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PRINCIPLE OF MATHEMATICAL INDUCTION — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPRINCIPLE OF MATHEMATICAL INDUCTION1 Mark
MCQ
For every positive integer $n, 7^n-3^n$ is divisible by:
  • A
    3
  • ✓
    4
  • C
    7
  • D
    5
✓

Answer

Correct option: B.
4
  1. 4
Solution:
Let $P(n)=7^n-3^n$
Substituting $\mathrm{n}=1,2,3, \ldots$
$P(1)=7^1-3^1=7-3=4$
$P(2)=7^2-3^2=49-9=40$
$P(3)=7^{3-} 3^3=343-27=316$
Thus, for every positive integer $n, 7^n-3^n$ is divisible by 4 .

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