Groups RT

If a * b = a + b – 2, then inverse of ‘ 1’ is

• 1

• 2

• 3

• 4

• 5

If  a*b =  $\frac{ab}{3}$ , (Q+,*) is an abelian group which of the following is not true

• e = 3

•   $a^{-1}\ =\ \frac{9}{a}$  

•   $\left(\frac{2}{3}\right)^{-1}\ =\ 6$  

•  $3^{-1}\ =\ 3$   

For all numbers s and t, the operation is defined by s * t = (s – 1)(t + 1). If (-2) * x = - 12 then x =?

• 2

• 3

• 5

• 6

• 11

If the operation O is defined by the equation xOy = 2x + y, what is the value of a in the equation 2 O a = a O 3

• 0

• -1

• 1

• 1.5

• 4

Let S = {A, B, C, D} where A = {a}, B = { a, b} , C = { a, b, c} and D = ф, then the missing elements of the composition table

• C,D

• A, A

• A, B

• B, B

• C, C

If S = { A, B, C, D}, where A= {a, b}, B = {a, c} , C = {a, b, c} and D = ф , then which one of the following statement is true.

• $\cup$ is not a binary option on S

• $\cap$ is not a binary option on S

• $\cap$ is a binary operation on S

• $\cup$ is not a binary operations on S

• A & B Both

A monoid is always a;

• Group

• A commutative group

• A non abelian group

• Groupoid

If (N,*) where N is natural number a*b=a^b

• Semi Group

• Not Semi Group

• Monoid but not group

• Group

The set S = {1, -1, 0} is ;

• Closed for addition as well as multiplication

• Closed for addition but not for multiplication

• Closed for multiplication but not for addition

• Closed for division but not for addition

• -1

• 0

• 1