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Question: If \(\frac{(2n)!3!3!}{(2n - m)!}\) then \[\frac{(2n)!}{\left( \frac{2n - m}{3} \right) ⥂ !\left( \f...

If (2n)!3!3!(2n−m)!\frac{(2n)!3!3!}{(2n - m)!} then

(2n)!(2n−m3)⥂!(4n+m3)!\frac{(2n)!}{\left( \frac{2n - m}{3} \right) ⥂ !\left( \frac{4n + m}{3} \right)!}

A

(1+x+x3+x4)10(1 + x + x^{3} + x^{4})^{10}

B

x4x^{4}

C

40C440C_{4}

D

None of these

Answer

x4x^{4}

Explanation

Solution

We have 2n−12^{n - 1}

⇒ 2n−12^{n - 1}

Differentiating both sides with respect to x, we get

2n2^{n}

= 2n−1−12^{n - 1} - 1

Putting C0,C1,C2,.......,CnC_{0},C_{1},C_{2},.......,C_{n}, we get

2.C1+23.C3+25.C5+....2.C_{1} + 2^{3}.C_{3} + 2^{5}.C_{5} + ....