Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

2

Answer 2

$^{39}C_{3r-1} - ^{39}C_{r^{2}} = ^{39}C_{r^{2}-1} - ^{39}C_{3r}$
$\Rightarrow ^{39} C_{3r-1} + ^{39}C_{3r} = ^{39}C_{r^{2}-1} + ^{39}C_{r^{2}}$
$\Rightarrow ^{40}C_{3r} = ^{40}C_{r^{2}}$
$\Rightarrow r^{2} = 3r$ or $r^{2} = 40 - 3r$
$\Rightarrow r=0 ,3$ 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 $2$.