JEE Main 2026 · 2 Apr 2026 Shift 1

Let α, α + 2, α ∈ Z, be the roots of the quadratic equation x(x + 2) + (x + 1)(x + 3) + (x + 2)(x + 4) + .... + (x + n − 1)(x + n + 1) = 4n for some n ∈ N. Then n + α is equal to :

1. A0
2. B1
3. C2
4. D3

Let x and y be real numbers such that 50(2x/(1 + 3i) − y/(1 − 2i)) = 31 + 17i, i = √−1. Then the value of 10(x − 3y) is :

1. A20
2. B31
3. C35
4. D75

Let α, β ∈ R be such that the system of linear equations x + 2y + z = 5, 2x + y + αz = 5, 8x + 4y + βz = 18 has no solution. Then β/α is equal to :

1. A−4
2. B4
3. C8
4. D−8

Let A = [1 2; 1 α] and B = [3 3; β 2]. If A² − 4A + I = O and B² − 5B − 6I = O, then among the two statements : (S1) : [(B − A)(B + A)]ᵀ = [13 15; 7 10] and (S2) : det(adj(A + B)) = −5,

1. Aonly (S1) is correct
2. Bonly (S2) is correct
3. Cboth (S1) and (S2) are correct
4. Dboth (S1) and (S2) are wrong

Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 7. Then the number of elements in A∩B, which are divisible by 3, is :

1. A4
2. B5
3. C6
4. D7

The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is :

1. A15400
2. B17800
3. C16800
4. D29400

The number of elements in the set S = {(r, k) : k ∈ Z and ³⁶Cᵣ₊₁ = 6(³⁵Cᵣ)/(k² − 3)}, is :

1. A2
2. B4
3. C8
4. D16

Let the mid points of the sides of a triangle ABC be (5/2, 7), (5/2, 3) and (4, 5). If its incentre is (h, k), then 3h + k is equal to :

1. A11
2. B12
3. C13
4. D14