JEE Main 2024 · 4 Apr 2024 Shift 1

If the domain of the function sin⁻¹((3x − 22)/(2x − 19)) + logₑ((3x² − 8x + 5)/(x² − 3x − 10)) is (α, β], then 3α + 10β is equal to :

1. A95
2. B97
3. C98
4. D100

Let α and β be the sum and the product of all the non-zero solutions of the equation (z̄)² + |z| = 0, z ∈ C. Then 4(α² + β²) is equal to :

1. A2
2. B4
3. C6
4. D8

If 2 and 6 are the roots of the equation ax² + bx + 1 = 0, then the quadratic equation, whose roots are 1/(2a + b) and 1/(6a + b), is :

1. Ax² + 8x + 12 = 0
2. B4x² + 14x + 12 = 0
3. C2x² + 11x + 12 = 0
4. Dx² + 10x + 16 = 0

If the system of equations x + (√2 sin α)y + (√2 cos α)z = 0, x + (cos α)y + (sin α)z = 0, x + (sin α)y − (cos α)z = 0 has a non-trivial solution, then α ∈ (0, π/2) is equal to :

1. A3π/4
2. B7π/24
3. C5π/24
4. D11π/24

Let α ∈ (0, ∞) and A = [[1, 2, α], [1, 0, 1], [0, 1, 2]]. If det(adj(2A − Aᵀ) · adj(A − 2Aᵀ)) = 2⁸, then (det(A))² is equal to :

1. A1
2. B16
3. C36
4. D49

Let f : R → R be a function given by f(x) = (1 − cos 2x)/x², x < 0; α, x = 0; β√(1 − cos x)/x, x > 0, where α, β ∈ R. If f is continuous at x = 0, then α² + β² is equal to :

1. A3
2. B6
3. C12
4. D48

There are 5 points P₁, P₂, P₃, P₄, P₅ on the side AB, excluding A and B, of a triangle ABC. Similarly there are 6 points P₆, P₇, ..., P₁₁ on the side BC and 7 points P₁₂, P₁₃, ..., P₁₈ on the side CA of the triangle. The number of triangles, that can be formed using the points P₁, P₂, ..., P₁₈ as vertices, is :

1. A771
2. B776
3. C796
4. D751

The sum of all rational terms in the expansion of (2¹⁄⁵ + 5¹⁄³)¹⁵ is equal to :

1. A931
2. B3133
3. C633
4. D6131