MA8551 / ANT - MODEL II

Find all the subgroup of

 $\left(Z_{12},+\right)$  

•  $\left\{0,\ 6\right\},\left\{0,\ 3,\ 6,\ 9\right\},\ \left\{0,\ 4,\ 8\right\},\left\{0,\ 2,\ 4,\ 6,\ 8,\ 10\right\}$  

•  $\left\{0,\ 3,\ 6,\ 9\right\},\ \left\{0,\ 4,\ 8\right\},\left\{0,\ 2,\ 4,\ 6,\ 8,\ 10\right\}$  

•  $\left\{0,\ 6\right\},\left\{0,\ 4,\ 8\right\},\left\{0,\ 2,\ 4,\ 6,\ 8,\ 10\right\}$  

 $When\ the\ function\ f\ is\$  

 $called\ an\ isomorphism$  

•  $A\ \hom ogeneous\ function\ is\ statifies\$  $both\ one-to-one\ and\ onto$   

•  $function\ is\ statifies\ both\ one-to-one\ and\ onto$  

•  $None\ of\ these$  

 $Deter\min e\ U_{14},\ the\ group\ of\ units\ of\ the\ ring\ \left(Z_n,\ +,\ \circ\right)$  

•  $\left\{1,3,5,7,9,11,13\right\}$  

•  $\left\{1,3,5,9,11,13\right\}$  

•  $\left\{1,3,7,9,11,13\right\}$  

 $When\ the\ ring\ R\ is\ called\ commutative\ ring$  

•  $If\ ab=ba\ for\ all\ a,b\in R$  

•  $If\ ab\ne ba\ for\ all\ a,b\in R$  

•  $If\ ab=ba\ for\ all\ a,b\notin R$  

 $Find\ the\ value\ of\ additive$  $\ identity\ from\ the\ given\ equation$   $x+y=x+y-7,\ x\circ y=x+y-3xy$  

•  $Z=0$  

•  $Z=-1$  

•  $Z=7$  

 $Find\ \left[100\right]^{-1}\ in\ the\ ring\ Z_{1009}$  

• 110

• 101

• 111

 $FInd\ the\ multiplicative\ inverse\ of\ 4\ in\ Z_{11}$  

• 4

• 1

• 3

 $What\ is\ the\ last\ digit\ in\ 3^{55}$  

• 1

• 5

• 7

 $Howmany\ units\ are\ there\ in\ the\ ring\ Z_8?$  

• 7

• 4

• 2

 $Which\ one\ is\ the\ correct\ form\ of$   $Division\ a\lg orithm$  

•  $f\left(x\right)=q\left(x\right)g\left(x\right)+r\left(x\right)$  

•  $f\left(x\right)=q\left(x\right)g\left(x\right)-r\left(x\right)$  

•  $f\left(x\right)=q\left(x\right)+r\left(x\right)$