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Grade: 12th pass

                        

The number of ordered pairs (m,n),m,n€{1,2,.......50} such that 6 n + 9 m is a multiple of 5.

2 years ago

Answers : (2)

Tony
108 Points
							
I have done it with modulus(remainder) function. Modulus of 6^m will be 1 ^m anr that of 4^n is (-1)^n.
The key is to find a relation between m and n. For this question, if you take modulus 5, you get 1m +(-1)n = 1+(-1)n. The first thing to notice is that this is independent of m. Therefore, every value of m is possible. Thus, there are 50 possible m values. To make this equal to 0, you want n to be odd. Thus, there are 25 possible n values. Therefore, there are (50)(25)=1250 number of possible pairs.
2 years ago
Tony
108 Points
							
Sry bro , by mistake in the above answer I have took the question as 6^m but it is 6^n.
Sry for that.Method is still same but bro just swap m with n wherever written in above answer!
2 years ago
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