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JEE Mains · Maths · STD 12 - 1. relation and function

ધારો કે \(S =\{1,2,3,4\}\) તો ગણ \(\{f: S \times S \rightarrow S : f\) એ વ્યાત્પ છે અને \(f( a , b )=f( b , a ) \geqslant a ;  \forall( a , b ) \in S \times S \}\) નાં ધટકોની સંખ્યા...........છે

  1. A \(37\)
  2. B \(378\)
  3. C \(97\)
  4. D \(30\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(37\)

Step-by-step Solution

Detailed explanation

\((1,1),(1,4),(4,1),(2,4),(4,2),(3,4),(4,3)\), \((4,4)-\) all have one choice for image. \((2,1),(1,2),(2,2)\) - all have three choices for image \((3,2),(2,3),(3,1),(1,3),(3,3)-\) all have two choices for image. So the total functions…
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