Question

If n₁, n₂, n₃,….., n₁₀₀ are positive real numbers such that n₁ + n₂ + n₃ +….+ n₁₀₀ = 20 and k = n₁(n₂ + n₃ + n₄)

(n₅ + n₆ +…. + n₉) (n₁₀ + ……+ n₁₆) …. (…. + n₁₀₀), then k

belongs to-

• A. (0, 100]
• B. (0, 128]
• C. [0, 144]
• D. None

Answer 1

Answer: (D)

None

Answer 2

$\left[ \mathrm { n } _ { 1 } + \left( \mathrm { n } _ { 2 } + \mathrm { n } _ { 3 } + \mathrm { n } _ { 4 } \right) + \left( \mathrm { n } _ { 5 } + \mathrm { n } _ { 6 } + \ldots + \mathrm { n } _ { 9 } \right) \right.$ $\left. + \ldots + \left( \ldots + \mathrm { n } _ { 100 } \right) \right]$ 10³ (AM

³ GM)

Ž 2 ³

Ž 0 < k £ 1024 .