JEE PYQ: Permutation And Combination Question 26
Question 26 - 2020 (08 Jan Shift 1)
If $a$, $b$ and $c$ are the greatest values of ${}^{19}C_p$, ${}^{20}C_q$ and ${}^{21}C_r$ respectively, then:
(1) $\frac{a}{11} = \frac{b}{22} = \frac{c}{21}$
(2) $\frac{a}{10} = \frac{b}{11} = \frac{c}{21}$
(3) $\frac{a}{11} = \frac{b}{22} = \frac{c}{42}$
(4) $\frac{a}{10} = \frac{b}{11} = \frac{c}{42}$
Show Answer
Answer: (3)
Solution
$a = {}^{19}C_9 = {}^{19}C_{10}$, $b = {}^{20}C_{10}$, $c = {}^{21}C_{10} = {}^{21}C_{11}$. $\frac{b}{a} = \frac{{}^{20}C_{10}}{{}^{19}C_9} = \frac{20}{10} = 2$. $\frac{c}{b} = \frac{{}^{21}C_{10}}{{}^{20}C_{10}} = \frac{21}{11}$. So $\frac{a}{1} = \frac{b}{2} = \frac{c}{42/11}$, i.e., $\frac{a}{11} = \frac{b}{22} = \frac{c}{42}$.
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