JEE Main 2026 · 6 Apr 2026 Shift 2

Let f: R → R be defined as f(x) = (2x² − 3x + 2)/(3x² + x + 3). Then f is:

1. Aboth one-one and onto
2. Bone-one but not onto
3. Conto but not one-one
4. Dneither one-one nor onto

Consider the quadratic equation (n² − 2n + 2)x² − 3x + (n² − 2n + 2)² = 0, n ∈ R. Let α be the minimum value of the product of its roots and β be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is α and the common ratio is α/β, is:

1. A61/37
2. B121/81
3. C364/243
4. D1093/729

Let S = {z ∈ C : z² + √6 iz − 3 = 0}. Then ∑₍z∈S₎ z⁸ is equal to:

1. A162
2. B184
3. C262
4. D324

The sum of all possible values of θ ∈ [0, 2π], for which the system of equations: x cos 3θ − 8y − 12z = 0; x cos 2θ + 3y + 3z = 0; x + y + 3z = 0 has a non-trivial solution, is equal to:

1. Aπ
2. B2π
3. C3π
4. D4π

Let A = [[1, 0, 0], [3, 1, 0], [9, 3, 1]] and B = [bᵢⱼ], 1 ≤ i, j ≤ 3. If B = A⁹⁹ − I, then the value of (b₃₁ − b₂₁)/b₃₂ is:

1. A99
2. B199
3. C149
4. D159

The sum 1 + 1/2(1² + 2²) + 1/3(1² + 2² + 3²) + .... upto 10 terms is equal to:

1. A130
2. B155
3. C315/2
4. D325/2

A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the 10th floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to:

1. A2184
2. B3064
3. C7056
4. D11340

Let the mean and the variance of seven observations 2, 4, α, 8, β, 12, 14, α < β, be 8 and 16 respectively. Then the quadratic equation whose roots are 3α + 2 and 2β + 1 is:

1. Ax² − 35x + 306 = 0
2. Bx² − 41x + 420 = 0
3. Cx² − 45x + 506 = 0
4. Dx² − 37x + 342 = 0