JEE Main 2025 · 3 Apr 2025 Shift 1

Let A = {−3, −2, −1, 0, 1, 2, 3}. Let R be a relation on A defined by xRy if and only if 0 ≤ x² + 2y ≤ 4. Let l be the number of elements in R and m be the minimum number of elements required to be added in R to make it a reflexive relation. Then l + m is equal to

1. A20
2. B17
3. C18
4. D19

If the domain of the function f(x) = logₑ((2x − 3)/(5 + 4x)) + sin⁻¹((4 + 3x)/(2 − x)) is [α, β), then α² + 4β is equal to

1. A3
2. B4
3. C5
4. D7

Let α and β be the roots of x² + √3x − 16 = 0, and γ and δ be the roots of x² + 3x − 1 = 0. If Pₙ = αⁿ + βⁿ and Qₙ = γⁿ + δⁿ, then (P₂₅ + √3P₂₄)/(2P₂₃) + (Q₂₅ − Q₂₃)/Q₂₄ is equal to

1. A3
2. B4
3. C5
4. D7

Let z ∈ C be such that (z² + 3i)/(z − 2 + i) = 2 + 3i. Then the sum of all possible values of z² is

1. A19 − 2i
2. B−19 + 2i
3. C19 + 2i
4. D−19 − 2i

Let A be a matrix of order 3 × 3 and |A| = 5. If |2 adj(3A adj(2A))| = 2ᵅ · 3ᵝ · 5ᵞ, α, β, γ ∈ N, then α + β + γ is equal to

1. A25
2. B26
3. C27
4. D28

Let a₁, a₂, a₃,.... be a G.P. of increasing positive numbers. If a₃a₅ = 729 and a₂ + a₄ = 111/4, then 24 (a₁ + a₂ + a₃) is equal to

1. A128
2. B129
3. C130
4. D131

The sum 1 + 3 + 11 +25 + 45 + 71 + ... upto 20 terms, is equal to

1. A6982
2. B7130
3. C7240
4. D8124

If ∑ᵣ₌₁⁹ ((r + 3)/2ʳ) · ⁹Cᵣ = α(3/2)⁹ − β, α, β ∈ N, then (α + β)² is equal to

1. A27
2. B18
3. C9
4. D81