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={1,2,3,4,6,12}), (a*b) is the greatest common divisor of (a) and (b). What is the identity element?On real numbers, (a*b=a^2+b) is defined. Is this operation commutative?On integers, (a*b=a+b+ab) is defined. Is this operation closed on integers?On natural numbers, (a*b=\frac{a+b}{2}) is defined. Is this a binary operation?On (A={0,1}), (a*b=a+b-ab) is defined. What is the value of (1*0)?On real numbers, (a*b=3a+3b-2ab) is defined. Is this operation commutative?On real numbers, (a*b=a+b+2ab) is defined. What is the identity element?On real numbers, (a*b=a+b+2ab) is defined. What is the inverse of (1)?On (A={0,1,2,3,4}), (a*b) is the remainder obtained when (a+b) is divided by (5). What is the value of (2*4)?On (A={0,1,2,3,4}), (a*b) is the remainder obtained when (ab) is divided by (5). What is the identity element?On (A={1,2,3,4}), (a*b=|a-b|) is defined. Is this a binary operation?On (A={0,1,2,3}), (a*b=|a-b|) is defined. Is this operation commutative?On integers, (a*b=a+b-1) is defined. What is the identity element?On integers, (a*b=a+b-1) is defined. What is the inverse of (4)?On real numbers, (a*b=a+b+5) is defined. Which type of operation is it?On real numbers, (a*b=a+b+5) is defined. What is the identity element?On positive real numbers, (a*b=\sqrt{ab}) is defined. Is this operation commutative?On positive real numbers, (a*b=\sqrt{ab}) is defined. Is this operation associative?On real numbers, (a*b=a+b-2ab) is defined. What is the identity element?On (A={0,1,2}), (a*b) is the remainder obtained when (ab) is divided by (3). What is the inverse of (2)?