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Class 12 · Mathematics · Hard

If (a*b=a+b-ab), then (1-(a*b)) is equal to what?

Class 12 · Mathematics · Hard

On (\mathbb{R}), (a*b=a+b+ab). What is the absorbing element of this operation?

Class 12 · Mathematics · Hard

On (A={0,1}), (a*b=a+b-ab). Which element is absorbing?

Class 12 · Mathematics · Hard

On (A={0,1}), (a*b=ab). Which is the identity element?

Class 12 · Mathematics · Hard

On (A={0,1}), (a*b=|a-b|). What is its identity element?

Class 12 · Mathematics · Hard

On (\mathbb{R}), (a*b=a+b-2). What is the inverse of (-3)?

Class 12 · Mathematics · Hard

On (\mathbb{R}), (a*b=a+b-2). What will be the identity element?

Class 12 · Mathematics · Hard

On (\mathbb{Z}), (a*b=a+b+1). What is the inverse of (5)?

Class 12 · Mathematics · Hard

On (\mathbb{R}^+), (a*b=\frac{a}{b}). What is the correct statement?

Class 12 · Mathematics · Hard

On (\mathbb{R}^+), (a*b=ab). What is its identity element?

Class 12 · Mathematics · Hard

On (\mathbb{R}), (a*b=a+b+c). What will be the inverse of an element (p)?

Class 12 · Mathematics · Hard

If (a*b=a+b+kab) on (\mathbb{R}), for which values of (k) is the operation associative?

Class 12 · Mathematics · Hard

If (a*b=ka+b) on (\mathbb{R}) is commutative, what is the value of (k)?

Class 12 · Mathematics · Hard

On (\mathbb{R}), (a*b=a^2+b^2). Choose the correct property.

Class 12 · Mathematics · Hard

On (\mathbb{Z}), (a*b=\frac{a+b}{2}) is defined. Why is it not a binary operation?

Class 12 · Mathematics · Hard

On (\mathbb{Z}), (a*b=a-b). Which statement is correct?

Class 12 · Mathematics · Hard

On (A={1,2,3,6}), (a*b=\operatorname{lcm}(a,b)). What will be the identity element?

Class 12 · Mathematics · Hard

On (A={1,2,3,6}), (a*b=\gcd(a,b)). What is the identity element of this operation?

Class 12 · Mathematics · Hard

On (A={2,4,6,8}), (a*b=\min(a,b)). Which is the identity element?

Class 12 · Mathematics · Hard

On (A={2,4,6,8}), (a*b=\max(a,b)). What is its identity element?