Medium MCQ +4 / -1 PYQ · JEE Mains 2020

If a, b and c are the greatest value of 19Cp, 20Cq and 21Cr respectively, then :

  1. A ${a \over {11}} = {b \over {22}} = {c \over {21}}$
  2. B ${a \over {10}} = {b \over {22}} = {c \over {21}}$
  3. C ${a \over {10}} = {b \over {11}} = {c \over {42}}$
  4. D ${a \over {11}} = {b \over {22}} = {c \over {42}}$ Correct answer

Solution

( <sup>19</sup>C<sub>p</sub>)<sub>max</sub> = <sup>19</sup>C<sub>9</sub> or <sup>19</sup>C<sub>10</sub> = a <br><br>( <sup>20</sup>C<sub>p</sub>)<sub>max</sub> = <sup>20</sup>C<sub>10</sub> = b <br><br>( <sup>21</sup>C<sub>r</sub>)<sub>max</sub> = <sup>21</sup>C<sub>10</sub> or <sup>21</sup>C<sub>11</sub> = c <br><br>1 = $${a \over {^{19}{C_{10}}}} = {b \over {^{20}{C_{10}}}} = {c \over {^{21}{C_{10}}}}$$ <br><br>$\Rightarrow$ ${a \over {11}} = {b \over {22}} = {c \over {42}}$

About this question

Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle

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