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Q.

Let R= ac0     325      bd0:a,b,c,d0,3,5,7,11,13,17,19  Then the number of invertible matrices in R is ‘L’ . Then sum of the digits of L6

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answer is 3.

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Detailed Solution

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Case(i):-
ad = bc = 0
Now ad=0   Tota – (none of a&d is 0)
821=15  wayssimilarly  bc=015ways225ways 
Case (ii):-
ad=bc0either   a=d=b=c                    OR            adbd
                           Question Image                                           But ad=bc

                    7C1  ways                                           7C2×2×2=84ways
                   Total =91ways
 |R|=0225+91=316|R|084316=3780

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