Question

The number of ordered pairs (r, k) for which 6·³⁵C_r = (k² – 3)·³⁶C_r + 1, where k is an integer, is :

(1) 3 

(2) 2 

(3) 4 

(4) 6

Comments

why not r=77

---

∵ {35}C_r term is present.
therefore, r must be less than or equal to 35.
Then r never be 77.

Answer 1

Answer is (3)

Possible values of r for integral values of k, are

r = 5, 35

number of ordered pairs are 4

(5, 2), (5, –2), (35, 3), (35, –3)