Practice Questions

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.If nC4, nC5 and nC6 are in A.P., then n can be (1) 9 (2) 14 (3) 12 (4) 11

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

Q66.The product of three consecutive terms of a G. P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A. P., then the sum of the original three terms of the given G. P. is : (1) 28 (2) 24 (3) 32 (4) 36

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

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

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.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 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.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.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)

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

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.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.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 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.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