Let ${a_1},{a_2},{a_3}, \ldots $ be terms of $A.P.$  If $\frac{{{a_1} + {a_2} + \ldots + {a_p}}}{{{a_1} + {a_2} + \ldots + {a_q}}} = \frac{{{p^2}}}{{{q^2}}},p \ne q$ then $\frac{{{a_6}}}{{{a_{21}}}}$ equals

  • [AIEEE 2006]
  • A

    $\frac{{41}}{{11}}$

  • B

    $\frac{7}{2}$

  • C

    $\frac{2}{7}$

  • D

    $\frac{{11}}{{41}}$

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Find the sum of all numbers between $200$ and $400$ which are divisible by $7.$

For any three positive real numbers $a,b,c$ ; $9\left( {25{a^2} + {b^2}} \right) + 25\left( {{c^2} - 3ac} \right) = 15b\left( {3a + c} \right)$ then

  • [JEE MAIN 2017]

Let $S_n$ and  $s_n$ deontes the sum of first $n$ terms of two different $A.P$. for which $\frac{{{s_n}}}{{{S_n}}} = \frac{{3n - 13}}{{7n + 13}}$ then  $\frac{{{s_n}}}{{{S_{2n}}}}$