JEE Main 2025 · 7 Apr 2025 Shift 2

Let A = {(α, β) ∈ R × R : |α − 1| ≤ 4 and |β − 5| ≤ 6} and B = {(α, β) ∈ R × R : 16(α − 2)² + 9(β − 6)² ≤ 144}. Then

1. AA ⊂ B
2. BB ⊂ A
3. CA ∪ B = {(x, y) : −4 ≤ x ≤ 4, −1 ≤ y ≤ 11}
4. Dneither A ⊂ B nor B ⊂ A

If the range of the function f(x) = (5 − x)/(x² − 3x + 2), x ≠ 1, 2, is (−∞, α] ∪ [β, ∞), then α² + β² is equal to :

1. A188
2. B190
3. C192
4. D194

The number of real roots of the equation x|x − 2| + 3|x − 3| + 1 = 0 is :

1. A1
2. B2
3. C3
4. D4

If the locus of z ∈ C, such that Re((z − 1)/(2z + i)) + Re((z̄ − 1)/(2z̄ − i)) = 2, is a circle of radius r and center (a, b), then 15ab/r² is equal to :

1. A12
2. B16
3. C18
4. D24

Let the system of equations x + 5y − z = 1, 4x + 3y − 3z = 7, 24x + y + λz = μ, λ, μ ∈ R, have infinitely many solutions. Then the number of the solutions of this system, if x, y, z are integers and satisfy 7 ≤ x + y + z ≤ 77, is :

1. A3
2. B4
3. C5
4. D6

Let aₙ be the nᵗʰ term of an A.P. If Sₙ = a₁ + a₂ + a₃ + ... + aₙ = 700, a₆ = 7 and S₇ = 7, then aₙ is equal to :

1. A56
2. B64
3. C65
4. D70

If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15309, then the sum of its first nine terms is :

1. A750
2. B755
3. C757
4. D760

Let p be the number of all triangles that can be formed by joining the vertices of a regular polygon P of n sides and q be the number of all quadrilaterals that can be formed by joining the vertices of P. If p + q = 126, then the eccentricity of the ellipse x²/16 + y²/n = 1 is :

1. A1/2
2. B1/√2
3. C√7/4
4. D3/4