Correct Answer - Option 3 : 55
Calculation:
⇒ Let (r – 1)th, (r)th and (r + 1)th be the three consecutive terms.
Then, the given ratio is 1:7:42
Now (nCr-2 / nCr – 1) = (1/7)
⇒ (nCr-2 / nCr – 1) = (1/7) ⇒ [(r – 1)/(n − r+2)] = (1/7) ⇒ n − 8r + 9 = 0 → (1)
And,
⇒ (nCr-1 / nCr) = (7/42) ⇒ [(r)/(n – r +1)] =(1/6) ⇒ n − 7r + 1 = 0 → (2)
From (1) & (2), n = 55
Ratio of Consecutive Terms/Coefficients:
⇒ Coefficients of xr and xr + 1 are nCr – 1 and nCr respectively.
⇒ (nCr / nCr – 1) = (n – r + 1) / r