11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer If \[a\] be the arithmetic mean of \[b\] and \[c\] and \[{{G}_{1}},\ {{G}_{2}}\] be the two geometric means between them, then \[G_{1}^{3}+G_{2}^{3}=\]

    A) \[{{G}_{1}}{{G}_{2}}a\]

    B) \[2{{G}_{1}}{{G}_{2}}a\]

    C) \[3{{G}_{1}}{{G}_{2}}a\]

    D) None of these

    Correct Answer: B

    Solution :

    Trick: Put \[b=1\] and \[c=8\] so that \[a=4.5\] and \[{{G}_{1}}=2,\ {{G}_{2}}=4\]. Now \[G_{1}^{3}+G_{2}^{3}=72\]. Also option (b) gives this value\[i.e.\]\[2\times 2\times 4\times \frac{9}{2}=72\].

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