Practice Questions

Q69.If the line y = mx + 1 meets the circle x2 + y2 + 3x = 0 in two points equidistant from and on opposite sides of x -axis, then (1) 3m + 2 = 0 (2) 3m −2 = 0 (3) 2m + 3 = 0 (4) 2m −3 = 0

Q69.The equation of the circle passing through the point (1, 2) and through the points of intersection of x2 + y2 −4x −6y −21 = 0 and 3x + 4y + 5 = 0 is given by (1) x2 + y2 + 2x + 2y + 11 = 0 (2) x2 + y2 −2x + 2y −7 = 0 (3) x2 + y2 + 2x −2y −3 = 0 (4) x2 + y2 + 2x + 2y −11 = 0

Q69.Consider the straight lines L1 : x −y = 1 L2 : x + y = 1 L3 : 2x + 2y = 5 L4 : 2x −2y = 7 The correct statement is JEE Main 2012 (26 May Online) JEE Main Previous Year Paper (1) L1 ∥L4, L2∥L3, L1 intersect L4 . (2) L1 ⊥L2, L1∥L3, L1 intersect L2 . (3) L1 ⊥L2, L2∥L3, L1 intersect L4 . (4) L1 ⊥L2, L1 ⊥L3, L2 intersect L4 .

Q70.The equation of the normal to the parabola, x2 = 8y at x = 4 is (1) x + 2y = 0 (2) x + y = 2 (3) x −2y = 0 (4) x + y = 6 y2

Q70.Statement 1: y = mx − m1 is always a tangent to the parabola, y2 = −4x for all non-zero values of m. Statement 2: Every tangent to the parabola, y2 = −4x will meet its axis at a point whose abscissa is non- negative. (1) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1. (2) Statement 1 is false, Statement 2 is true. (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 of Statement 1.

Q70.The logically equivalent preposition of p ⇔q is (1) (p ⇒q∧)q ⇒p ) (2) p ∧q (3) (p ∧q∨)q ≠p ) (4) (p ∧q ⇒q ∨(p )

Q70.The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is (1) 10 (2) 3 3 5 (3) 56 (4) 53

Q70.The number of common tangents of the circles given by x2 + y2 −8x −2y + 1 = 0 and x2 + y2 + 6x + 8y = 0 is (1) one (2) four (3) two (4) three

Q71.If the foci of the ellipse x2 , then b2 is equal 16 + = 1 coincide with the foci of the hyperbola 144x2 −y281 = 251 b2 to (1) 8 (2) 10 (3) 7 (4) 9

Q71.The chord PQ of the parabola y2 = x, where one end P of the chord is at point (4, −2), is perpendicular to the axis of the parabola. Then the slope of the normal at Q is (1) −4 (2) −14 (3) 4 (4) 1 4

Q71.If the mean of 4, 7, 2, 8, 6 and a is 7 , then the mean deviation from the median of these observations is (1) 8 (2) 5 (3) 1 (4) 3

Q71.Statement 1 : An equation of a common tangent to the parabola y2 = 16√3x and the ellipse 2x2 + y2 = 4 is y = 2x + 2√3 . Statement 2 : If the line y = mx + 4√3m , (m ≠0) is a common tangent to the parabola y2 = 16√3x and the ellipse 2x2 + y2 = 4 , then m satisfies m4 + 2m2 = 24 . (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

Q71.If the eccentricity of a hyperbola x2 K 2 is = 1, which passes through (K, 2), is √133 , then the value of 9 −y2b2 (1) 18 (2) 8 (3) 1 (4) 2

Q72.If in a triangle ABC, b+c11 = c+a12 = a+b13 , then cos A is equal to (1) 5/7 (2) 1/5 (3) 35/19 (4) 19/35

Q72.If f(x) = 3x10 −7x8 + 5x6 −21x3 + 3x2 −7 , then limα→0 f(1−α)−f(1)α3+3α is (1) −533 (2) 533 (3) −553 (4) 553

Q72.An ellipse is drawn by taking a diameter of the circle (x −1)2 + y2 = 1 as its semiminor axis and a diameter of the circle x2 + (y −2)2 = 4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is (1) 4x2 + y2 = 4 (2) x2 + 4y2 = 8 (3) 4x2 + y2 = 8 (4) x2 + 4y2 = 16

Q72. limx→0 ( x−sinx x ) sin ( x1 ) (1) equals 1 (2) equals 0 (3) does not exist (4) equals −1

Q72.The normal at (2, 23 ) to the ellipse, x216 + y23 = 1 touches a parabola, whose equation is (1) y2 = −104x (2) y2 = 14x (3) y2 = 26x (4) y2 = −14x sin(π cos2 x)

Q73. equals limx→0 x2 (1) −π (2) 1 (3) −1 (4) π

Q73.If A = {x ∈z+ : x < 10 and x is a multiple of 3 or 4}, where z+ is the set of positive integers, then the total number of symmetric relations on A is JEE Main 2012 (12 May Online) JEE Main Previous Year Paper (1) 25 (2) 215 (3) 210 (4) 220 and , respectively. Statement 1: AB −BA is always

Q73.The Statement that is TRUE among the following is (1) The contrapositive of 3x + 2 = 8 ⇒x = 2 is (2) The converse of tan x = 0 ⇒x = 0 is x ≠0 ⇒ x ≠2 ⇒3x + 2 ≠8. tan x = 0. (3) p ⇒q is equivalent to p∨∼q . (4) p ∨q and p ∧q have the same truth table. JEE Main 2012 (07 May Online) JEE Main Previous Year Paper

Q73.The negation of the statement "If I become a teacher, then I will open a school" is (1) I will become a teacher and I will not open a (2) Either I will not become a teacher or I will not school open a school (3) Neither I will become a teacher nor I will open a (4) I will not become a teacher or I will open a school school

Q73.Let p and q be two Statements. Amongst the following, the Statement that is equivalent to p →q is (1) p∧∼q (2) ∼p ∨q (3) ∼p ∧q (4) p∨∼q

Q74.Let x1, x2, … … , xn be n observations, and let –x be their arithematic mean and σ2 be their variance. Statement 1: Variance of 2x1, 2x2, … … , 2xn is 4σ2 . Statement 2: Arithmetic mean of 2x1, 2x2, … . . , 2xn is 4–x. (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

Q74.Let A and B be real matrices of the form [0α 0β ] [0δ γ0 ] an invertible matrix. Statement 2 : AB −BA is never an identity matrix. (1) Statement 1 is true, Statement 2 is false. (2) Statement 1 is false, Statement 2 is true. (3) Statement 1 is true, Statement 2 is true; (4) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement Statement 2 is not a correct explanation of 1 . Statement 1. Q75. −2a a + b a + c If b + a −2b b + c c + a b + c −2c = α(a + b()b + c()c + a) ≠0 then α is equal to (1) a + b + c (2) abc (3) 4 (4) 1