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6th Class Mathematics Algebra Question Bank Algebra

  • question_answer
    Read the following statements and choose the correct option. (i) If \[\frac{P}{Q}=7\] then the value of \[\frac{P+Q}{P-Q}\] is (ii) If \[P=\frac{{{x}^{2}}-36}{{{x}^{2}}-49}\] and \[Q-\frac{x-6}{x+7}\] then the value of \[\frac{P}{Q}\] is \[\frac{x-6}{x-7}\]

    A)  (i) and (ii) are false.

    B)  (i) and (ii) are true.

    C)  (i) is true while (ii) is false.

    D)  (i) is false while (ii) is true.

    Correct Answer: D

    Solution :

     (i) \[\frac{P+Q}{P-Q}\,=\frac{\frac{P}{Q}+1}{\frac{P}{Q}-1}\,=\frac{7+1}{7-1}\,=\frac{8}{6}=\frac{4}{3}\] (ii) \[P=\frac{(x-6)\,(x+6)}{(x-7)\,(x+7)},\,\,Q=\frac{x+6}{x-7}\] \[\frac{P}{Q}\,=\frac{(x-6)\,(x+6)}{(x-7)\,(x+7)}\times \frac{(x+7)}{(x+6)}\,=\frac{x-6}{x-7}\]


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