JEE Main 2024 · 9 Apr 2024 Shift 2

Let the range of the function f(x) = 1/(2 + sin 3x + cos 3x), x ∈ R be [a, b]. If α and β are respectively the A.M. and the G.M. of a and b, then α/β is equal to

1. A2
2. B√2
3. Cπ
4. D√π

Let z be a complex number such that the real part of (z − 2i)/(z + 2i) is zero. Then, the maximum value of |z − (6 + 8i)| is equal to

1. A8
2. B10
3. C12
4. D∞

Let α, β; α > β, be the roots of the equation x² − √2x − √3 = 0. Let Pₙ = αⁿ − βⁿ, n ∈ N. Then (11√3 − 10√2)P₁₀ + (11√2 + 10)P₁₁ − 11P₁₂ is equal to

1. A11√3 P₉
2. B11√2 P₉
3. C10√3 P₉
4. D10√2 P₉

Let B = [[1, 3], [1, 5]] and A be a 2 × 2 matrix such that AB⁻¹ = A⁻¹. If BCB⁻¹ = A and C⁴ + αC² + βI = O, then 2β − α is equal to

1. A2
2. B8
3. C10
4. D16

limₓ→₀ [e − (1 + 2x)^(1/(2x))]/x is equal to

1. Ae
2. B0
3. Ce − e²
4. D−2/e

The sum of the coefficient of x²⁄³ and x⁻²⁄⁵ in the binomial expansion of (x²⁄³ + ½x⁻²⁄⁵)⁹ is

1. A21/4
2. B63/16
3. C19/4
4. D69/16

Let a, ar, ar², ...... be an infinite G.P. If ∑ₙ₌₀^∞ arⁿ = 57 and ∑ₙ₌₀^∞ a³r³ⁿ = 9747, then a + 18r is equal to

1. A27
2. B31
3. C38
4. D46

If logₑ y = 3 sin⁻¹ x, then (1 − x²)y″ − xy′ at x = 1/2 is equal to

1. A9e^(π/2)
2. B9e^(π/6)
3. C3e^(π/2)
4. D3e^(π/6)