Practice Questions

Q61.If x is a solution of the equation √2x + 1 − √2x −1 = 1, (x ≥12 ) , then √4x2 −1 is equal to : (1) 3 (2) 1 4 2 (3) 2√2 (4) 2 JEE Main 2016 (10 Apr Online) JEE Main Previous Year Paper

Q61.The sum of all real values of x satisfying the equation (x2 −5x + 5) x2+4x−60 = 1 is (1) 6 (2) 5 (3) 3 (4) −4

Q62.A value of θ for which 2+3i sin θ is purely imaginary, is 1−2i sin θ (1) sin−1( √34 ) (2) sin−1( √31 ) (3) π (4) π 3 6

Q62.Let z = 1 + ai , be a complex number, a > 0, such that z3 is a real number. Then, the sum 1 + z + z2 + … . +z11 is equal to : (1) 1365 √3i (2) −1365 √3i (3) −1250 √3i (4) 1250 √3i

Q62.The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there 2√2 units in the south-west wards direction. Then its new position in the Argand plane is at the point represented by : (1) 1 + i (2) 2 + 2i (3) −2 −2i (4) −1 −i

Q63.If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all such words is : (1) 110 (2) 59 (3) 11! (4) 56 (2!)3

Q63.If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is (1) 52nd (2) 58th (3) 46th (4) 59th

Q63.If n+2C6 = 11, then n satisfies the equation: n−2P2 (1) n2 + n −110 = 0 (2) n2 + 2n −80 = 0 (3) n2 + 3n −108 = 0 (4) n2 + 5n −84 = 0

Q64.Let a1, a2, a3, … an, … ,be in A.P. If a3 + a7 + a11 + a15 = 72, then the sum of its first 17 terms is equal to : (1) 306 (2) 204 (3) 153 (4) 612

Q64.If the 2nd, 5th and 9th terms of a non-constant arithmetic progression are in geometric progression, then the common ratio of this geometric progression is (1) 1 (2) 74 (3) 8 (4) 4 5 3 is 16 m , then m

Q64.Let x, y, z be positive real numbers such that x + y + z = 12 and x3y4z5 = (0 .1)(600)3. Then x3 + y3 + z3 is equal to (1) 342 (2) 216 (3) 258 (4) 270 is equal to:

Q65.The sum ∑10r=1(r2 + 1) × (r!), is equal to: (1) 11 × (11!) (2) 10 × (11! ) (3) (11)! (4) 101 × (10!) 1

Q65.If the sum of the first ten terms of the series (1 35 ) 2 + (2 25 ) 2 + (3 15 ) 2 + 42 + (4 45 ) 2 + … . , 5 is equal to (1) 100 (2) 99 (3) 102 (4) 101 n , x, y ≠0, is 28, then the sum of the coefficients

Q65.The value of ∑15r=1 r2( 15Cr−115Cr ) (1) 1240 (2) 560 (3) 1085 (4) 680 JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper

Q66.If the number of terms in the expansion of (1 −2x + y24 ) of all the terms in this expansion is (1) 243 (2) 729 (3) 64 (4) 2187

Q66.For x ∈R, x ≠−1, if (1 + x)2016 + x(1 + x)2015 + x2(1 + x)2014 + … + x2016 = 2016 aixi , then a17 is ∑ i=0 equal to (1) 2017! (2) 2016! 17!2000! 17!1999! (3) 2016! (4) 2017! 16! 2000!

Q66.If the coefficients of x−2 and x−4 , in the expansion of 3 18 + 1 1 , (x > 0) , are m and n respectively, then (x 2x 3 ) m is equal to n (1) 27 (2) 182 (3) 54 (4) 54

Q67.If m and M are the minimum and the maximum values of 4 + 12 sin22x −2cos4x, x ∈R, then M −m is equal to: (1) 15 (2) 9 4 4 (3) 7 (4) 1 4 4

Q67.If A > 0, B > 0 and A + B = π6 , then the minimum positive value of (tan A + tan B) is : (1) √3 −√2 (2) 4 −2√3 (3) 2 (4) 2 −√3 √3 be two sets. Then and Q = : sin θ −cos θ = √2 cos θ} {θ : sin θ + cos θ = √2 sin θ},

Q67.If 0 ≤x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x + cos 3x + cos 4x = 0, is (1) 7 (2) 9 (3) 3 (4) 5 JEE Main 2016 (03 Apr) JEE Main Previous Year Paper

Q68.Let P = {θ (1) P ⊂Q and Q −P ≠ ϕ (2) Q ⊄ P (3) P = Q (4) P ⊄ Q

Q68.Two sides of a rhombus are along the lines, x −y + 1 = 0 and 7x −y −5 = 0 . If its diagonals intersect at (−1, −2) , then which one of the following is a vertex of this rhombus ? (1) ( 31 , −83 ) (2) (−103 , −73 ) (3) (−3, −9) (4) (−3, −8)

Q68.The number of x ∈[0, 2π] for which √2 sin4 x + 18 cos2 x − √2 cos4 x + 18 sin2 x = 1 is: (1) 2 (2) 6 (3) 4 (4) 8

Q69.If a variable line drawn through the intersection of the lines x 3 + 4y = 1 and x4 + 3y = 1 , meets the coordinate axes at A and B, (A ≠B),then the locus of the midpoint of AB is: (1) 7xy = 6(x + y) (2) 4(x + y)2 −28(x + y) + 49 = 0 (3) 6xy = 7(x + y) (4) 14(x + y)2 −97(x + y) + 168 = 0

Q69.The centres of those circles which touch the circle, x2 + y2 −8x −8y −4 = 0, externally and also touch the x - axis, lie on (1) A hyperbola (2) A parabola (3) A circle (4) An ellipse which is not a circle