Practice Questions

Q64.The value of ∑30r=16(r + 2)(r −3) is equal to: (1) 7775 (2) 7785 (3) 7780 (4) 7770

Q64.Let A = {x1, x2, … , x7} and B = {y1, y2, y3} be two sets containing seven and three distinct elements respectively. Then the total number of functions f : A →B that are onto, if there exist exactly three elements x in A such that f(x) = y2, is equal to: (1) 12 ⋅7 C2 (2) 16 ⋅7 C3 (3) 14 ⋅ 7C3 (4) 14 ⋅7 C2

Q64.The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0) is JEE Main 2015 (04 Apr) JEE Main Previous Year Paper (1) 780 (2) 901 (3) 861 (4) 820

Q65.If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is: (1) 12 (2) 10 (3) 6 (4) 9

Q65.Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is (1) 510 (2) 219 (3) 256 (4) 275

Q65.Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is : (1) 26. 5 (2) 29. 5 (3) 28 (4) 31

Q66.The sum of the 3rd and the 4th terms of a G. P. is 60 and the product of its first three terms is 1000. If the first term of this G. P. is positive, then its 7th term is: (1) 320 (2) 640 (3) 2430 (4) 7290 5 1 k

Q66.If the coefficient of the three successive terms in the binomial expansion of (1 + x)n are in the ratio 1 : 7 : 42, then the first of these terms in the expansion is (1) 9th (2) 6th (3) 8th (4) 7th

Q66.The sum of first 9 terms of the series 131 + 13+231+3 + 13+23+331+3+5 +. . . is (1) 192 (2) 71 (3) 96 (4) 142

Q67.If = 3 , then k is equal to: ∑ n(n+1)(n+2)(n+3) n=1 (1) 33655 (2) 10517 (3) 19 (4) 1 112 6 is

Q67.In a ΔABC , ab = 2 + √3, and ∠C = 60°. Then the ordered pair (∠A, ∠B) is equal to: (1) (105°, 15°) (2) (15°, 105°) (3) (45°, 75°) (4) (75°, 45°)

Q67.If m is the A. M. of two distinct real numbers I and n (I, n > 1) and G1, G2 and G3 are three geometric means between I and n, then G41 + 2G42 + G43 equals (1) 4l2m2 n2 (2) 4 l2mn (3) 4 lm2 n (4) 4lmn2

Q68.The term independent of x in the binomial expansion of (1 −1x + 3x5) (2x2 −1x ) 8 (1) − 496 (2) −400 (3) 496 (4) 400

Q68.The sum of coefficients of integral powers of x in the binomial expansion of (1 −2√x) 50 is (1) 2 1 (250 + 1) (2) 12 (350 + 1) (3) 1 2 (350) (4) 12 (350 −1)

Q69.The points (0, 38 ), (1, 3) and (82, 30) (1) form an obtuse angled triangle (2) form an acute angled triangle (3) lie on a straight line (4) form a right angled triangle

Q69.Locus of the image of the point (2, 3) in the line (2x −3y + 4) + k(x −2y + 3) = 0, k∈R , is a (1) Circle of radius √3 (2) Straight line parallel to x-axis. (3) Straight line parallel to y-axis. (4) Circle of radius √2

Q69.If cos α + cos β = 23 and sin α + sin β = 12 and θ is the arithmetic mean of α & β, then sin 2θ + cos 2θ is equal to: (1) 3 (2) 7 5 5 (3) 4 (4) 8 5 5

Q70.The number of common tangents to the circles x2 + y2 −4x −6y −12 = 0 and x2 + y2 + 6x + 18y + 26 = 0 , is (1) 4 (2) 1 (3) 2 (4) 3

Q70.A straight line L through the point (3, −2) is inclined at an angle of 60° to the line √3x + y = 1. If L also intersects the X -axis, then the equation of L is: (1) y + √3 x + 2 −3√3 = 0 (2) √3 y −x + 3 + 2√3 = 0 (3) √3 y + x −3 + 2√3 = 0 (4) y −√3x + 2 + 3√3 = 0

Q71.If a circle passing through the point (−1, 0) touches y-axis at (0, 2), then the x-intercept of the circle is (1) 5 (2) 5 2 (3) 3 (4) 3 2

Q71.Let O be the vertex and Q be any point on the parabola, x2 = 8y. If the point P divides the line segment OQ internally in the ratio 1 : 3 , then the locus of P is (1) x2 = 2y (2) x2 = y (3) y2 = x (4) y2 = 2x

Q72.If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is 3x + 4y + 3 = 0 , then the equation of the circumcircle of this triangle is: (1) x2 + y2 −2x −2y −2 = 0 (2) x2 + y2 −2x −2y + 2 = 0 (3) x2 + y2 −2x −2y −7 = 0 (4) x2 + y2 −2x −2y −14 = 0

Q72.The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latus ractum to the x2 y2 ellipse 9 + 5 = 1, is (1) 27 (2) 274 (3) 18 (4) 272

Q73. lim (1−cos2x)(3+cosx)xtan4x = x→0 (1) 12 (2) 4 (3) 3 (4) 2

Q73.If PQ be a double ordinate of the parabola, y2 = −4x, where P lies in the second quadrant. If R divides PQ in the ratio 2 : 1, then the locus of R is: JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper (1) 3y2 = −2x (2) 9y2 = 4x (3) 9y2 = −4x (4) 3y2 = 2x