The number of values of satisfying the equation ^ 39 C_ 3 r-1 - ^ 39 C_ ^ 2 = ^ 39 C_ ^ 2 -1 - ^ 39 C_ 3 r is

Correct answer: B. 2 ^ 39 C_ 3 r-1 - ^ 39 C_ ^ 2 = ^ 39 C_ ^ 2 -1 - ^ 39 C_ 3 r ^ 39 C_ 3 r-1 + ^ 39 C_ 3 r = ^ 39 C_ ^ 2 -1 + ^ 39 C_ ^ 2 ^ 40 C_ 3 r = ^ 40 C_ ^ 2 ^ 2 =3 r or ^ 2 =40-3 r r=0,3 or -8,5 3 and 5 are the values as the given equation is not defined by r=0 and r=-8 . Hence, the number of values of r is 2.

BITSAT 2016

Exam: BITSAT
Year: 2016
Subject: Mathematics
Chapter: Binomial Theorem

BITSAT 2016 · Mathematics · Binomial Theorem

The number of values of satisfying the equation ^ 39 C_ 3 r-1 - ^...

The number of values of satisfying the equation

{ }^{39} \mathrm{C}_{3 \mathrm{r}-1}-{ }^{39} \mathrm{C}_{\mathrmr^{2}}={ }^{39} \mathrm{C}_{\mathrmr^{2}-1}-{ }^{39} \mathrm{C}_{3 \mathrm{r}}

Options

Correct answer

B. 2

Step-by-step solution

{ }^{39} \mathrm{C}_{3 \mathrm{r}-1}-{ }^{39} \mathrm{C}_{\mathrmr^{2}}={ }^{39} \mathrm{C}_{\mathrmr^{2}-1}-{ }^{39} \mathrm{C}_{3 \mathrm{r}}\Rightarrow{ }^{39} \mathrm{C}_{3 \mathrm{r}-1}+{ }^{39} \mathrm{C}_{3 \mathrm{r}}={ }^{39} \mathrm{C}_{\mathrmr^{2}-1}+{ }^{39} \mathrm{C}_{\mathrmr^{2}}\Rightarrow{ }^{40} \mathrm{C}_{3 \mathrm{r}}={ }^{40} \mathrm{C}_{\mathrmr^{2}}\Rightarrow \mathrmr^{2}=3 \mathrm{r}

\mathrmr^{2}=40-3 \mathrm{r}\Rightarrow \mathrm{r}=0,3

or -8,5 3 and 5 are the values as the given equation is not defined by

r=0

and

r=-8

. Hence, the number of values of

\mathrm{r}

is 2.

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