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Q.

If the number of elements in the G and A are 3 and 4 respectively , then match the items of List I with one of List II

LIST-ILIST-II           
A) The number of non bijetive  function from G× G to GI) 24
B) The number of bijective functions from A to A II) 0
C) The number of functions from G to G × A III) 1728
D) The numer of surjective function from A to A× A IV) 12
 V)19683

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a

A    B     C    D

V     I     III     II

b

A      B     C     D

V     III     IV     II

c

A     B      C    D

III     IV    V     II

d

A    B     C    D

I     II     III     IV

answer is A.

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Detailed Solution

n(G)=3,     n(A)=4,     n(GxG)=3x3=9,    n(GxA)=12,     n(AxA)=4x4=16

(A)  No of non surjective functions from G x G to G = 39=19,683

(B)  ME no of bijective functions from A to A = (n(A))!=4!=24

(C)  No of functions from G to G x A = n(6xn) n(G)=123=1728

(D)  No of surjective functions from A to AxA=0 

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