JEE Main 2026 · 4 Apr 2026 Shift 1

Let [.] denote the greatest integer function. If the domain of the function f(x) = cos⁻¹((4x + 2[x])/3) is [α, β], then 12 (α + β) is equal to:

1. A6
2. B8
3. C9
4. D4

If the set of all solutions of |x² + x − 9| = |x| + |x² − 9| is [α, β] ∪ [γ, ∞), then (α² + β² + γ²) is equal to:

1. A9
2. B18
3. C36
4. D72

Let z be a complex number such that |z + 2| = |z − 2| and arg((z + 3)/(z − i)) = π/4. Then |z|² is equal to:

1. A9
2. B4
3. C5
4. D1

The number of functions f : {1, 2, 3, 4} → {a, b, c}, which are not onto, is:

1. A48
2. B45
3. C51
4. D35

Let S = {A = [a b; c d] : a, b, c, d ∈ {0, 1, 2, 3, 4} and A² − 4A + 3I = 0} be a set of 2 × 2 matrices. Then the number of matrices in S, for which the sum of the diagonal elements is equal to 4, is:

1. A20
2. B17
3. C21
4. D19

Let A = [1 1 2; −2 0 1; 1 3 5]. Then the sum of all elements of the matrix adj(adj(2(adj A)⁻¹)) is equal to:

1. A3
2. B4
3. C−4
4. D−3

The first term of an A.P. of 30 non-negative terms is 10/3. If the sum of this A.P. is the cube of its last term, then its common difference is:

1. A5/87
2. B25/83
3. C15/29
4. D5/29

The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:

1. A5040
2. B3050
3. C3410
4. D4320