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Question

The sum of coefficient of integral powers of x in the binomial expansion of (12x)50 is :

A
12(350+1)
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B
12(350)
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C
12(3501)
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D
12(250+1)
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Solution

The correct option is A 12(350+1)
(12x)50=50C050C1(2x)+50C2(2x)2.....

we need to find sum of even forms, so

Put x=1(12)50=1=50C050C1(2)+50C2(2)2.........(1)

and x=1(1+2)50=350=50C0+50C12+50C2(2)2.......(2)

Adding (1) and (2) we get,

350+1=2(50C0+50C2(2)2+........)

(50C0+50C2(2)2+........)=12(1+350)

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