A GoodProblem for JEE

Algebra Level 4

If the value of 2[(101)+(103)]+(105)2 \left [ { 10 \choose 1} + { 10 \choose 3 } \right ] + { 10 \choose 5} is in the form of 10!×2ab! \frac {10! \times 2^a}{b!} for positive integers a,ba,b.

Expression the value of x35x2+33x10x^3 - 5x^2 + 33x - 10 in terms of aa and bb when x=2+5ix = 2+5i

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