JEE Main 2026 · 6 Apr 2026 Shift 1

Let [·] denote the greatest integer function. If the domain of the function f(x) = sin⁻¹((x + [x])/3) is [α, β), then α² + β² is equal to:

1. A2
2. B5
3. C10
4. D13

Let one root of the quadratic equation in x: (k² − 15k + 27)x² + 9(k − 1)x + 18 = 0 be twice the other. Then the length of the latus rectum of the parabola y² = 6kx is equal to:

1. A4
2. B6
3. C8
4. D12

Let e₁ and e₂ be two distinct roots of the equation x² − ax + 2 = 0. Let the sets {a ∈ R : e₁ and e₂ are the eccentricities of hyperbolas} = (α, β), and {a ∈ R : e₁ and e₂ are the eccentricities of an ellipse and a hyperbola, respectively} = (γ, ∞). Then α² + β² + γ² is equal to:

1. A18
2. B22
3. C26
4. D34

Let the set of all values of k ∈ R such that the equation z(z̄ + 2 + i) + k(2 + 3i) = 0, z ∈ C, has at least one solution, be the interval [α, β]. Then 9(α + β) is equal to:

1. A−10
2. B−8
3. C10√13
4. D8√13

The value of 1³ − 2³ + 3³ − ... + 15³ is:

1. A1706
2. B1856
3. C1982
4. D2403

The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to common difference of the A.P., then the sum of all possible values of the first term of the G.P. is:

1. A34/9
2. B34/13
3. C32/9
4. D32/13

The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is:

1. A2670
2. B2840
3. C2920
4. D3600

If the coefficients of the middle terms in the binomial expansions of (1 + αx)²⁶ and (1 − αx)²⁸, α ≠ 0, are equal, then the value of α is:

1. A1
2. B14/13
3. C27/7
4. D7/27