Practice Questions

Q66.Let a, b and c be the 7th, 11th and 13th terms respectively of a non-constant A.P. . If these are also the three consecutive terms of a G.P. , then a is equal to: c (1) 2 (2) 137 (3) 1 (4) 4 2

Q66.If the coefficients of x2 and x3 , are both zero, in the expansion of the expression (1 + ax + bx2)(1 −3x)15 , in powers of x , then the ordered pair (a, b) is equal to (1) (28, 315) (2) (−21, 714) (3) (28, 861) (4) (−54, 315)

Q66.The term independent of x in the expansion of ( 601 −x881 ). (2x2 (1) −72 (2) 36 (3) −108 (4) −36

Q66.If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1,2),(3,4) and (2, 5), then the equation of the diagonal AD is : (1) 5x −3y + 1 = 0 (2) 5x + 3y −11 = 0 (3) 3x −5y + 7 = 0 (4) 3x + 5y −13 = 0

Q67.Two sides of a parallelogram are along the lines, x + y = 3 and x −y + 3 = 0. If its diagonals intersect at (2, 4), then one of its vertex is: (1) (3, 6) (2) (2, 6) (3) (2, 1) (4) (3, 5)

Q67.Let S = {θ ∈[−2π, 2π] : 2 cos2 θ + 3 sin θ = 0}. Then the sum of the elements of S is: (1) π (2) 13π 6 (3) 5π (4) 2π 3

Q67.The equation 𝑦= 𝑠𝑖𝑛𝑥sin⁡𝑥+ 2 - sin2⁡( 𝑥+ 1 ) represents a straight line lying in: (1) first, third and fourth quadrants (2) second and third quadrants only (3) first, second and fourth quadrants (4) third and fourth quadrants only 5𝜋 5𝜋

Q67.The total number of irrational terms in the binomial expansion of 1 1 60 is 5 −3 10 (7 ) (1) 48 (2) 55 (3) 54 (4) 49

Q67.The sum of all values of θ ∈(0, π2 ) satisfying sin2 2θ + cos4 2θ = 43 is JEE Main 2019 (10 Jan Shift 1) JEE Main Previous Year Paper (1) π (2) 3π 2 8 (3) 5π (4) π 4

Q67.If cos𝛼+ 𝛽= 3 , sin⁡( 𝛼- 𝛽) = 5 and 0 < 𝛼, 𝛽< 𝜋 then tan⁡2𝛼 is equal to: 5 13 4, (1) 21 (2) 63 (3) 33 (4) 63 16 52 52 16

Q67.For any 𝜃∈ 4, 2, the expression 3sin𝜃- cos𝜃4 + 6sin𝜃+ cos𝜃2 + 4 sin6𝜃 equals: (1) 13 - 4cos2𝜃+ 6cos4𝜃 (2) 13 - 4cos2𝜃+ 6sin2𝜃cos2𝜃 (3) 13 - 4cos6𝜃 (4) 13 - 4cos4𝜃+ 2sin2𝜃cos2𝜃

Q67.Suppose that the points ℎ, 𝑘, 1, 2 and -3, 4 lie on the line 𝐿1 . If a line 𝐿2 passing through the points ℎ, 𝑘 and 𝑘 4, 3 is perpendicular to 𝐿1, then ℎ equals: (1) -1 (2) 3 7 (3) 0 (4) 1 3

Q67.The smallest natural number 𝑛 , such that the coefficient of 𝑥 in the expansion of 𝑥2 + is 𝑛𝐶23 , is 𝑥3 (1) 58 (2) 38 (3) 35 (4) 23 3

Q67.The value of sin10°sin30°sin50°sin70° is: (1) 1 (2) 1 36 16 (3) 1 (4) 1 18 32

Q67.All the pairs (x, y), that satisfy the inequality 2√sin2x−2sinx+5 ⋅ 1 ≤1 also satisfy the equation: 4sin2y (1) 2 sin x = sin y (2) sin x = 2 sin y (3) |sin x| = |sin y| (4) 2|sin x| = 3 sin y

Q67.Let S be the set of all α ∈R such that the equation, cos2x + αsinx = 2α −7 has a solution. Then S is equal to: (1) [3, 7] (2) [2, 6] (3) [1, 4] (4) R

Q67.The coefficient of t4 in the expansion of 3 ( 1−t61−t ) is JEE Main 2019 (09 Jan Shift 2) JEE Main Previous Year Paper (1) 10 (2) 14 (3) 15 (4) 12

Q67.A circle cuts a chord of length 4 a on the x -axis and passes through a point on the y -axis, distant 2 b from the origin. Then the locus of the centre of this circle, is: (1) a hyperbola (2) an ellipse (3) a straight line (4) a parabola

Q67.A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of 10 1 1 3 + 1 is (2 2(3) 3 ) (1) 1 : 4(16) 1 1 3 (2) 4(36) 3 : 1 3 (3) 2(36) 1 1 3 : 1 (4) 1 : 2(6)

Q67.Let fk(x) = k1 (sink x + cosk x) for k = 1, 2, 3, … Then for all x ∈R, the value of f4(x) −f6(x) is equal to : (1) 1 (2) 1 12 4 (3) −1 (4) 5 12 12

Q68.Lines are drawn parallel to the line 4𝑥- 3𝑦+ 2 = 0, at a distance units from the origin. Then which one of 5 the following points lies on any of these lines? JEE Main 2019 (10 Apr Shift 2) JEE Main Previous Year Paper 1 1 1 2 (1) 4, - 3 (2) - 4, 3 (3) -1 - 2 (4) 1 1 4, 3 4, 3

Q68.If a straight line passing through the point P(−3, 4) is such that its intercepted portion between the coordinate axes is bisected at P , then its equation is : (1) 4x + 3y = 0 (2) 4x −3y + 24 = 0 (3) 3x −4y + 25 = 0 (4) x −y + 7 = 0

Q68.If 0 ≤x < π2 , then the number of values of x for which sin x −sin 2x + sin 3x = 0, is: (1) 4 (2) 3 (3) 2 (4) 1

Q68.In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. if x2 −c2 = y, where c is the length of the third side of the triangle, then the circumradius of the triangle is (1) 3 y (2) c 2 √3 (3) 3c (4) √3y

Q68.Consider the set of all lines 𝑝𝑥+ 𝑞𝑦+ 𝑟= 0 such that 3𝑝+ 2𝑞+ 4𝑟= 0 . Which one of the following statements is true? 3 1 (1) The lines are not concurrent. (2) The lines are concurrent at the point 4, 2 . (3) The lines are all parallel. (4) Each line passes through the origin.