Practice Questions

Q81.Let f : R →R be defined by f(x) = {k2x−2x,+ 3, ifif xx ≤−1> −1 possible value of k is (1) 0 (2) −12 (3) −1 (4) 1

Q82.Let p(x) be a function defined on R such that p′(x) = p′(1 −x), for all x ∈[0, 1], p(0) = 1 and p(1) = 41 . Then ∫10 p(x)dx equals (1) 21 (2) 41 (3) 42 (4) √41

Q83.The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = 3π2 is (1) 4√2 + 2 (2) 4√2 −1 (3) 4√2 + 1 (4) 4√2 −2

Q84.Solution of the differential equation cos xdy = y(sin x −y)dx, 0 < x < π2 is (1) y sec x = tan x + c (2) y tan x = sec x + c (3) tan x = (sec x + c)y (4) sec x = (tan x + c)y

Q85.Let →a = ^j −^k and →c = ^i −^j −^k. Then vector →b satisfying →a × →b + →c =→0 and →a ⋅→b = 3 is (1) 2^i −^j + 2^k (2) ^i −^j −2^k (3) ^i + ^j −2^k (4) −^i + ^j −2^k →

Q86.If the vectors →a = ^i −^j + 2^k, b = 2^i + 4^j + ^k and→c= λ^i +^j + μ^k are mutually orthogonal, then (λ, μ) = (1) (2, −3) (2) (−2, 3) (3) (3, −2) (4) (−3, 2)

Q87.Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x −y + z = 5. Statement-2: The plane x −y + z = 5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4). (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is false Statement-2 is not the correct explanation for Statement-1 (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1 JEE Main 2010 JEE Main Previous Year Paper

Q88.A line AB in three-dimensional space makes angles 45∘ and 120∘ with the positive x-axis and the positive y- axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals (1) 45∘ (2) 60∘ (3) 75∘ (4) 30∘

Q89.Four numbers are chosen at random (without replacement) from the set {1, 2, 3, … . , 20} . Statement-1: The probability that the chosen numbers when arranged in some order will form an AP is 1 . Statement-2: If the 85 four chosen numbers from an AP, then the set of all possible values of common difference is {±1, ±2, ±3, ±4, ±5}. (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is false Statement-2 is not the correct explanation for Statement-1 (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Q90.An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is (1) 2 (2) 1 7 21 (3) 2 (4) 1 23 3 JEE Main 2010 JEE Main Previous Year Paper

Q61.If the roots of the equation bx2 + cx + a = 0 be imaginary, then for all real values of x, the expression 3b2x2 + 6bcx + 2c2 is (1) greater than 4ab (2) less than 4ab (3) greater than −4ab (4) less than - 4ab

Q62.If z −4z = 2, then the maximum value of |z| is equal to (1) √3 + 1 (2) √5 + 1 (3) 2 (4) 2 + √2

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

Q64.The sum to the infinity of the series 1 + 32 + 326 + 1033 + 1434 + … … is (1) 2 (2) 3 (3) 4 (4) 6

Q65.The remainder left out when 82n −(62)2n+1 is divided by 9 is (1) 0 (2) 2 (3) 7 (4) 8

Q66.The lines p (p2 + 1)x −y + q = 0 and (p2 + 1)2x + (p2 + 1)y + 2q = 0 are perpendicular to a common line for (1) no value of p (2) exactly one value of p (3) exactly two values of p (4) more than two values of p

Q67.Three distinct points A, B and C are given in the 2 - dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (−1, 0) is equal to 31 . Then the circumcentre of the triangle ABC is at the point JEE Main 2009 JEE Main Previous Year Paper (1) (0, 0) (2) ( 54 , 0) (3) ( 25 , 0) (4) ( 53 , 0)

Q68.If P and Q are the points of intersection of the circles x2 + y2 + 3x + 7y + 2p −5 = 0 and x2 + y2 + 2x + 2y −p2 = 0, then there is a circle passing through P, Q and (1, 1) for (1) all values of p (2) all except one value of p (3) all except two values of p (4) exactly one value of p

Q69.The ellipse x2 + 4y2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is (1) x2 + 16y2 = 16 (2) x2 + 12y2 = 16 (3) 4x2 + 48y2 = 48 (4) 4x2 + 64y2 = 48

Q70.Statement-1: ∼(p ↔∼q) is equivalent to p ↔q . Statement-2 : ∼(p ↔∼q) is a tautology. (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true

Q71.If the mean deviation of number 1, 1 + d, 1 + 2d, … . , 1 + 100d from their mean is 255 , then the d is equal to (1) 10.0 (2) 20.0 (3) 10.1 (4) 20.2

Q72.Statement-1 : The variance of first n even natural numbers is n2−14 Statement-2 : The sum of first n natural numbers is n(n+1) 2 and the sum of squares of first n natural numbers is n(n+1)(2n+1)6 (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true

Q73.If A, B and C are three sets such that A ∩B = A ∩C and A ∪B = A ∪C , then (1) A = B (2) A = C (3) B = C (4) A ∩B = ϕ

Q74.Let A be a 2 × 2 matrix Statement-1 : adj(adj A) = A Statement-2 : |adj A| = |A| (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true

Q75. a a + 1 a −1 a + 1 b + 1 c −1 Let a, b, c be such that b(a + c) ≠0. If −b b + 1 b −1 + a −1 b −1 c + 1 = 0, then the c c −1 c + 1 (−1)n+2a (−1)n+1b (−1)nc value of ' n ' is (1) zero (2) any even integer (3) any odd integer (4) any integer JEE Main 2009 JEE Main Previous Year Paper