Practice Questions

Q65.The least positive integer n such that 1 −23 − 322 −… . − 3n−12 < 1001 , is: (1) 4 (2) 5 (3) 6 (4) 7

Q65.Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12 , then its 4th term is : (1) 8 (2) 24 (3) 20 (4) 16

Q66.The coefficient of x50 in the binomial expansion of (1 + x)1000 + x(1 + x)999 + x2(1 + x)998 + … +x1000 is: (1) (1000)! (2) (1000)! (50)(!95φ! (49)(!95)! (3) (1001)! (4) (1001)! (51)(!95ϕ! (50)(!95)!

Q66.The coefficient of x1012 in the expansion of (1 + xn + x253) 10, (where n≤22 is any positive integer), is (1) 253C4 (2) 10C4 (3) 4n (4) 1

Q66.If the coefficients of x3 and x4 in the expansion of (1 + ax + bx2)(1 −2x)18 in powers of x are both zero, then (a, b) is equal to (1) (14, 2723 ) (2) (16, 2723 ) (3) (16, 2513 ) (4) (14, 2513 )

Q66.If 1 + x4 + x5 = ∑5i=0 ai (1 + xi), for all x in R, then a2 is: (1) −4 (2) 6 (3) −8 (4) 10 is expanded in the ascending powers of x and the coefficients of powers of x in two consecutive

Q66.If the sum 3 + 5 + 7 + .... .+ up to 20 terms is equal to 21k , then k is equal to 12 12+22 12+22+32 (1) 240 (2) 120 (3) 60 (4) 180

Q67.If (2 + x3 ) 55 terms of the expansion are equal, then these terms are: (1) 7th and 8th (2) 8th and 9th (3) 28th and 29th (4) 27th and 28th

Q67.If a line L is perpendicular to the line 5x −y = 1, and the area of the triangle formed by the line L and the coordinate axes is 5 sq units, then the distance of the line L from the line x + 5y = 0 is (1) 7 units (2) 7 units √13 √5 (3) 5 units (4) 5 units √13 √7

Q67.Let fk(x) = k1 (sink x + cosk x) where x ∈R and k≥1. Then f4(x) −f6(x) equals (1) 1 (2) 1 4 12 (3) 1 (4) 1 6 3

Q67.The number of terms in the expansion of (1 + x)101(1 −x + x2) 100 in powers of x is (1) 301 (2) 302 (3) 101 (4) 202

Q67.If 2 cos θ + sin θ = 1 (θ ≠π2 ), then 7 cos θ + 6 sin θ is equal to: (1) 1 (2) 2 2 (3) 11 (4) 46 2 5

Q68.The circumcentre of a triangle lies at the origin and its centroid is the midpoint of the line segment joining the points (a2 + 1, a2 + 1) and (2a , - 2 a), a≠0. Then for any a, the orthocentre of this triangle lies on the line (1) y −(a2 + 1)x = 0 (2) y −2ax = 0 (3) y + x = 0 (4) (a −1)2x −(a + 1)2y = 0

Q68.If a line intercepted between the coordinate axes is trisected at a point A(4, 3), which is nearer to x-axis, then its equation is: (1) 4x −3y = 7 (2) 3x + 2y = 18 (3) 3x + 8y = 36 (4) x + 3y = 13

Q68.If cosec θ = p−qp+q (p ≠q, p ≠0), then cot( π4 + 2θ ) is equals to: (1) pq (2) √pq (3) √qp (4) √pq

Q68.Let PS be the median of the triangle with vertices P(2, 2), Q(6, −1) and R(7, 3). The equation of the line passing through (1, −1) and parallel to PS is (1) 4x + 7y + 3 = 0 (2) 2x −9y −11 = 0 (3) 4x −7y −11 = 0 (4) 2x + 9y + 7 = 0

Q68.The base of an equilateral triangle is along the line given by 3x + 4y = 9. If a vertex of the triangle is (1, 2), then the length of a side of the triangle is: (1) 2√3 (2) 4√3 15 15 (3) 4√3 (4) 2√3 5 5

Q69.The set of all real values of λ for which exactly two common tangents can be drawn to the circles x2 + y2 −4x −4y + 6 = 0 and x2 + y2 −10x −10y + λ = 0 is the interval: (1) (12, 32) (2) (18, 42) (3) (12, 24) (4) (18, 48)

Q69.The equation of the circle described on the chord 3x + y + 5 = 0 of the circle x2 + y2 = 16 as the diameter is (1) x2 + y2 + 3x + y + 1 = 0 (2) x2 + y2 + 3x + y −22 = 0 (3) x2 + y2 + 3x + y −11 = 0 (4) x2 + y2 + 3x + y −2 = 0

Q69.Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax + 2ay + c = 0 & 5bx + 2by + d = 0 lies in the fourth quadrant and is equidistant from the two axes then (1) 3bc −2ad = 0 (2) 3bc + 2ad = 0 (3) 2bc −3ad = 0 (4) 2bc + 3ad = 0

Q69.The number of values of α in [0, 2π] for which 2 sin3 α −7 sin2 α + 7sinα = 2, is : (1) 3 (2) 1 (3) 6 (4) 4 JEE Main 2014 (09 Apr Online) JEE Main Previous Year Paper

Q69.If the three distinct lines x + 2ay + a = 0, x + 3by +b = 0 and x + 4ay + a = 0 are concurrent, then the point (a, b) lies on a : (1) circle (2) hyperbola (3) straight line (4) parabola

Q70.For the two circles x2 + y2 = 16 and x2 + y2 −2y = 0, there is/are (1) one pair of common tangents (2) two pair of common tangents (3) three pair of common tangents (4) no common tangent

Q70.Given three points P, Q, R with P(5, 3) and R lies on the x−axis. If the equation of RQ is x −2y = 2 and PQ is parallel to the x−axis, then the centroid of ΔPQR lies on the line (1) x −2y + 1 = 0 (2) 2x + y −9 = 0 (3) 2x −5y = 0 (4) 5x −2y = 0

Q70.A chord is drawn through the focus of the parabola y2 = 6x such that its distance from the vertex of this parabola is √5 , then its slope can be 2 (1) √5 (2) 2 2 √3 (3) √3 (4) 2 2 √5 JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper