Practice Questions

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

Q76.Let A and B denote the statements A: cos α + cos β + cos γ = 0 B: sin α + sin β + sin γ = 0 If cos(β −γ) + cos(γ −α) + cos(α −β) = −32 , then (1) A is true and B is false (2) A is false and B is true (3) both A and B are true (4) both A and B are false

Q77.For real x, let f(x) = x3 + 5x + 1, then (1) f is one-one but not onto R (2) f is onto R but not one-one (3) f is one-one and onto R (4) f is neither one-one nor onto R

Q78.Let f(x) = (x + 1)2 −1, x ≥−1 Statement-1: The set {x : f(x) = f −1(x)} = {0, −1} Statement-2 : f is a bijection. (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

Q79.Let f(x) = x|x| and g(x) = sin x. Statement-1 : gof is differentiable at x = 0 and its derivative is continuous at that point. Statement-2 : gof is twice differentiable at x = 0 . (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

Q80.Let y be an implicit function of x defined by x2x −2xx cot y −1 = 0 . Then y′(1) equals (1) −1 (2) 1 (3) log 2 (4) −log 2

Q81.Given P(x) = x4 + ax3 + bx2 + cx + d such that x = 0 is the only real root of P ′(x) = 0 . If P(−1) < P(1), then in the interval [−1, 1] (1) P(−1) is the minimum and P(1) is the (2) P(−1) is not minimum but P(1) is the maximum maximum of P of P (3) P(−1) is the minimum and P(1) is not the (4) neither P(−1) is the minimum nor P(1) is the maximum of P maximum of P

Q82.The shortest distance between the line y −x = 1 and the curve x = y2 is (1) 3√2 (2) 2√3 8 8 (3) 3√2 (4) √3 5 4 Q83. ∫π0 [cot x]dx, [∙] denotes the greatest integer function, is equal to (1) π (2) 1 2 (3) −1 (4) −π2

Q84.The area of the region bounded by the parabola (y −2)2 = x −1, the tangent to the parabola at the point (2, 3) and the x-axis is (1) 3 (2) 6 (3) 9 (4) 12 JEE Main 2009 JEE Main Previous Year Paper

Q85.The differential equation which represents the family of curves y = c1ec2x , where c1 and c2 are arbitrary constants is (1) y′ = y2 (2) y′′ = y′y (3) yy′′ = y′ (4) yy′′ = (y′)2

Q86.If →u, →v, ¯w are non-coplanar vectors and p, q are real numbers, then the equality [ 3→u p→v p→w ] −[ p→v →w q→u ] −[ 2→w q→v q→u ] = 0 holds for (1) exactly one value of (p, q) (2) exactly two values of (p, q) (3) more than two but not all values of (p, q) (4) all values of (p, q)

Q87.Let the line x−2 3 = y−1−5 = z+22 lies in the plane x + 3y −αz + β = 0. Then (α, β) equals (1) (6, −17) (2) (−6, 7) (3) (5, −15) (4) (−5, 15)

Q88.The projections of a vector on the three coordinate axis are 6, −3, 2 respectively. The direction cosines of the vector are (1) 6, −3, 2 (2) 65 , −35 , 25 (3) 7 6 , −37 , 27 (4) −67 , −37 , 27

Q89.In a binomial distribution B (n, p = 41 ), if the probability of at least one success is greater than or equal to 109 , then n is greater than 1 1 (1) 3 (2) 3 log10 4+log10 log10 4−log10 (3) 9 (4) 4 log10 4−log10 3 log10 4−log10 3

Q90.One ticket is selected at random from 50 tickets numbered 00, 01, 02, … , 49. Then the probability that the sum of the digits on the selected ticket is 8 , given that the product of these digits is zero, equals (1) 1 (2) 1 14 7 (3) 5 (4) 1 14 50 JEE Main 2009 JEE Main Previous Year Paper

Q1. The dimension of magnetic field in M, L, T and C (Coulomb) is given as (1) MLT−1C−1 (2) MT2C−2 (3) MT−1C−1 (4) MT−2C−1

Q2. A body is at rest at x = 0. At t = 0 , it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive x direction with a constant speed. The position of the first body is given by x1(t) after time ' t ' and that of the second body by x2(t) after the same time interval. Which of the following graphs correctly describes (x1 −x2) as a function of time ' t '? (1) (2) (3) (4)

Q3. An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range (1) 200 J −500 J (2) 2 × 105 J −3 × 105 J (3) 20, 000 J −50, 000 J (4) 2, 000 J −5, 000 J

Q4. A thin rod of length ' L ' is lying along the x-axis with its ends at x = 0 and x = L . Its linear density (mass/length) varies with x ask ( Lx )n , where n can be zero or any positive number. If the position xCM of the centre of mass of the rod is plotted against ' n ', which of the following graphs best approximates the dependence of xCM on n ? (1) (2) (3) (4) JEE Main 2008 JEE Main Previous Year Paper

Q5. A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms−1 . The magnitude of its momentum is recorded as (1) 17.6 kg ms−1 (2) 17.565 kg ms−1 (3) 17.56 kg ms−1 (4) 17.57 kg ms−1

Q6. A block of mass 0.50 kg is moving with a speed of 2.00 m/s on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is (1) 0.16 J (2) 1.00 J (3) 0.67 J (4) 0.34 J

Q7. Consider a uniform square plate of side ' a ' and mass ' m '. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is (1) 5 ma2 (2) 1 ma2 6 12 (3) 7 ma2 (4) 2 ma2 12 3