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

Question

If a, b and c are the greatest values of 19Cp, 20Cq and 21Cr respectively, then : (A) (a/11) = (b/22) = (c/42) (B) (a/10) = (b/11) = (c/42) (C) (a/11) = (b/22) = (c/21) (D) (a/10) = (b/11) = (c/21)

Tardigrade Admin · Accepted Answer

a=10C10, b=20C10 and c=21C10 ⇒ a=19C9, b=2(19C9) and c=(21/11)(20C10) ⇒ b=2a and c=(21/11)b=(42a/11) ⇒ a: b: c=a: 2a: (42a/11)=11: 22: 42

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

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

$\frac{a}{10} = \frac{b}{11} = \frac{c}{42}$

$\frac{a}{11} = \frac{b}{22} = \frac{c}{21}$

$\frac{a}{10} = \frac{b}{11} = \frac{c}{21}$

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

Q. If a, b and c are the greatest values of 19Cp​,20Cq​ and 21Cr​ respectively, then :

11a​=22b​=42c​

10a​=11b​=42c​

11a​=22b​=21c​

10a​=11b​=21c​