Practice Questions

Q64.If a1, a2, a3. . . . . . . . . , an are in A. P. and a1 + a4 + a7. . . . . . . . . +a16 = 114 , then a1 + a6 + a11 + a16 is equal to : (1) 64 (2) 98 (3) 38 (4) 76 JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper

Q64.If a1, a2, a3, . . . . are in A.P. such that a1 + a7 + a16 = 40, then the sum of the first 15 terms of this A.P is: (1) 280 (2) 120 (3) 150 (4) 200

Q64.The number of four-digit numbers strictly greater than 4321 that can be formed using the digit 0,1, 2,3, 4,5 (repetition of digits is allowed) is: (1) 360 (2) 288 (3) 306 (4) 310 JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper 20 1

Q64.The positive value of λ for which the co-efficient of x2 in the expansion x2(√x + x2λ ) 10 (1) √5 (2) 3 (3) 4 (4) 2√2

Q64.If 𝑎, 𝑏 and 𝑐 be three distinct real numbers in G.P. and 𝑎+ 𝑏+ 𝑐= 𝑥𝑏, then 𝑥 cannot be: (1) -3 (2) 2 (3) 4 (4) -2

Q64.If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is: 1 3 (1) (2) 10 10 (3) 1 (4) 3 5 20

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.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

Q65.The sum of the following series 1 + 6 + 9(12+22+32)7 + 12(12+22+32+42)9 + 15(12+22+…+52)11 +. . . . is: (1) 7520 (2) 7510 (3) 7830 (4) 7820

Q65.Let (x + 10)50 + (x −10)50 = a0 + a1x + a2x2 + … . +a50x50 , for all x ∈R; then a2 is equal to : a0 (1) 12.5 (2) 12 (3) 12.25 (4) 12.75

Q65.Let 𝑆𝑛 denote the sum of the first 𝑛 terms of an 𝐴. 𝑃. . If 𝑆4 = 16 and 𝑆6 = - 48 , then 𝑆10 is equal to: (1) -320 (2) -380 (3) -260 (4) -410

Q65.Let 𝑎1, 𝑎2, 𝑎3 . . . be an 𝐴. 𝑃. with 𝑎6 = 2 . Then, the common difference of this 𝐴. 𝑃. , which maximise the product 𝑎1 · 𝑎4 · 𝑎5, is : 2 3 (1) (2) 3 2 6 8 (3) (4) 5 5

Q65.The value of cos π ⋅cos π ⋅… ⋅cos π ⋅sin π is: 22 23 210 210 (1) 1 (2) 1 1024 512 (3) 1 (4) 1 2 256

Q65.The sum ∑ 𝑘 is equal to 𝑘= 1 2𝑘 11 21 (1) 1 – (2) 2 – 220 220 3 11 (3) 2 – (4) 2 – 217 219 6 Q66. 1 1 If the fourth term in the binomial expansion of √𝑥 1 + log10𝑥+ 𝑥 12 is equal to 200, and 𝑥> 1, then the value of 𝑥 is (1) 100 (2) 104 (3) 103 (4) 10

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.The sum of the co-efficient of all even degree terms in 𝑥 in the expansion of 6 6 𝑥+ √𝑥3 - 1 +𝑥- √𝑥3 - 1 , 𝑥> 1 is equal to (1) 26 (2) 32 (3) 24 (4) 29

Q65.If sin4α + 4cos4β + 2 = 4√2sinαcosβ, α, β ∈[0, π] , then cos(α + β) −cos(α −β) is equal to (1) −1 (2) −√2 (3) √2 (4) 0 JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper

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 Sk = 1 + 2 + k3+…+k . If S 12 + S 22 + … + S 102 = 125 A, then A is equal to : (1) 301 (2) 303 (3) 156 (4) 283

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

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 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.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