Manipal MET2023MathematicsBinomial Theorem

Last two digits in (9)⁵⁰ be____

Correct answer

Step-by-step solution

(9)⁵⁰=(10-1)⁵⁰ aligned &= [ ⁵⁰ C₀(10)⁵⁰(-1)^0- ⁵⁰ C₁(10)⁴⁹(1) .+ .]- 50 49 (10)^1 &+ 50 50 (10)^0 aligned All the terms in the bracket are multiples of 10^2 . So, we can write as 100 =100 -50 10+1=100 -500+1 so, last 2 digits will be =01 .

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