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Question

The reminder of $$\displaystyle 2005^{2002}+2002^{2005}$$ when divided by $$200$$ is $$........$$


A
0
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B
1
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C
2
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D
3
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Solution

The correct option is A $$0$$
Suppose $$ (2005)^{2002}+(2002)^{2005}$$
When we divide $$2005$$ by $$200$$ we get remainder as $$ \dfrac {5}{200}$$
Now, Remainder $$= \dfrac {5}{200} < 1$$
and $$($$Remainder$$)^{0}$$ tends to $$0(\because $$ Remainder is small $$)$$
Similarly, when we divide $$2002$$ by $$200$$ we get
remainder as $$ \dfrac {2}{200}$$
Again $$($$Remainder$$)^{0}$$ tends to $$0$$.
$$\therefore $$ Required answer $$=0$$

Mathematics

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