Question 76

If $$m$$ and $$n$$ are natural number such that $$2^m - 2^n = 960$$, what is the value of $$m$$?

Solution

Expression : $$2^m - 2^n = 960$$ -------------(i)

=> $$2^m>960$$

=> $$m\geq10$$

If, $$m=10$$

Substituting in equation (i), we get : $$1024-2^n=960$$

=> $$2^n=64=2^6$$

=> $$n=6$$

Since, both are natural numbers, => $$m=10$$

=> Ans - (A)

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