Question

The value of (5C₀ + 5C₁) + (5C₁ + 5C₂) + (5C₂ + 5C₃) + (5C₃ + 5C₄) + (5C₄ + 5C₅) is:

पर्याय

• 2⁶ – 2

• 2⁵ – 1

• 2⁸

• 2⁷

Answer 1

2⁶ – 2

Explanation: 

(5C₀ + 5C₁ + 5C₂ + 5C₃ + 5C₄ + 5C₅) + (5C₁ + 5C₂ + 5C₃ + 5C₄)

= 2⁵ + (5C₀ + 5C₁ + 5C₂ + 5C₃ + 5C₄ + 5C₅) – (5C₀ + 5C₅)

= 2⁵ + 2⁵ – (1 + 1) (∵ Adding and subtracting of 5C₀ and 5C₅)

= 2(2⁵) – 2 (∵ 5C₀ = 5C₅ = 1)

= 2⁶ – 2