Practice Questions

Q89.The equation of a plane through the line of intersection of the planes x + 2y = 3, y −2z + 1 = 0 , and perpendicular to the first plane is : (1) 2x −y −10z = 9 (2) 2x −y + 7z = 11 (3) 2x −y + 10z = 11 (4) 2x −y −9z = 10

Q89.If the projections of a line segment on the x, y and z-axes in 3-dimensional space are 2, 3 and 6 respectively, then the length of the line segment is : (1) 12 (2) 7 (3) 9 (4) 6

Q90. A, B, C try to hit a target simultaneously but independently. Their respective probabilities of hitting the targets are 3 4 , 12 , 85 . The probability that the target is hit by A or B but not by C is : (1) 21/64 (2) 7/8 (3) 7/32 (4) 9/64 JEE Main 2013 (23 Apr Online) JEE Main Previous Year Paper

Q90.The probability of a man hitting a target is 2 . He fires at the target k times (k, a given number). Then the 5 minimum k, so that the probability of hitting the target at least once is more than 7 , is : 10 (1) 3 (2) 5 (3) 2 (4) 4 JEE Main 2013 (09 Apr Online) JEE Main Previous Year Paper

Q90.A multiple choice examination has 5 questions. Each question has three alternative answers out of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is : (1) 11 (2) 10 35 35 (3) 17 (4) 13 35 35 JEE Main 2013 (07 Apr) JEE Main Previous Year Paper

Q90.Given two independent events, if the probability that exactly one of them occurs is 26 and the probability that 49 none of them occurs is 15 , then the probability of more probable of the two events is : 49 (1) 4/7 (2) 6/7 (3) 3/7 (4) 5/7 JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper

Q90.If the events A and B are mutually exclusive events such that P(A) = 3x+13 and P(B) = 1−x4 , then the set of possible values of x lies in the interval : (1) [0, 1] (2) [ 13 , 23 ] (3) [−13 , 59 ] (4) [−79 , 49 ] JEE Main 2013 (25 Apr Online) JEE Main Previous Year Paper

Q61.If a, b, c, d and p are distinct real numbers such that (a2 + b2 + c2)p2 −2p(ab + bc + cd) + (b2+ c2 + d2) ≤0, then (1) a, b, c, d are in A.P. (2) ab = cd (3) ac = bd (4) a, b, c, d are in G.P.

Q61.If z ≠1 and z−1z2 is real, then the point represented by the complex number (1) either on the real axis or on a circle passing (2) on a circle with centre at the origin through the origin (3) either on the real axis or on a circle not passing (4) on the imaginary axis through the origin

Q61.Let p, q, r ∈R and r > p > 0. If the quadratic equation px2 + qx + r = 0 has two complex roots α and β, then |α| + |β| is (1) equal to 1 (2) less than 2 but not equal to 1 (3) greater than 2 (4) equal to 2 x2 b

Q61.If a, b, c ∈R and 1 is a root of equation ax2 + bx +c = 0, then the curve y = 4ax2 + 3bx + 2c, a ≠0 intersect x-axis at JEE Main 2012 (26 May Online) JEE Main Previous Year Paper (1) two distinct points whose coordinates are always (2) no point rational numbers (3) exactly two distinct points (4) exactly one point Q62. |z1 + z2|2 + |z1 −z2|2 is equal to + (1) 2 (|z1| + |z2| (2) 2 (|z1|2 |z2|2) (3) |z1| |z2| (4) |z1|2 + |z2|2

Q61.The value of k for which the equation (K −2)x2 + 8x + K + 4 = 0 has both roots real, distinct and negative is (1) 6 (2) 3 (3) 4 (4) 1

Q62.Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is (1) 880 (2) 629 (3) 630 (4) 879

Q62.If the sum of the square of the roots of the equation x2 −(sin α −2)x −(1 + sin α) = 0 is least, then α is equal to (1) π (2) π 6 4 (3) π (4) π 3 2

Q62.Consider a quadratic equation ax2 + bx + c = 0, where 2a + 3b + 6c = 0 and let g(x) = a x33 + 2 + cx. Statement 1: The quadratic equation has at least one root in the interval (0, 1). Statement 2: The Rolle's theorem is applicable to function g(x) on the interval [0, 1]. (1) Statement 1 is false, Statement 2 is true. (2) Statement 1 is true, Statement 2 is false. (3) Statement 1 is true, Statement 2 is true, (4) Statement 1 is true, Statement 2 is true, , Statement 2 is not a correct explanation for Statement 2 is a correct explanation for Statement 1. Statement 1.

Q62.Let Z1 and Z2 be any two complex number. Statement 1: |Z1 −Z2| ≥|Z1| −|Z2| Statement 2: |Z1 + Z2| ≤|Z1| + |Z2| (1) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1. (2) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1. (3) Statement 1 is true, Statement 2 is false. (4) Statement 1 is false, Statement 2 is true.

Q63.If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman, then the number of seating arrangements is (1) 6!7! (2) (6!)2 (3) (7!)2 (4) 7 !

Q63.Let X = {1, 2, 3, 4, 5} . The number of different ordered pairs (Y , Z) that can be formed such that Y ⊆X, Z ⊆X and Y ∩Z is empty, is (1) 52 (2) 35 (3) 25 (4) 53

Q63.If the number of 5-element subsets of the set A = {a1, a2, … , a20} of 20 distinct elements is k times the number of 5-element subsets containing a4 , then k is (1) 5 (2) 20 7 (3) 4 (4) 10 3

Q63.The area of the triangle whose vertices are complex numbers z, iz, z + iz in the Argand diagram is (1) 2|z|2 (2) 1/2|z|2 (3) 4|z|2 (4) |z|2 JEE Main 2012 (12 May Online) JEE Main Previous Year Paper

Q63.Let Z and W be complex numbers such that |Z| = |W|, and arg Z denotes the principal argument of Z . Statement 1:If arg Z + arg W = π, then Z = −¯W . Statement 2: |Z| = |W|, implies arg Z −arg ¯W = π. (1) Statement 1 is true, Statement 2 is false. (2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1. (3) Statement 1 is true, Statement 2 is true, (4) Statement 1 is false, Statement 2 is true. Statement 2 is not a correct explanation for Statement 1.

Q64.The number of arrangements that can be formed from the letters a, b, c, d, e, f taken 3 at a time without repetition and each arrangement containing at least one vowel, is (1) 96 (2) 128 (3) 24 (4) 72

Q64.If the A.M. between pth and qth terms of an A.P. is equal to the A.M. between rth and sth terms of the same A.P., then p + q is equal to (1) r + s −1 (2) r + s −2 (3) r + s + 1 (4) r + s ,

Q64.The sum of the series 1 1 1 + + + … 1 + √2 √2 + √3 √3 + √4 upto 15 terms is (1) 1 (2) 2 (3) 3 (4) 4

Q64.Statement 1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + … … + (361 + 380 + 400) is 8000 . Statement 2 : ∑nk=1 (k3 −(k −1)3) = n3 for any natural number n. (1) Statement 1 is false, statement 2 is true. (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement (4) Statement 1 is true, statement 2 is false 2 is not a correct explanation for statement 1