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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2007

  • question_answer
        Let\[{{T}_{r}}\]be the rth term of an A P whose first term is a and common difference is d. If for some positive  integers\[m,n,m\ne n,{{T}_{m}}=\frac{1}{n}\]and \[{{T}_{n}}=\frac{1}{m},\]then\[a-d\]equals

    A)  \[0\]                                    

    B)  \[1\]

    C)  \[\frac{1}{mn}\]                             

    D)  \[\frac{1}{m}+\frac{1}{n}\]

    Correct Answer: A

    Solution :

                    Given that, \[{{T}_{m}}=\frac{1}{n}\] \[\Rightarrow \]       \[a+(m-1)d=\frac{1}{n}\]                                ...(i) and       \[{{T}_{n}}=\frac{1}{m}\] \[\Rightarrow \]               \[a+(n-1)d=\frac{1}{m}\]                           ...(ii) On solving Eqs. (i) and (ii), we get                 \[a=\frac{1}{mn}\]and \[d=\frac{1}{mn}\] So,          \[a-d=\frac{1}{mn}-\frac{1}{mn}=0\]


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