Practice Questions

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.Let f(x) be a quadratic polynomial such that f(−2) +f(3) = 0. If one of the roots of f(x) = 0 is −1, then the sum of the roots of f(x) = 0 is equal to (1) 11 (2) 7 3 3 (3) 12 (4) 14 3 3

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

Q61.Let α be a root of the equation 1 + x2 + x4 = 0. Then the value of α1011 + α2022 −α3033 is equal to: (1) 1 (2) α (3) 1 + α (4) 1 + 2α

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.If 𝑧≠0 be a complex number such that 𝑧- 𝑧= 2, then the maximum value of 𝑧 is (1) √2 (2) 1 (3) √2 - 1 (4) √2 + 1

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.Let S = {x |x|−2 ≥0} and elements in S ∩T is JEE Main 2022 (28 Jul Shift 2) JEE Main Previous Year Paper (1) 7 (2) 5 (3) 4 (4) 3

Q62.The sum ∑21n=1 (4n−1)(4n+3)3 is equal to (1) 7 (2) 7 87 29 (3) 14 (4) 21 87 29

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

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 A1, A2, A3, … … be an increasing geometric progression of positive real numbers. If A1 A3 A5 A7 = 12961 and A2 + A4 = 367 , then, the value of A6 + A8 + A10 is equal to (1) 43 (2) 33 (3) 37 (4) 48 JEE Main 2022 (28 Jun Shift 1) JEE Main Previous Year Paper α ∈R, then the value of 16α is equal to

Q62.The remainder when (2021)2023 is divided by 7 is JEE Main 2022 (26 Jun Shift 1) JEE Main Previous Year Paper (1) 2 (2) 3 (3) 4 (4) 5

Q62.If + + … + = then the remainder when 𝐾 is divided by 6 is 2 · 310 22 · 39 210 · 3 210 · 310, (1) 2 (2) 3 (3) 4 (4) 5

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.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.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.Let A = {z ∈C : 1 ⩽|z −(1 + i)| ⩽2} and B = {z ∈A : |z −(1 −i)| = 1} . Then, B (1) is an empty set (2) contains exactly two elements (3) contains exactly three elements (4) is an infinite set

Q62.Let 𝑆= 𝑧= 𝑥+ 𝑖𝑦: 𝑧- 1 + 𝑖≥𝑧, 𝑧< 2, 𝑧+ 𝑖= 𝑧- 1. Then the set of all values of 𝑥, for which 𝑤= 2𝑥+ 𝑖𝑦∈𝑆 for some 𝑦∈ℝ, is 1 1 1 (2) - (1) -√2, 4 2√2 √2, (3) -√2, 1 (4) - 1 1 2 √2, 2√2

Q62.Let for some real numbers α and β, a = α −iβ . If the system of equations 4ix + (1 + i)y = 0 and ¯8(cos 2π3 + i sin 2π3 )x + ay = 0 has more than one solution then αβ is equal to (1) 2 −√3 (2) 2 + √3 (3) −2 + √3 (4) −2 −√3

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.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.Let α, β be the roots of the equation x2 −√2x + √6 = 0 and 1 + 1, 1 + 1 be the roots of the equation α2 β2 x2 + ax + b = 0 . Then the roots of the equation x2 −(a + b −2)x + (a + b + 2) = 0 are : (1) non-real complex numbers (2) real and both negative (3) real and both positive (4) real and exactly one of them is positive