 (2) 41 (3) 16 (4) 32 a1+a2+…+ap p3 a6 is equal to: = ; p ≠q . Then

Q63.The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is : (1) 30C7 (2) 21C8 (3) 21C7 (4) 30C8

Q63.The sum of the series : (2)2 + 2(4)2 + 3(6)2 + … upto 10 terms is : (1) 11300 (2) 11200 (3) 12100 (4) 12300

Q64.Given sum of the first n terms of an A.P. is 2n+ 3n2 . Another A.P. is formed with the same first term and double of the common difference, the sum of n terms of the new A.P. is : JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper (1) n + 4n2 (2) 6n2 −n (3) n2 + 4n (4) 3n + 2n2