JEE Main 2026 · 5 Apr 2026 Shift 1

Let a, b ∈ C. Let α, β be the roots of the equation x² + ax + b = 0. If β − α = √11 and β² − α² = 3i√11, then (β³ − α³)² is equal to:

1. A160
2. B176
3. C194
4. D187

Let the sum of the first n terms of an A.P. be 3n² + 5n. Then the sum of squares of the first 10 terms of the A.P. is:

1. A10220
2. B12860
3. C15220
4. D19780

Let A be a 3 × 3 matrix such that Aᵀ[1, 0, 1]ᵀ = [5, 2, 2]ᵀ, Aᵀ[0, 0, 1]ᵀ = [3, 1, 1]ᵀ, A[1, 0, 1]ᵀ = [3, 4, 4]ᵀ and A[0, 0, 1]ᵀ = [1, 3, 1]ᵀ. If det(A) = 1, then det(adj(A² + A)) is equal to:

1. A16
2. B25
3. C49
4. D64

Consider the system of linear equations in x, y, z: x + 2y + tz = 0, 6x + y + 5t z = 0, 3x + 2y + f(t)z = 0, where f : R → R is a differentiable function. If this system has infinitely many solutions for all t ∈ R, then f

1. Ais a constant function
2. Bis strictly increasing on R
3. Cis strictly decreasing on R
4. Dhas two critical points

∑ₙ₌₁¹⁰ (528/[n(n+1)(n+2)]) is equal to:

1. A65
2. B130
3. C220
4. D440

Let tan A, tan B, where A, B ∈ (−π/2, π/2), be the roots of the quadratic equation x² − 2x − 5 = 0. Then 20 sin²((A + B)/2) is equal to:

1. A10 + √10
2. B10 − 2√10
3. C10 − 3√10
4. D10 − √10

A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is:

1. A7/10
2. B10/17
3. C12/19
4. D7/19

Let a focus of the ellipse E : x²/a² + y²/b² = 1 be S(4, 0) and its eccentricity be 4/5. If the point P(3, α) lies on E and O is the origin, then the area of ΔPOS is equal to:

1. A12/5
2. B14/5
3. C24/5
4. D48/5