Practice Questions

Q64.The number of arrangements that can be formed from the letters a, b, c, d, e, f taken 3 at a time without repetition and each arrangement containing at least one vowel, is (1) 96 (2) 128 (3) 24 (4) 72

Q64.The sum of the series 1 1 1 + + + … 1 + √2 √2 + √3 √3 + √4 upto 15 terms is (1) 1 (2) 2 (3) 3 (4) 4

Q64.If the A.M. between pth and qth terms of an A.P. is equal to the A.M. between rth and sth terms of the same A.P., then p + q is equal to (1) r + s −1 (2) r + s −2 (3) r + s + 1 (4) r + s ,

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.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.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.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 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.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 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 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.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 = 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.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.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.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

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

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 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.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.

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.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

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