JEE Main 2023 · 13 Apr 2023 Shift 2

The range of f(x) = 4sin⁻¹(x²/(x² + 1)) is

1. A[0, π]
2. B[0, π)
3. C[0, 2π]
4. D[0, 2π)

Let α, β be the roots of the equation x² − √2x + 2 = 0. Then α¹⁴ + β¹⁴ is equal to

1. A−64
2. B−64√2
3. C−128
4. D−128√2

If the system of equations 2x + y − z = 5, 2x − 5y + λz = μ, x + 2y − 5z = 7 has infinitely many solutions, then (λ + μ)² + (λ − μ)² is equal to

1. A904
2. B912
3. C916
4. D920

Let for A = ⎡1 2 3; α 3 1; 1 1 2⎤, |A| = 2. If |2 adj (2 adj (2A))| = 32ⁿ, then 3n + α is equal to

1. A9
2. B10
3. C11
4. D12

All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is

1. A324
2. B326
3. C327
4. D328

The coefficient of x⁵ in the expansion of (2x³ − 1/(3x²))⁵ is

1. A8
2. B9
3. C80/9
4. D26/3

Let a₁, a₂, a₃, .... be a G. P. of increasing positive numbers. Let the sum of its 6th and 8th terms be 2 and the product of its 3rd and 5th terms be 1/9. Then 6(a₂ + a₄)(a₄ + a₆) is equal to

1. A2
2. B2√2
3. C3√3
4. D3

If limₓ→₀ (eᵃˣ − cos(bx) − cxe⁻ᶜˣ/2)/(1 − cos(2x)) = 17, then 5a² + b² is equal to

1. A68
2. B64
3. C72
4. D76