Practice Questions

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.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 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 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.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

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 )

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

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.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.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

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.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. 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.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

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

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.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.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

Q74.Let p and q denote the following statements p : The sun is shining q : I shall play tennis in the afternoon The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is (1) q ⇒∼p (2) q∧∼p (3) p∧∼q (4) ∼q ⇒∼p

Q74.The median of 100 observations grouped in classes of equal width is 25 . If the median class interval is 20-30 and the number of observations less than 20 is 45 , then the frequency of median class is (1) 10 (2) 20 (3) 15 (4) 12 JEE Main 2012 (19 May Online) JEE Main Previous Year Paper

Q74.The frequency distribution of daily working expenditure of families in a locality is as follows: If the mode of the distribution is Rs. 140, then the value of b is (1) 34 (2) 31 (3) 26 (4) 36

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