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 (A=\mathbb{R}\setminus{-1}), (a*b=a+b+ab) is defined. Which statement about this operation is correct?On real numbers, (a*b=a+b+ab) is defined. What is the simplified form of (a*(b*c))?On real numbers, (a*b=a+b+ab) is defined. Which is the most suitable reason for this operation being associative?On (A={0,1,2,3,4}), (a*b) is the remainder when (ab) is divided by (5). What is the inverse of (2)?On (A={0,1,2,3,4}), (a*b) is the remainder when (ab) is divided by (5). Which element does not have an inverse?On positive real numbers, (a*b=\frac{a}{b}) is defined. Which property is not satisfied by this operation?On real numbers, (a*b=a+b+ab) is defined. Why is (a*b=b*a) true?On real numbers, (a*b=a+b+ab) is defined. If (a*b=a), what is the value of (b), where (a\neq -1)?On real numbers, (a*b=a+b+ab) is defined. If ((x*1)=5), what is the value of (x)?On the set (A=\mathbb{R}\setminus{-1}), the operation (a*b=a+b+ab) is defined. If (x) is the inverse of (5), what is the value of (x*2)?On the set (\mathbb{R}\setminus{-1}), the operation (a*b=a+b+ab) is defined. What is the identity element for this operation?On (\mathbb{R}\setminus{-1}), for (a*b=a+b+ab), what is the inverse of (a)?On positive real numbers, (a*b=a^{\log b}), where (\log) has base (10). When is this operation commutative?On (\mathbb{R}), (a*b=a+b+kab). Which value of (k) makes this operation associative?On (\mathbb{Z}), (a*b=a+b-2). What is the inverse of (7) under this operation?On (\mathbb{N}), (a*b=\max(a,b)). Which statement about this operation is correct?On (\mathbb{N}), (a*b=\min(a,b)). What is the correct conclusion about the identity element?On ({1,2,3,4,5}), (a*b=\min(a,b)). What is the identity element of this operation?On (\mathbb{R}), (a*b=a^2+b^2). Which property does this operation satisfy?On (\mathbb{Q}\setminus{0}), (a*b=\frac{ab}{2}). What is the identity element of this operation?