Practice Questions

Q64.The difference between the fourth term and the first term of a Geometrical Progresssion is 52. If the sum of its first three terms is 26 , then the sum of the first six terms of the progression is JEE Main 2012 (07 May Online) JEE Main Previous Year Paper (1) 63 (2) 189 (3) 728 (4) 364

Q65.If the sum of the series 12 + 2 ⋅22 + 32 + 2 ⋅42 + 52+ ... 2.62 + … upto n terms, when n is even, is n(n+1)22 then the sum of the series, when n is odd, is (1) n2(n + 1) (2) n2(n−1) 2 (3) n2(n+1) (4) n2(n −1) 2

Q65.The number of terms in the expansion of (y1/5 + x1/10) 55 , in which powers of x and y are free from radical signs are (1) six (2) twelve (3) seven (4) five

Q65.If 100 times the 100th term of an AP with non zero common difference equals the 50 times its 50th term, then the 150th term of this AP is (1) −150 (2) 150 times its 50th term (3) 150 (4) zero

Q65.The sum of the series 1 + 34 + 109 + 2728 + … upto n terms is (1) 67 n + 16 − 3.2n−12 (2) 53 n −76 + 2.3n−11 (3) n + 21 − 2.3n1 (4) n −13 − 3.2n−11

Q65.The sum of the series 12 + 2.22 + 32 + 2.42 + 52 + 2.62 + … . . +2(2m)2 is (1) m(2m + 1)2 (2) m2(m + 2) (3) m2(2m + 1) (4) m(m + 2)2

Q66.The middle term in the expansion of (1 −1x ) n (1 −xn) in powers of x is (1) −2nCn−1 (2) −2nCn (3) 2nCn−1 (4) 2nCn

Q66.If n is a positive integer, then (√3 + 1)2n −(√3 −1)2n is (1) an irrational number (2) an odd positive integer (3) an even positive integer (4) a rational number other than positive integers

Q66.If the point (1, a) lies between the straight lines x + y = 1 and 2(x + y) = 3 then a lies in interval (1) ( 23 , ∞) (2) (1, 23 ) (3) (−∞, 0) (4) (0, 12 )

Q66.If f(y) = 1 −(y −1) + (y −1)2 −(y −1)3 + … −(y −1)17 then the coefficient of y2 in it is (1) 17C2 (2) 17C3 (3) 18C2 (4) 18C3

Q66.If n = mC2 , then the value of nC2 is given by JEE Main 2012 (19 May Online) JEE Main Previous Year Paper (1) 3 (m+1C4) (2) m−1C4 (3) m+1C4 (4) 2 (m+2C4)

Q67.The equation esin x −e−sin x −4 = 0 has (1) infinite number of real roots (2) no real roots (3) exactly one real root (4) exactly four real roots

Q67.Suppose θ and ϕ(≠0) are such that sec(θ + ϕ), sec θ and sec(θ −ϕ) are in A.P. If cos θ = k cos ( ϕ2 ) for some k, then k is equal to (1) ±√2 (2) ±1 (3) ± 1 (4) ±2 √2

Q67.If two vertices of a triangle are (5, −1) and (−2, 3) and its orthocentre is at (0, 0), then the third vertex is (1) (4, −7) (2) (−4, −7) (3) (−4, 7) (4) (4, 7)

Q67.The value of cos 255∘+ sin 195∘ is (1) √3−1 (2) √3−1 2√2 √2 (3) −√3−1 (4) √3+1 √2 √2

Q67.If the straight lines x + 3y = 4, 3x + y = 4 and x + y = 0 form a triangle, then the triangle is (1) scalene (2) equilateral triangle (3) isosceles (4) right angled isosceles

Q68.The line parallel to x-axis and passing through the point of intersection of lines ax + 2by + 3b = 0 and bx −2ay −3a = 0, where (a, b) ≠(0, 0) is (1) above x-axis at a distance 2/3 from it (2) above x-axis at a distance 3/2 from it (3) below x-axis at a distance 3/2 from it (4) below x-axis at a distance 2/3 from it

Q68.If the line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals JEE Main 2012 (Offline) JEE Main Previous Year Paper (1) 29 (2) 5 5 (3) 6 (4) 115

Q68.The area of triangle formed by the lines joining the vertex of the parabola, x2 = 8y, to the extremities of its latus rectum is (1) 2 (2) 8 (3) 1 (4) 4

Q68.The point of intersection of the lines (a3 + 3)x + ay + a −3 = 0 and (a5 + 2)x + (a + 2)y + 2a + 3 = 0 (a real) lies on the y-axis for (1) no value of a (2) more than two values of a (3) exactly one value of a (4) exactly two values of a

Q68.Let L be the line y = 2x, in the two dimensional plane. Statement 1: The image of the point (0, 1) in L is the point ( 54 , 35 ) Statement 2: The points (0, 1) and ( 45 , 35 ) lie on opposite sides of the line L and are at equal distance from it. (1) Statement 1 is true, Statement 2 is false. (2) Statement 1 is true, Statement 2 is true, Statement 2 is not 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 a correct explanation for Statement 1.

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.A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is (1) −14 (2) −4 (3) −2 (4) −12

Q69.If P1 and P2 are two points on the ellipse x24 + y2 = 1 at which the tangents are parallel to the chord joining the points (0, 1) and (2, 0), then the distance between P1 and P2 is (1) 2√2 (2) √5 (3) 2√3 (4) √10

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 .