JEE PYQ: Permutation And Combination Question 11
Question 11 - 2021 (25 Feb Shift 2)
The total number of two digit numbers ‘$n$’, such that $3^n + 7^n$ is a multiple of 10, is
Show Answer
Answer: 45
Solution
$7^n = (10-3)^n = 10K + (-3)^n$. So $7^n + 3^n = 10K + (-3)^n + 3^n$. If $n$ is even, $(-3)^n + 3^n = 2 \cdot 3^n$ which is not a multiple of 10. If $n$ is odd, $(-3)^n + 3^n = 0$, so $7^n + 3^n$ is a multiple of 10. Odd two-digit numbers: $11, 13, 15, \ldots, 99$, which is 45 numbers.
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