Question

If a, b and c are the greatest values of $^{19}C_{p}, \, ^{20}C_{q}$ and $^{21}C_{r}$ respectively, then :

• A. $\frac{a}{11} = \frac{b}{22} = \frac{c}{42}$
• B. $\frac{a}{10} = \frac{b}{11} = \frac{c}{42}$
• C. $\frac{a}{11} = \frac{b}{22} = \frac{c}{21}$
• D. $\frac{a}{10} = \frac{b}{11} = \frac{c}{21}$

Answer 1

Answer: (A)

$\frac{a}{11} = \frac{b}{22} = \frac{c}{42}$

Answer 2

$a=^{10}C_{10}, b=^{20}C_{10}$ and $c=^{21}C_{10}$
$\Rightarrow a=^{19}C_{9}, b=2\left(^{19}C_{9}\right)$ and $c=\frac{21}{11}\left(^{20}C_{10}\right)$
$\Rightarrow b=2a$ and $c=\frac{21}{11}b=\frac{42a}{11}$
$\Rightarrow a : b : c=a : 2a : \frac{42a}{11}=11 : 22 : 42$