Practice Questions

Q66.If the third term in the binomial expansion of (1 + xlog2 x)5 equals 2560, then a possible value of x is (1) 4√2 (2) 18 (3) 2 √2 (4) 14

Q66.The value of r for which 20Cr20C0 + 20Cr−120C1 + 20Cr−220C2 + … + 20C020Cr is maximum, is: (1) 15 (2) 20 (3) 11 (4) 10

Q66.If the fractional part of the number 2403 is 𝑘 then 𝑘 is equal to 15 15, (1) 4 (2) 14 (3) 8 (4) 6 𝜋 𝜋

Q66.The coefficient of 𝑥18 in the product 1 + 𝑥1 - 𝑥101 + 𝑥+ 𝑥29 is (1) 84 (2) -84 (3) -126 (4) 126

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

Q66.The value of cos2 10°– cos 10° cos 50°+cos250° is (1) 3 (2) 3 4 4 + cos 20° (3) 3 (4) 3 2 2 (1 + cos 20°)

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

Q66.The sum of the series 2 . 20𝐶0 + 5 . 20𝐶1 + 8 . 20𝐶2 + 11 . 20𝐶3 + . . . . . . . + 62 . 20𝐶20 is equal to (1) 226 (2) 225 (3) 224 (4) 223

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.Let 𝑎, 𝑏 and 𝑐 be in 𝐺. 𝑃. with common ratio 𝑟, where 𝑎≠0 and 0 < 𝑟≤1 . If 3𝑎, 7𝑏 and 15𝑐 are the 2 first three terms of an 𝐴. 𝑃. , then the 4𝑡ℎ term of this 𝐴. 𝑃. is : 7 (1) 𝑎 (2) 3𝑎 2 (3) 5𝑎 (4) 3𝑎 1 𝑛

Q66.If some three consecutive coefficients in the binomial expansion of (x + 1)n in powers of x are in the ratio 2 : 15 : 70, then the average of these three coefficients is: (1) 227 (2) 964 (3) 625 (4) 232

Q66.Two vertices of a triangle are (0, 2) and (4, 3). If its orthocenter is at the origin, then its third vertex lies in which quadrant? (1) Fourth (2) Second (3) Third (4) First

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

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 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 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.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.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 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

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.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.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.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)