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1. relation and function — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths1. relation and function1 Mark
MCQ
Let $A=\{2,3,6,7\}$ and $B=\{4,5,6,8\}$. Let $R$ be a relation defined on A $\times$ B by $\left(a_1, b_1\right) R\left(a_2, b_2\right)$ is and only if $a_1+a_2=b_1+b_2$. Then the number of elements in $\mathrm{R}$ is ...........
  • A
    $34$
  • ✓
    $25$
  • C
    $31$
  • D
    $20$
✓

Answer

Correct option: B.
$25$
b
$ A=\{2,3,6,7\} $

$ B=\{2,5,6,8\} $

$ \left(a_1, b_1\right) R\left(a_2, b_2\right) $

$ a_1+a_2=b_1+b_2$

$1$. $(2,4) \mathrm{R}(6,4) \quad$ 2. $(2,4) \mathrm{R}(7,5)$

$3$. $(2,5) \mathrm{R}(7,4) \quad$ 4. $(3,4) \mathrm{R}(6,5)$

$5$. $(3,5) \mathrm{R}(6,4) \quad$ 6. $(3,5) \mathrm{R}(7,5)$

$7$. $(3,6) \mathrm{R}(7,4) \quad$ 8. $(3,4) \mathrm{R}(7,6)$ $\times 2$

$9$. $(6,5) \mathrm{R}(7,8) \quad$ 10. $(6,8) \mathrm{R}(7,5)$

$11$. $(7,8) \mathrm{R}(7,6) \quad$ 12. $(6,8) \mathrm{R}(6,4)$

$13$. $(6,6) \mathrm{R}(6,6)$

Total $24+1=25$

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