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If x ,2y ,3z are in A.P., where the dist...

If `x ,2y ,3z` are in A.P., where the distinct numbers `x ,y ,z` are in G.P, then the common ratio of the G.P. is a.`3` b. `1/3` c. `2` d. `1/2`

Text Solution

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The correct Answer is:
35
Number of integral solutions
=coefficient of `p^(24) " in" (p+p^(2)+p^(3)+p^(4)+p^(5))`
`(p^(12)+p^(13)+..+p^(18))(p^(-1)+p^(0)+p^(1)+..+p^(11))`
=coefficient of `p^(24) " in" (p(1-p^(5)))/(1-p).(p^(12)(1-p^(7)))/(a-p).(p^(-1)(1-p^(13)))/(1-p)`
coefficient of `p^(12) " in" (1-p^(5))(1-p^(7))(1-p^(13))(1-p)^(-3)`
=coefficient of `p^(12) "in" (1-p^(5)-p^(7)+p^(12)(1-p)^(-3)`
`= .^(14)C_(12)- .^(9)C_(7)- .^(7)C_(5)+1`
=91-36-21+1=35
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