In the expansion of [3 -x/4 + 3 5x/4]n the sum of the binomial coefficients is 64 and the term with the greatest binomial coefficient exceeds the third term by (n-1), then the value of x must be
A) 1 B) 2 C) 0 D) 1
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The sum of binomial coefficients in the expansion of (x+a)n is 2n.
So, here
2n=64 = 28
So, n = 8.
The term with greatest binomial coefficient is the middle term.
So, the middle term when n= 2 is, Tn/2 + 1=T6/2 + 1=T4
It is given that,
T4=T3 + n - 1
T4=T3 + 6 - 1
T4=T3 + 5
6C3(3−x4)3 (35x4)3=6C2(3−x4)4 (35x4)2+520. 33x=15 . 33x2+5This is true only when x=0 because20. 30=15 . 30+520=20, which is true.
So, the answer is x=0.
option c is the answer
So, here
2n=64 = 28
So, n = 8.
The term with greatest binomial coefficient is the middle term.
So, the middle term when n= 2 is, Tn/2 + 1=T6/2 + 1=T4
It is given that,
T4=T3 + n - 1
T4=T3 + 6 - 1
T4=T3 + 5
6C3(3−x4)3 (35x4)3=6C2(3−x4)4 (35x4)2+520. 33x=15 . 33x2+5This is true only when x=0 because20. 30=15 . 30+520=20, which is true.
So, the answer is x=0.
option c is the answer
YASHASVIYADAV:
the answer given in my book is n=6 but 8n your answer n=8 why so
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