Question

Set of values of r for which, ${}^{18}{C}_{r-2}+{2.}^{18}{C}_{r-1}{+}^{18}{C}_r{\ge }^{20}{C}_{13}$ contains

• A. 4 elements
• B. 5 elements
• C. 7 elements
• D. 10 elements

Answer 1

Answer: (C)

7 elements

$(\frac{18}{r-2})+(\frac{18}{r-1})+(\frac{18}{r-1})+(\frac{18}{r})\ge (\frac{20}{7})$

$\Rightarrow (\frac{19}{r-1})+(\frac{19}{r})\ge (\frac{20}{7})$

$\Rightarrow (\frac{20}{r})\ge (\frac{20}{7})$

$\Rightarrow r=7,8,9,10,11,12,13$
$\Rightarrow$r has $7$ elements
Correct option is C