If a , b and c are the greatest values of C p 19 , C q 20 and C r 21 respectively, then:

We know that, n C r is maximum at middle term. a = 19 C p = 19 C 10 = 19 C 9 b = 20 C q = 20 C 10 c = 21 C 6 = 21 C 10 = 21 C 11 Hence, a 19 C 9 = a 20 10 . 19 C 9 = a 21 11 . 20 10 . 19 C 9 ⇒ a 1 = b 2 = c 42 11 ⇒ a 11 = b 22 = c 42

Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremProperties of Binomial coefficientsMedium2 minPYQ_2020

MathematicsMediumsingle choice

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

Options:

Answer:

Solution:

We know that, $^{n} C_{r}$ is maximum at middle term.

$a =^{19} C_{p} =^{19} C_{10} =^{19} C_{9}$

$b =^{20} C_{q} =^{20} C_{10}$

$c =^{21} C_{6} =^{21} C_{10} =^{21} C_{11}$

Hence,

$\frac{a}{^{19} C_{9}} = \frac{a}{\frac{20}{10} .^{19} C_{9}} = \frac{a}{\frac{21}{11} . \frac{20}{10} .^{19} C_{9}}$

$\Rightarrow \frac{a}{1} = \frac{b}{2} = \frac{c}{(\frac{42}{11})}$

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

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Properties of Binomial coefficients

⏱ 2mℹ️ Source: PYQ_2020

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