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Urmi Thakkar
Asked: 2022-11-11T07:21:57+05:30 In:

Consider the ten numbers `a r ,a r^2, a r^3, ,a r^(10)dot`If their sum is 18 and the sum of their reciprocals is 6, then theproduct of these ten numbers is`81`b. `243`c. `343`d. 324
A. 81
B. 243
C. 343
D. 324

Consider the ten numbers `a r ,a r^2, a r^3, ,a r^(10)dot`If their sum is 18 and the sum of their reciprocals is 6, then theproduct of these ten numbers is`81`b. `243`c. `343`d. 324
A. 81
B. 243
C. 343
D. 324
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  1. Correct Answer – B
    Given `(ar(r^(10)-1))/(r-1)=18` (1)
    Also `(1/(ar)(1-1/r^(10)))/(1-1/r)=6`
    or `1/(ar^(11))cdot((r^(10)-1)r)/(r-1)=6`
    or `1/(a^(2)r^(11))cdot(ar(r^(10)-1))/(r-1)=6`
    From (1) and (2),
    `1/(a^(2)r^(11))xx18=6`
    or `a^(2)r^(11)=3`
    Now P`=a^(10)^(55)=(a^(2)r^(11))^(5)=3^(5)=243`

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