JEE Main 2026 · 5 Apr 2026 Shift 2

Let α, β be the roots of the equation x² − x + p = 0 and γ, δ be the roots the equation x² − 4x + q = 0; p, q ∈ Z. If α, β, γ, δ are in G.P., then |p + q| equals :

1. A16
2. B32
3. C34
4. D38

Let z₁, z₂ ∈ C be the distinct solutions of the equation z² + 4z − (1 + 12i) = 0. Then |z₁|² + |z₂|² is equal to :

1. A18
2. B22
3. C29
4. D34

If f : N → Z is defined by f(n) = | n −1 −5; −2n² 3(2k + 1) 2k + 1; −3n³ 3k(2k + 1) 3k(k + 2) + 1 |, k ∈ N, and ∑ₙ₌₁ᵏ f(n) = 98, then k is equal to :

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

Let M be a 3 × 3 matrix such that M(1, 0, 0)ᵀ = (1, 2, 3)ᵀ, M(0, 1, 0)ᵀ = (0, 1, 2)ᵀ and M(0, 0, 1)ᵀ = (−1, 1, 1)ᵀ. If M(x, y, z)ᵀ = (1, 7, 11)ᵀ, then x + y + z equals :

1. A4
2. B5
3. C7
4. D11

If the sum of the first 10 terms of the series 1/(1 + 1⁴ × 4) + 2/(1 + 2⁴ × 4) + 3/(1 + 3⁴ × 4) + 4/(1 + 4⁴ × 4) + ...... is m/n, gcd (m, n) = 1, then m + n is equal to :

1. A256
2. B264
3. C276
4. D284

Let A₁, A₂, A₃, ......, A₃₉ be 39 arithmetic means between the numbers 59 and 159. Then the mean of A₂₅, A₂₈, A₃₁ and A₃₆ is equal to :

1. A129
2. B136
3. C131.50
4. D134

The coefficient of x² in the expansion of (2x² + 1/x)¹⁰, x ≠ 0, is :

1. A3240
2. B3360
3. C3480
4. D3600

The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4, respectively. If A is selected the captain, the probability that the team wins the tournament is 0.8 and if B is selected the captain, the probability that the team wins the tournament is 0.7. Then the probability, that the team wins the tournament, is :

1. A0.74
2. B0.76
3. C0.72
4. D0.78