JEE Main 2026 · 2 Apr 2026 Shift 2

Let α, β be the roots of the equation x² − 3x + r = 0, and α/2, 2β be the roots of the equation x² + 3x + r = 0. If the roots of the equation x² + 6x = m are 2α + β + 2r and α − 2β − r/2, then m is equal to :

1. A−135
2. B−567
3. C135
4. D567

Let the circles C₁ : |z| = r and C₂ : |z − 3 − 4i| = 5, z ∈ C, be such that C₂ lies within C₁. If z₁ moves on C₁, z₂ moves on C₂ and min |z₁ − z₂| = 2, then max |z₁ − z₂| is equal to :

1. A12
2. B17
3. C22
4. D24

If the system of equations x + 5y + 6z = 4, 2x + 3y + 4z = 7, x + 6y + az = b has infinitely many solutions, then the point (a, b) lies on the line

1. Ay − x = 3
2. Bx − y = 3
3. Cx + y = 11
4. Dx + y = 12

Let a₁, a₂, a₃, ..... be an A.P. and g₁ = a₁, g₂, g₃, ..... be an increasing G.P. If a₁ = a₂ + g₂ = 1 and a₃ + g₃ = 4, then a₁₀ + g₅ is equal to :

1. A81
2. B76
3. C62
4. D55

The sum 1³/1 + (1³ + 2³)/(1 + 3) + (1³ + 2³ + 3³)/(1 + 3 + 5) + ... up to 8 terms, is :

1. A70
2. B71
3. C72
4. D73

If for 3 ≤ r ≤ 30, (³⁰C₃₀₋ᵣ) + 3(³⁰C₃₁₋ᵣ) + 3(³⁰C₃₂₋ᵣ) + (³⁰C₃₃₋ᵣ) = ᵐCᵣ, then m equals :

1. A31
2. B32
3. C33
4. D34

Let pₙ denote the total number of triangles formed by joining the vertices of an n-side regular polygon. If pₙ₊₁ − pₙ = 66, then the sum of all distinct prime divisors of n is :

1. A7
2. B8
3. C5
4. D6

A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability that he gets exactly 30 points is m/n, gcd (m, n) = 1, then m + n is equal to :

1. A53
2. B55
3. C107
4. D105