If n - N - 72 n -23 n -3 is always divisible byA- 35B- 25C- None of theseD- 45

The correct option is B 25Putting n=1 in 7^2n+2^3n 3.3^n 1 then, n ϵ N, 7^2n+2^3n 3.3^n 1 7^2×1+2^3×1 3.3^3 3 7^2+2^0.3^0=49+1=50 ......(i) Also,n=2 7^ ...

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Byju's Answer

Standard XII

Mathematics

Combination of Atleast One Thing from n Things When All Are Not Different

If n ∈ N , 72...

Question

If $n ϵ N, 7^{2 n} + 2^{3 n - 3}$ is always divisible by

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None of these

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Solution

The correct option is A 25
Putting n=1 in $7^{2 n} + 2^{3 n - 3} {.3}^{n - 1}$
then, $n ϵ N, 7^{2 n} + 2^{3 n - 3} {.3}^{n - 1}$
$7^{2 \times 1} + 2^{3 \times 1 - 3} {.3}^{3 - 3}$
$7^{2} + 2^{0} {.3}^{0} = 49 + 1 = 50 . . . . . . (i)$
$Also,n=2$
$7^{2 \times 2} + 2^{3 \times 2} {.3}^{2 - 1} = 2401 + 24 = 2425 (i i)$
From (i) and (ii) it is always divisible by 25.

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The correct option is A 25Putting n=1 in 72n+23n−3.3n−1 then, nϵ N,72n+23n−3.3n−1 72×1+23×1−3.33−3 72+20.30=49+1=50 ......(i) Also,n=2 72×2+23×2.32−1=2401+24=2425 (ii) From (i) and (ii) it is always divisible by 25.

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