Practice Questions

Q61.The area of the polygon, whose vertices are the non-real roots of the equation z = iz2 is (1) 3√3 (2) 3√3 2 4 (3) √3 (4) √3 4 2

Q61.The minimum value of the sum of the squares of the roots of 𝑥2 + 3 - 𝑎𝑥= 2𝑎- 1 is (1) 6 (2) 4 (3) 5 (4) 8

Q61.Let a circle 𝐶 in complex plane pass through the points 𝑧1 = 3 + 4𝑖, 𝑧2 = 4 + 3𝑖 and 𝑧3 = 5𝑖. If 𝑧≠𝑧1 is a point on 𝐶 such that the line through 𝑧 and 𝑧1 is perpendicular to the line through 𝑧2 and 𝑧3, then arg𝑧 is equal to 2 (1) tan-124 - 𝜋 (2) tan-1 - 𝜋 7 √5 (3) tan-13 - 𝜋 (4) tan-13 - 𝜋 4 JEE Main 2022 (25 Jun Shift 1) JEE Main Previous Year Paper 1 1 1 𝐾

Q61.The sum of all real roots of equation (e2x −4)(6e2x −5ex + 1) = 0 is (1) ln 4 (2) −ln 3 (3) ln 3 (4) ln 5

Q61.For z ∈C if the minimum value of ( z −3√2 + z −p√2i ) is 5√2 , then a value of (1) 3 (2) 72 (3) 4 (4) 92

Q61.If the sum of the squares of the reciprocals of the roots α and β of the equation 3x2 + λx −1 = 0 is 15 , then 6(α3 + β3)2 is equal to (1) 46 (2) 36 (3) 24 (4) 18

Q61.If 𝛼, 𝛽, 𝛾, 𝛿 are the roots of the equation 𝑥4 + 𝑥3 + 𝑥2 + 𝑥+ 1 = 0, then 𝛼2021 + 𝛽2021 + 𝛾2021 + 𝛿2021 is equal to (1) 4 (2) 1 (3) -4 (4) -1

Q61.Let 𝐴= 𝑥∈𝑅: 𝑥+ 1 < 2 and 𝐵= 𝑥∈𝑅: 𝑥- 1 ≥2. Then which one the following statements is NOT true? (1) 𝐴- 𝐵= -1, 1 (2) 𝐵- 𝐴= 𝑅- -3, 1 (3) 𝐴∩𝐵= ( - 3, - 1] (4) 𝐴∪𝐵= 𝑅- [1, 3 )

Q61.The number of points of intersection |z −(4 + 3i)| = 2| and |z| + |z −4| = 6, z ∈C is (1) 1 (2) 2 (3) 3 (4) 4

Q61.The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is (1) 72 (2) 48 (3) 24 (4) 60

Q61.If z = 2 + 3i, then z5 + (z)5 is equal to: (1) 244 (2) 224 (3) 245 (4) 265

Q61.If α, β are the roots of the equation x2 −(5 + 3√log3 −5√log5 3)x 3(3(log3 −1) the equation, whose roots are α + β1 and β + α1 , (1) 3x2 −20x −12 = 0 (2) 3x2 −10x −4 = 0 (3) 3x2 −10x + 2 = 0 (4) 3x2 −20x + 16 = 0

Q61.Let 𝑆1 = 𝑧1 ∈𝐶: 𝑧1 - 3 = 2 and 𝑆2 = 𝑧2 ∈𝐶: 𝑧2 - 𝑧2 + 1 = 𝑧2 + 𝑧2 - 1 . Then, for 𝑧1 ∈𝑆1 and 𝑧2 ∈𝑆2, the least value of 𝑧2 - 𝑧1 is (1) 0 (2) 1 2 3 5 (3) (4) 2 2

Q61.Let α and β be the roots of the equation x2 + (2i −1) = 0 . Then, the value of α8 + β8 is equal to (1) 50 (2) 250 (3) 1250 (4) 1550

