1.Relation and Function
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माना $\mathrm{A}=\{1,2,3,4\}$ है तथा $\mathrm{A} \times \mathrm{A}$ पर एक संबंध $\mathrm{R}$ निम्न प्रकार परिभाषित है

A

$6$

B

$5$

C

$4$

D

$3$

(JEE MAIN-2023)

Solution

$A =\{1,2,3,4\}$

$R =\{( a , b ),( c , d )\}$

$2 a +3 b =4 c +5 d =\alpha \text { let }$

$2 a =\{2,4,6,8\} \quad 4 c =\{4,8,12,16\}$

$3 b =\{3,6,9,12\} \quad 5 d =\{5,10,15,20\}$

$2 a +3 b =\left\{\begin{array}{l}5,8,11,14 \\ 7,10,13,16 \\ 9,12,15,18 \\ 11,14,17,20\end{array}\right\} \quad 4 c +5 d \left\{\begin{array}{l}9,14,19,24 \\ 13,18 \ldots . \\ 17,22 \ldots \\ 21,26 \ldots\end{array}\right\}$

Possible value of $\alpha=9,13,14,14,17,18$

Pairs of $\{( a , b ),( c , d )\}=6$

Standard 12
Mathematics

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