The number of values of r satisfying the equation 39 C3 r-1- 39 Cr2= 39 Cr2-1- 39 C3 r is

Question

The number of values of r satisfying the equation 39 C3 r-1- 39 Cr2= 39 Cr2-1- 39 C3 r is (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

39 C3 r-1- 39 Cr2= 39 Cr2-1- 39 C3 r ⇒ 39 C3 r-1+ 39 C3 r= 39 Cr2-1+ 39 Cr2 ⇒ 40 C3 r= 40 Cr2 ⇒ r2=3 r or r2=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 .

Q. The number of values of r satisfying the equation 39C3r−1​−39Cr2​=39Cr2−1​−39C3r​ is

1

2

3

4

39C3r−1​−39Cr2​=39Cr2−1​−39C3r​ ⇒39C3r−1​+39C3r​=39Cr2−1​+39Cr2​ ⇒40C3r​=40Cr2​ ⇒r2=3r or r2=40−3r ⇒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 .

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