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Binomial Theorem — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsBinomial Theorem1 Mark
MCQ
If $n$ is the positive integer, then $2^{3n}- 7n - 1$ is divisible by.
  • A
    $7$
  • B
    $10$
  • ✓
    $49$
  • D
    $81$
✓

Answer

Correct option: C.
$49$
Given: $2^{3 n}-7 n-1$.
It can also be written as $8^n-7 n-1$
Let $8^n-7 n-1=0$
So, $8^n=7 n+1$
$8^n=(1+7)^n$
By applying binomial theorem, we get
$8 n-1-7 n=49 \text { (or) } 2^{3 n}-7 n-1=49$
Hence, $2^{3 n}-7 n-1$ is divisible by $49.$

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