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STD 12 - 1. relation and function — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 1. relation and function1 Mark
MCQ
Let $X$ be a set with exactly $5$ elements and $Y$ be a set with exactly $7$ elements. If $\alpha$ is the number of one-one functions from $X$ to $Y$ and $\beta$ is the number of onto functions from $Y$ to $X$, then the value of $\frac{1}{5!}(\beta-\alpha)$ is. . . . . .
  • A
    $120$
  • ✓
    $119$
  • C
    $130$
  • D
    $135$
✓

Answer

Correct option: B.
$119$
b
$\alpha={ }^7 C _5 \times 5!=21 \times 5!$

$\beta={ }^7 C _4 \times 3 \times 2 \times{ }^5 C _2 \times 3!+{ }^7 C _3 \times 5 \times 4!$

$\therefore \frac{\alpha-\beta}{5!}=119.00$

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