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Let x(1) lt x(2) lt x(3) lt x(4) lt x(5)...

Let `x_(1) lt x_(2) lt x_(3) lt x_(4) lt x_(5)` and `y_(1) lt y_(2) lt y_(3) lt y_(4) lt y_(5)` are in AP such that `underset(I = 1)overset(5)(sum) x_(i) = underset(I = 1)overset(5)(sum) y_(i) = 25` and `underset(I =1)overset(5)(II) x_(i) = underset(I = 1)overset(5)(II) y_(i) = 0` then `|y_(5) - x_(5)|`

A. `5//2`
B. 5
C. 10
D. 15

A

44318

B

5

C

10

D

15

Text Solution

Verified by Experts

The correct Answer is:
B
Let 5 nos in AP are .
`a - 2s , a - d,a,+d , a+2d `
ATQ `5a = 25 rArr" "a = 5`
And `(a^(2) - 4d^(2))(a^(2) - d^(2)) a = 0 " " rArr d = (5)/(2) or d = 3`
So nos would be .
`0,(5)/(2) , 5, (15)/(2), 10 or -5,0,5,10,15`
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