Assertion (A) : Greatest binomial coefficient in the expansion of (1+5x)8 is 8C454 Reason (R) : Greatest coefficient in the expansion of (1+x)2n is the middle term
A
Both A and R are individually true and R is the correct explanation of A.
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B
Both A and R are individually true and R is not correct explanation of A.
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C
A is true but R is false
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D
A is false but R is true
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Solution
The correct option is D A is false but R is true The greatest binomial coefficient is the middle term in the expansion. This is true for any binomial expansion. Hence Greatest binomial coefficient in the expansion of (1+5x)8 is of the middle term 8C4(5x)4 the coefficient being 8C4 Similarly for (1+x)2n the middle term is =2nCnxn and the greatest coefficient is =2nCn