Mathematics
Binary operations
द्विआधारी संक्रियाएँ
In Class 12 Mathematics, this topic introduces binary operations as functions that combine two elements of a set to produce another element of the same set. Within the chapter Relations and Functions, students learn to identify whether an operation is well-defined and closed, represent it through tables or algebraic rules, and examine key properties such as commutativity, associativity, identity elements, and inverses. Examples involving familiar number systems help connect these ideas with broader function concepts.
Practice questions
On (\mathbb{R}), (a*b=a+b-2). What will be the identity element?On (\mathbb{R}), (a*b=a+b-2). What is the inverse of (-3)?On (A={0,1}), (a*b=|a-b|). What is its identity element?On (A={0,1}), (a*b=ab). Which is the identity element?On (A={0,1}), (a*b=a+b-ab). Which element is absorbing?On (\mathbb{R}), (a*b=a+b+ab). What is the absorbing element of this operation?If (a*b=a+b-ab), then (1-(a*b)) is equal to what?On (A=\mathbb{R}-{1}), (a*b=a+b-ab). Why is it closed in (A)?On (\mathbb{R}), (a*b=a+b-ab). Which statement about this operation is correct?On (\mathbb{R}-{0}), (a*b=\frac{a}{b}). What is the correct conclusion about associativity?On (\mathbb{R}), (a*b=\sqrt{a^2+b^2}). What is its identity element?On (A={0,1,2,3}), (a*b) is the remainder obtained when (a+b) is divided by (4). What is the identity element?On (A={0,1,2,3,4,5,6}), (a*b) is the remainder when (a+b) is divided by (7). What is the inverse of (3)?On (A={1,2,3,4}), (a*b) is the remainder when (ab) is divided by (5). What is the inverse of (2)?On (A=\mathbb{R}-{1}), (a*b=a+b-ab). What is the value of ((2*3)*4)?On (\mathbb{R}), (a*b=\frac{a+b}{2}). What is the correct statement about its identity element?On (\mathbb{R}), (a*b=a+b+1). If (x*3=7), what is the value of (x)?On (\mathbb{R}), (a*b=2a+3b). If (x*2=16), what is the value of (x)?On (\mathbb{R}), the operation (a*b=a+b-2ab) is defined. What is the inverse of (3)?On (\mathbb{R}), the operation (a*b=a+b-2ab) is defined. What is the absorbing element of this operation?