JEE Main 2026 · 4 Apr 2026 Shift 2

For the function f : [1, ∞) → [1, ∞) defined by f(x) = (x − 1)⁴ + 1, among the two statements: (I) The set S = {x ∈ [1, ∞) : f(x) = f⁻¹(x)} contains exactly two elements, and (II) The set S = {x ∈ [1, ∞) : f(x) = f⁻¹(x + 1)} is an empty set.

1. Aonly (I) is TRUE
2. Bonly (II) is TRUE
3. Cboth (I) and (II) are TRUE
4. Dneither (I) nor (II) is TRUE

Let S = {z ∈ C : z² + 4z + 16 = 0}. Then ∑₍z∈S₎ |z + √3i|² is equal to:

1. A42
2. B23
3. C27
4. D38

If the system of equations: x + y + z = 5; x + 2y + 3z = 9; x + 3y + λz = μ has infinitely many solutions, then the value of λ + μ is:

1. A16
2. B18
3. C19
4. D21

If α = 1 and β = 1 + i√2, where i = √−1 are two roots of the equation x³ + ax² + bx + c = 0, a, b, c ∈ R, then ∫₋₁¹ (x³ + ax² + bx + c) dx is equal to:

1. A−2
2. B−4
3. C−8
4. D−10

If the quadratic equation (λ + 2)x² − 3λx + 4λ = 0, λ ≠ −2, has two positive roots, then the number of possible integral values of λ is:

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

Let A = [[1, 2, 7], [4, −2, 8], [3, 8, −7]] and det(A − αI) = 0, where α is a real number. If the largest possible value of α is p, then the circle (x − p)² + (y − 2p)² = 320, intersects the co-ordinate axes at

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

Let α = 1/4 + 1/8 + 1/16 + …∞ and β = 1/3 + 1/9 + 1/27 + … . Then the value of (0.2)^(log₍√5₎(α)) + (0.04)^(log₍5₎(β)) is equal to:

1. A4
2. B5
3. C8
4. D25

For 10 observations x₁, x₂, …, x₁₀, if ∑ᵢ₌₁¹⁰ (xᵢ + 2)² = 180 and ∑ᵢ₌₁¹⁰ (xᵢ − 1)² = 90, then their standard deviation is:

1. A2
2. B√3
3. C2√2
4. D3