Q61.If A = ∑∞n=1 (3+(−1)n)n and B = ∑∞n=1 (3+(−1)n)n , then B is equal to (1) 11 (2) 1 9 (3) −119 (4) −113 Q62. 16 sin(20°) sin(40°) sin(80°) is equal to (1) √3 (2) 2√3 (3) 3 (4) 4√3 y2

Q62.If 𝑧= 𝑥+ 𝑖𝑦 satisfies 𝑧- 2 = 0 and 𝑧- 𝑖- 𝑧+ 5𝑖= 0, then (1) 𝑥+ 2𝑦- 4 = 0 (2) 𝑥2 + 𝑦- 4 = 0 (3) 𝑥+ 2𝑦+ 4 = 0 (4) 𝑥2 - 𝑦+ 3 = 0 Q63. ∑𝑖,𝑛 𝑗= 0 𝑛𝐶𝑖 𝑛𝐶𝑗 is equal to 𝑖≠𝑗 (1) 22𝑛- 2𝑛𝐶𝑛 (2) 22𝑛- 1 - 2𝑛- 1𝐶𝑛- 1 1 1 2𝑛- (3) 22𝑛- 2 2𝑛𝐶𝑛 (4) 2𝑛- + 1𝐶𝑛

Q62.If the minimum value of 𝑓𝑥= 5𝑥2 + 𝛼 𝑥> 0, is 14, then the value of 𝛼 is equal to 2 𝑥5, (1) 32 (2) 64 (3) 128 (4) 256 2

Q62.For 𝑛∈𝑁, let 𝑆𝑛= 𝑧∈𝐶: 𝑧- 3 + 2𝑖= 𝑛 and 𝑇𝑛= 𝑧∈𝐶: 𝑧- 2 + 3𝑖= 1 Then the number of elements in the 4 𝑛. set 𝑛∈𝑁: 𝑆𝑛∩𝑇𝑛= 𝜙 is (1) 0 (2) 2 (3) 3 (4) 4

Q62.Let x, y > 0 . If x3y2 = 215 , then the least value of 3x + 2y is JEE Main 2022 (24 Jun Shift 2) JEE Main Previous Year Paper (1) 30 (2) 32 (3) 36 (4) 40

Q62.Let (z) represent the principal argument of the complex number z. The, |z| = 3 and arg(z −1) −arg(z + 1) = π4 intersect: (1) Exactly at one point (2) Exactly at two points (3) Nowhere (4) At infinitely many points.

Q62.If x = ∑∞n=0 an, y = ∑∞n=0 bn, z = ∑∞n=0 cn , where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc ≠0, then (1) x, y, z are in A.P. (2) x, y, z are in G.P. (3) x 1 , 1y , 1z are in A.P. (4) x1 + 1y + 1z = 1 −(a + b + c)

Q62.Let {an}∞n=0 be a sequence such that a0 = a1 = 0 and an+2 = 2an+1 −an + 1 for all n ≥0 . Then, ∑∞n=2 an7n is equal to (1) 6 (2) 7 343 216 (3) 8 (4) 49 343 216 5 10

Q62.Suppose a1, a2, … , an, … be an arithmetic progression of natural numbers. If the ratio of the sum of the first five terms to the sum of first nine terms of the progression is 5 : 17 and 110 < a15 < 120 , then the sum of the JEE Main 2022 (27 Jul Shift 1) JEE Main Previous Year Paper first ten terms of the progression is equal to (1) 290 (2) 380 (3) 460 (4) 510

Q62.The number of ways to distribute 30 identical candies among four children C1, C2, C3 and C4 so that C2 receives atleast 4 and atmost 7 candies, C3 receives atleast 2 and atmost 6 candies, is equal to (1) 205 (2) 615 (3) 510 (4) 430 JEE Main 2022 (28 Jun Shift 2) JEE Main Previous Year Paper

Q62.If (20−a)(40−a) 1 + (40−a)(60−a)1 + … … + (180−a)(200−a)1 = 2561 , then the maximum value of a is (1) 198 (2) 202 (3) 212 (4) 218