The last digit in 7^ 300 is - Vidyadip

Question

The last digit in ${7^{300}}$ is

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Answer

c
(c) We have ${7^2} = 49 = 50 - 1$

Now, ${7^{300}} = {({7^2})^{150}} = {(50 - 1)^{150}}$

= $^{150}{C_0}{(50)^{150}}{( - 1)^0} + {\,^{150}}{C_1}{(50)^{149}}{( - 1)^1} + ...... + {\,^{150}}{C_{150}}{(50)^0}{( - 1)^{150}}$

Thus the last digits of ${7^{300}}$ are $^{150}{C_{150}}.1.1$ $i.e., 1$.

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