Practice Questions

Q65.If the sum and product of the first three terms in an A. P. are 33 and 1155, respectively, then a value of its 11th term is: (1) −25 (2) −35 (3) 25 (4) −36

Q65.If the fourth term in the Binomial expansion of ( x2 + xlog8x)6, (x > 0) is 20 × 87, then a value of (1) 8–2 (2) 8 (3) 83 (4) 82

Q65.Let 𝑎1, 𝑎2, … , 𝑎30 be an A.P., 𝑆= ∑𝑖=30 1 𝑎𝑖 and 𝑇= ∑𝑖=15 1 𝑎( 2𝑖- 1 ) . If 𝑎5 = 27 and 𝑆- 2𝑇= 75, then 𝑎10 is equal to: (1) 52 (2) 47 (3) 42 (4) 57

Q65.If 20C1 + (22) 20C2 + (32) 20C3+. . . . . +(202) 20C20 = A(2β), then the ordered pair (A, β) is equal to JEE Main 2019 (12 Apr Shift 2) JEE Main Previous Year Paper (1) (380, 19) (2) (420, 18) (3) (420, 19) (4) (380, 18) − 3 ) 6 is equal to x2

Q65.If ∑20i=1( 20Ci+20Ci−120Ci−1 ) 3 (1) 200 (2) 100 (3) 50 (4) 400

Q65.The sum 3×13 + 5×(13+23) + 7×(13+23+33) +. . . . . upto 10th term is 12 12+22 12+22+32 (1) 660 (2) 600 (3) 620 (4) 680

Q65.The sum of the real values of x for which the middle term in the binomial expansion of 8 + x3 ) equals ( x33 5670 is : (1) 0 (2) 6 (3) 4 (4) 8

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

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

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

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 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.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 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°)

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.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)