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Question

In the expansion of (512+718)1024, the number of integral terms is .

A
128
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B
129
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C
130
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D
131
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Solution

The correct option is B 129

Here, n=1024=210

Now, Tr+1=nCr(512)1024r(718)r

For Tr+1 to be an integer,
1024r must be a multiple of 2, or 0.
r must be a multiple of 8, or 0.

When r is a multiple of 8, say r=8k,
1024r=10248k, which is divisible by 2.

Thus, the number of multiples of 8 between 0 and 1024, including 0 is the number of integers in the expansion.

This number is given by 1024÷8 +1=128+1=129


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