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IPMAT Indore 2023 - QA (SA) Q2 Explanation
December 6, 2024
Explanation:
(39)
Let the coefficients of three consecutive terms in the expansion of (x + y)^π be ππΆπ, ππΆπ+1 and ππΆπ+2.
= n!/(n-r)! x r!/(n - r - 1)! (r + 1)! = 1 9
= (r + 1)/(n - r) = 1/9
= 9r + 9 = n - r
= 10r + 9 = n.......................(1)
Also nCr+1/nCr+2 = 9/63 = 1/7
= (n!)/((n - r - 1)! (r + 1)!)/n!/(n-r-2)! (r+2)! = 1/7
= (r + 2)/(n - r - 1) = 1/7
= 7r + 14 = n - r - 1
= 8r + 15 = n ..................(2)
From equations (1) and (2), we get
10r + 9 = 8r + 15
2r = 6
r = 3
Put r 3 in equation (1), we get n = 10(3) + 9 = 39 Ans