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Question

The coefficients of three consecutive terms of (1+x)n+5 are in the ratio 5 : 10 : 14. Then, n is equal to

A
3
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B
4
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C
5
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D
6
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Solution

The correct option is D 6
Let the three consecutive terms in (1+x)n+5 be tr,tr+1,tr+2 having coefficients
n+5Cr1, n+5Cr, n+5Cr+1
Given,
n+5Cr1, n+5Cr, n+5Cr+1=5:10:14
n+5Crn+5Cr1=105 and n+5Cr+1n+5Cr=1410 n+5(r1)r=2 and nr+5r+1=75
n – r + 6 = 2r and 5n – 5r + 25 = 7r + 7
n + 6 = 3r and 5n + 18 = 12r
n+63=5n+1812
4n + 24 = 5n + 18
n = 6

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