Question 133
If $$2^{36} - 1 = 68 a$$ 19476735, when all the digits are correct except a, the correct value of a is
Solution
Expression : $$(2)^{36}-1$$
= $$(2^3)^{12}-1=(8)^{12}-1$$
Now, to check whether the number is divisible by 9, we have : $$(-1)^{12}-1=0$$
Thus, $$(2)^{36}-1$$ is divisible by 9, hence sum of its digits is also divisible by 9.
=> $$6+8+a+1+9+4+7+6+7+3+5=56+a$$
Thus, $$56+a=63$$
=> $$a=7$$
=> Ans - (C)
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