Q. If $^{43} C_{r - 6} =^{43} C_{3 r + 1},$ then the value of r is:

1777 230 KEAMKEAM 2002 Report Error

A

12

B

8

C

6

D

10

E

14

Solution:

$∵$ $^{43} C_{r - 1} +^{n} C_{r} =^{n + 1} C_{r}$ $∴$ $r - 6 + 3 r + 1 = 43$ $\Rightarrow$ $4 r = 48$ $\Rightarrow$ $r = 12$