JEE Main 2024 · 9 Apr 2024 Shift 1

If the domain of the function f(x) = sin⁻¹((x − 1)/(2x + 3)) is R − (α, β), then 12αβ is equal to :

1. A24
2. B32
3. C36
4. D40

Let α, β be the roots of the equation x² + 2√2 x − 1 = 0. The quadratic equation, whose roots are α⁴ + β⁴ and 1/10 (α⁶ + β⁶), is:

1. Ax² − 180x + 9506 = 0
2. Bx² − 190x + 9466 = 0
3. Cx² − 195x + 9506 = 0
4. Dx² − 195x + 9466 = 0

Let λ, μ ∈ R. If the system of equations 3x + 5y + λz = 3, 7x + 11y − 9z = 2, 97x + 155y − 189z = μ has infinitely many solutions, then μ + 2λ is equal to :

1. A22
2. B24
3. C25
4. D27

The coefficient of x⁷⁰ in x²(1 + x)⁹⁸ + x³(1 + x)⁹⁷ + x⁴(1 + x)⁹⁶ + . . . + x⁵⁴(1 + x)⁴⁶ is ⁹⁹Cₚ − ⁴⁶C_q. Then a possible value of p + q is :

1. A55
2. B83
3. C68
4. D61

If the sum of the series 1/[1 · (1 + d)] + 1/[(1 + d)(1 + 2d)] + . . . + 1/[(1 + 9d)(1 + 10d)] is equal to 5, then 50d is equal to :

1. A5
2. B10
3. C15
4. D20

Let f(x) = ax³ + bx² + cx + 41 be such that f(1) = 40, f′(1) = 2 and f″(1) = 4. Then a² + b² + c² is equal to :

1. A51
2. B54
3. C62
4. D73

A variable line L passes through the point (3, 5) and intersects the positive coordinate axes at the points A and B. The minimum area of the triangle OAB, where O is the origin, is :

1. A40
2. B35
3. C25
4. D30

Let ∫ (2 − tan x)/(3 + tan x) dx = 1/2 (αx + logₑ|β sin x + γ cos x|) + C, where C is the constant of integration. Then α + γ/β is equal to :

1. A1
2. B3
3. C4
4. D7