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Principle of Mathematical Induction — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsPrinciple of Mathematical Induction1 Mark
MCQ
Let $P(n) : “2^n< (1 \times 2 \times 3 \times … \times n)”$. Then the smallest positive integer for which $P(n)$ is true is:
  • A
    $1$
  • B
    $2$
  • C
    $3$
  • ✓
    $4$
✓

Answer

Correct option: D.
$4$
$P(1) : 2^1 < 1$
$2< 1$ is false
$P(2) : 2^2 < 1 \times 2$
$4 < 2$ is false
$P(3) : 2^3 < 1 \times 2 \times 3$
$8 < 6$ is false
$P(4) : 2^4 < 1 \times 2 \times 3 \times 4$
$16 < 24$ is true

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