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Question

In the binomial expansion of (a+b)n,n5, the sum of the 5th and 6th term is zero. Then ab is equal to

A
16(n5)
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B
15(4n)
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C
5(n5)
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D
6(n5)
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Solution

The correct option is B 15(4n)
tr+1=nCrxnryr((x+y)n)
t5=nC4xn4y4
t6=nC5xn5yr
t5+t6=0
nC4xn4y4+nC5xn5y5=0
nC4an4b4+nC5an5b5=0
n!(n4)!4!anb4a4+n!(n5)!5!ana5×b5=0
1(n4)!4!+1(n5)!5!ba=0
1(n4)+15ba=0
14n=b5a
54n=ba
ab=4n5.

1080254_1160039_ans_564fa0ccc046417fa71a8caf92128b68.jpeg

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