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10th Class Mathematics Real Numbers Question Bank Real Number

  • question_answer
    \[{{\mathbf{X}}_{\mathbf{1}}}\mathbf{,}{{\mathbf{X}}_{\mathbf{2}}}\mathbf{,}{{\mathbf{X}}_{\mathbf{3}}}....\mathbf{,}{{\mathbf{X}}_{\mathbf{12}}}\] are integers none of which are divisible by 3. The remainder when\[\mathbf{X}_{\mathbf{1}}^{\mathbf{2}}\mathbf{,X}_{\mathbf{2}}^{\mathbf{2}}\mathbf{,X}_{\mathbf{3}}^{\mathbf{2}}\mathbf{+}....\mathbf{+X}_{\mathbf{12}}^{\mathbf{2}}\] is divided by 3 is

    A)  0   

    B)  0 or 2        

    C)  1 or 2                          

    D)  1

    Correct Answer: A

    Solution :

    (a): When a perfect square is divided by 3, remainder is 1. \[\therefore \]Each time remainder is 1 in all twelve terms. \[\therefore \]Sum of remainders = 1 + 1 +..........(12 times).                                                 = 12 Which is divisible by 3 \[\therefore \] Net remainder = zero                      


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