In the expansion of (3 –x/4 + 3 5x/4 ) n , the sum of the binomial coefficient is 64 and the term with greatest binomial coefficient exceeds the third by (n–1) then-
(i) The value of n is-
Text Solution
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Ans.
(i)
Sol. Given that sum of all binomial coefficient is 64 so
putting 3 –x/4 = 3 9x/4 = 1.
(1+1) n = 64
∴ 2 n = 64
∴ n = 6
(ii)
Sol. We know that middle term has the greatest binomial coefficient here n = 6
So middle term is 
= 4 th term
(iii)
Sol. Given T 4 = (n –1) + T 3
⇒ 6 C 3 (3 –x/4 ) 3 (3 5x/4 ) 3 = (6–1) +
6 C 2 (3 –x/4 ) 4 (3 5x/4 ) 2 ⇒ 
3
–3x/4 3 15x/4 = 5 + 
3 –x 3 5x/2 ⇒ 20.3
3x = 5 + 15.3 3x/2 = 3
3x/2 = t(say)
⇒ 20t 2 –15t –5 = 0
⇒ 4t 2 –3t –1 = 0
⇒ (4t + 1) (t–1) = 0
⇒ t = – 
, 1
3 3x/2 ≠ –1/4
So 3 3x/2 = 1
∴ x = 0
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