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 the set of real numbers, the operation (a*b=a+b+ab) is defined. If (a\neq -1), what will be the inverse of (2)?On the set of integers, (a*b=a+b-1) is defined. What is the inverse of (7) with respect to this operation?On positive real numbers, (a*b=\sqrt{ab}) is defined. Choose the correct statement about associativity of this operation.On the set (A={0,1,2,3}), (a*b) is defined as the remainder obtained when (a+b) is divided by (4). What is the inverse of (3)?On natural numbers, (a*b=a^b) is defined. Which statement about commutativity of this operation is correct?On real numbers, (a*b=a+b+kab) is defined. If the product of (2) and (3) is (11), what is the value of (k)?On real numbers, (a*b=a+b-2ab) is defined. What is the identity element of this operation?On non-zero real numbers, (a*b=\frac{ab}{2}) is defined. What is the identity element for this operation?On non-zero real numbers, (a*b=\frac{ab}{2}) is defined. What will be the inverse of (5)?On real numbers, (a*b=a+b+ab) is defined. Which element does not have an inverse?On the set (A={1,2,3,4,5}), (a*b=\max(a,b)) is defined. What is the identity element of this operation?On the set (A={1,2,3,4,5}), (a*b=\min(a,b)) is defined. What will be the identity element of this operation?On the set (A={1,2,3}), (a*b=a) is defined. Which property is satisfied by this operation?On real numbers, (a*b=a+b-ab) is defined. What is the inverse of (3) with respect to this operation?On real numbers, (a*b=a+b-3) is defined. Which statement is correct?On integers, (a*b=a+b+2ab) is defined. Is this a binary operation on integers?On natural numbers, (a*b=a-b) is defined. Why is it not a binary operation?On real numbers, (a*b=a^2+b^2) is defined. Choose the correct conclusion about this operation.On real numbers, (a*b=a+b+1) is defined. What will be the inverse of (a) in this operation?On positive real numbers, (a*b=ab) is defined. Choose the correct option about (a*b=b*a) and ((a*b)*c=a*(b*c)).