7th Class Mathematics Algebraic Expressions Question Bank Algebra

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    DIRECTIONS: The questions in this segment consists of two statements, one labelled as ?Assertion A? and the other labelled as ?Reason R?. You are to examine these two statements carefully and decide if the Assertion A and Reason R are individually true and if so, whether the reason is a correct explanation of the assertion. Select your answers to these items using codes given below. Assertion (A): Value of \[{{(27)}^{\frac{6}{5}}}\div {{(27)}^{\frac{1}{5}}}\] is \[1\times {{3}^{3}}\] Reason (R): For any two rational numbers a and b and for any integers m and n, we have\[{{a}^{m}}\div {{a}^{n}}={{a}^{m-n}}\]

    A) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

    B) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

    C) If Assertion is correct but Reason is incorrect.

    D) If Assertion is incorrect but Reason is correct.

    Correct Answer: A

    Solution :

    Both 'A' and 'R' are correct. 'R' is the correct explanation for 'A'. \[{{(27)}^{\frac{6}{5}}}\div {{(27)}^{\frac{1}{5}}}={{(27)}^{\frac{6}{5}-\frac{1}{5}}}={{(27)}^{\frac{5}{5}}}=27\] \[=1\times 27=1\times {{3}^{3}}\]


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