JEE Main 2023 · 10 Apr 2023 Shift 2

Let A = {2, 3, 4} and B = {8, 9, 12}. Then the number of elements in the relation R = {((a₁, b₁), (a₂, b₂)) ∈ (A × B, A × B) : a₁ divides b₂ and a₂ divides b₁} is

1. A12
2. B18
3. C24
4. D36

Let S = {x ∈ (−π/2, π/2) : 9¹⁻ᵗᵃⁿ²ˣ + 9ᵗᵃⁿ²ˣ = 10} and β = ∑ₓ∈ₛ tan²(x/3), then 1/6 (β − 14)² is equal to

1. A8
2. B16
3. C32
4. D64

Let S = {z = x + iy : (2z − 3i)/(4z + 2i) is a real number}. Then which of the following is NOT correct?

1. Ax = 0
2. By ∈ (−∞, −1/2) ∪ (−1/2, ∞)
3. Cy + x² + y² ≠ −1/4
4. D(x, y) = (0, −1/2)

If A = 1/(5! 6! 7!) [ [5!, 6!, 7!], [6!, 7!, 8!], [7!, 8!, 9!] ], then |adj(adj(2A))| is equal to

1. A2²⁰
2. B2¹⁶
3. C2¹²
4. D2⁸

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is

1. A560
2. B1120
3. C1680
4. D3360

If the coefficients of x and x² in (1 + x)ᵖ (1 − x)ᑫ are 4 and −5 respectively, then 2p + 3q is equal to

1. A60
2. B63
3. C66
4. D69

Let the number (22)²⁰²² + (2022)²² leave the remainder α when divided by 3 and β when divided by 7. Then (α² + β²) is equal to

1. A5
2. B10
3. C13
4. D20

If Sₙ = 4 + 11 + 21 + 34 + 50 + ... to n terms, then 1/60 (S₂₉ − S₉) is equal to

1. A220
2. B223
3. C226
4. D227