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UPSC CDS 1 2022 Math Paper

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Question : 43 of 100

Marks: +1, -0

27^{5}+3^{13}

is divisible by

8
10
12
21

Solution: 👈: Video Solution

Given:

Number is

27^{5}+3^{13}

Calculation:

We have

27^{5}+3^{13}

\Rightarrow (3^{3})^{5}+3^{13}

\Rightarrow 3^{15}+3^{13}

Taking 313 common from bothe side, we get

\Rightarrow 3^{13}(3^{2}+1)

\Rightarrow 3^{13} \times 10

So, we can write

3^{15}+3^{13}=3^{13} \times 10

It means the number is divisible by 10 or

(10 \times 3^{n})

where

1 \leq n \leq 13

According to the option

\therefore

The correct answer is 10 .

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