JEE MAIN - Mathematics (2021 - 25th July Evening Shift - No. 23)
If the co-efficient of x7 and x8 in the expansion of $${\left( {2 + {x \over 3}} \right)^n}$$ are equal, then the value of n is equal to _____________.
Answer
55
Explanation
$${}^n{C_7}{2^{n - 7}}{1 \over {{3^7}}} = {}^n{C_8}{2^{n - 8}}{1 \over {{3^8}}}$$
$$\Rightarrow$$ n $$-$$ 7 = 48 $$\Rightarrow$$ n = 55
$$\Rightarrow$$ n $$-$$ 7 = 48 $$\Rightarrow$$ n = 55
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