JEE Main 2023 · 6 Apr 2023 Shift 1

The sum of all the roots of the equation |x² − 8x + 15| − 2x + 7 = 0 is:

1. A9 − √3
2. B9 + √3
3. C11 + √3
4. D11 − √3

Let A = [aᵢⱼ]₂ₓ₂, where aᵢⱼ ≠ 0 for all i, j and A² = I. Let a be the sum of all diagonal elements of A and b = |A|. Then 3a² + 4b² is equal to

1. A3
2. B4
3. C7
4. D14

If the system of equations x + y + az = b, 2x + 5y + 2z = 6, x + 2y + 3z = 3 has infinitely many solutions, then 2a + 3b is equal to

1. A20
2. B23
3. C25
4. D28

If ²ⁿC₃ : ⁿC₃ = 10 : 1, then the ratio (n² + 3n) : (n² − 3n + 4) is

1. A27:11
2. B35:16
3. C2:1
4. D65:37

If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of (⁴√2 + 1/⁴√3)ⁿ is √6 : 1, then the third term from the beginning is:

1. A60√2
2. B60√3
3. C30√2
4. D30√3

The sum of the first 20 terms of the series 5 + 11 + 19 + 29 + 41 + ... is

1. A3250
2. B3450
3. C3420
4. D3520

Let a₁, a₂, a₃, ..., aₙ be n positive consecutive terms of an arithmetic progression. If d > 0 is its common difference, then limₙ→∞ √(d/n)(1/(√a₁ + √a₂) + 1/(√a₂ + √a₃) + ...... + 1/(√aₙ₋₁ + √aₙ)) is

1. A1
2. B0
3. C√d
4. D1/√d

If 2xʸ + 3yˣ = 20, then dy/dx at (2, 2) is equal to:

1. A−(3 + logₑ 4)/(2 + logₑ 8)
2. B−(3 + logₑ 16)/(4 + logₑ 8)
3. C−(3 + logₑ 8)/(2 + logₑ 4)
4. D−(2 + logₑ 8)/(3 + logₑ 4)