Practice Questions

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.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

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

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

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 = 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

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.Let L be the line passing through the point P(1, 2) such that its intercepted segment between the co-ordinate axes is bisected at P . If L1 is the line perpendicular to L and passing through the point (−2, 1), then the point of intersection of L and L1 is (1) ( 53 , 2310 ) (2) ( 45 , 125 ) (3) ( 2011 , 2910 ) (4) ( 103 , 175 )

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.If y + 3x = 0 is the equation of a chord of the circle x2 + y2 −30x = 0 , then the equation of the circle with this chord as diameter is : (1) x2 + y2 + 3x −9y = 0 (2) x2 + y2 −3x + 9y = 0 (3) x2 + y2 + 3x + 9y = 0 (4) x2 + y2 −3x −9y = 0 JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper

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.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

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

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

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

Q74. lim ex2−cos x→0 sin2 x (1) 2 (2) 32 (3) 5 (4) 3 4

Q75.Consider the following statements: P: Suman is brilliant Q: Suman is rich R: Suman is honest The negation of the statement, "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as (1) ~Q ↔~P ∨R (2) ~Q ↔P ∨~R (3) ~Q ↔P ∧~R (4) ~Q ↔~P ∧R

Q76.If the angles of elevation of the top of a tower from three collinear points A, B and C on a line leading to the foot of the tower are 30°, 45° and 60° respectively, then the ratio AB : BC , is (1) 2 : 3 (2) √3 : 1 (3) √3 : √2 (4) 1 : √3 Q77. ⎡ 1 2 2 ⎤ If A = 2 1 −2 is a matrix satisfying the equation AAT = 9I , where I is 3 × 3 identity matrix, then the ⎣ a 2 b ⎦ ordered pair (a, b) is equal to (1) (−2, −1) (2) (2, −1) (3) (−2, 1) (4) (2, 1)

Q76.Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation α at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is h and the distance of the foot of the smallest pole from O is a; then the distance between two consecutive poles, is (1) h sin α+a cos α (2) h cos α−a sinα 9 cos α 9 sin α (3) h sin α+a cos α (4) h cos α−a sin α 9 sin α 9 cos α

Q77.If A is a 3 × 3 matrix such that |5 adjA| = 5, then |A| is equal to (1) ± 251 (2) ±5 (3) ± 51 (4) ±1

Q77.In a certain town, 25% of the families own a phone and 15% own a car; 65% families own neither a phone nor a car and 2000 families own both a car and a phone. Consider the following three statements: (i) 5% families own both a car and a phone. (ii) 35% families own either a car or a phone. (iii) 40000 families live in the town. Then, (1) Only (ii) and (iii) are correct (2) Only (i) and (ii) are correct (3) All (i), (ii) and (iii) are correct (4) Only (i) and (iii) are correct

Q78.If A = [ 01 −10 ] , then which one of the following statements is not correct? (1) A3 + I = A(A3 − I) (2) A4 −I = A2 + I (3) A2 + I = A(A2 −I) (4) A3 −I = A(A −I) JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper

Q78. x2 + x x + 1 x −2 If 2x2 + 3x −1 3x 3x −3 = ax −12 , then a is equal to: x2 + 2x + 3 2x −1 2x −1 (1) −24 (2) 24 (3) −12 (4) 12