Question

The total number of integral solutions of the triplet (x,y,z) for the equation xyz = 24 is

(a) 30

(b) 60

(c) 120

(d)  None of these 

Answer 1

Correct option  (c) 120

Explanation:

24.1.1 → 2!/3! = 3 

12.2.1 → 3!/2i = 6

6.4.1 → 3! = 6

8.3.1 → 3! = 6

6.2.2 →  3!/2! = 3

4.3.2 → 3! = 6

∴ Total = 30

30 positive integral solutions Total number of integral solutions with negative integers included is 30 x 4 = 120