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Question

The coefficients of x16 and x17 in (a+bx)101 are equal. If a and b are natural numbers, then the least possible value of a is

A
1
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B
3
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C
5
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D
7
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Solution

The correct option is B 5
It is given that coefficients of T17 and T18 are equal
Hence
101C16a85b16=101C17a84b17
101!a16!85!=101!b17!84!
a85=b17
a=5b
Hence least value of a is 5 given that a,bϵN

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