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Binary Operations Maths - Binary Operations

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 134 questions in this chapter.

Question types

Binary Operations question types

134 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

134
Questions
4
Question groups
5
Question types
Sample Questions

Binary Operations questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 2M.C.Q (1 Marks)1 Mark
On the power set P of a non-empty set A, we define an operation $\triangle \text{ by }\text{X}\triangle\text{Y}=(\text{X}\cap\text{Y})∪(\text{X}∩\text{Y})\text{X}\triangle\text{Y}=\text{X}∩\text{Y}∪\text{X}∩\text{Y}$
Then which are of the following statements is true about $\triangle$
  1. Commutative and associative without an identity.
  2. Commutative but not associative with an identity.
  3. Associative but not commutative without an identity.
  4. Associative and commutative with an identity.
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Q 3M.C.Q (1 Marks)1 Mark
Let * be a binary operation defined on Q+ by the rule $\text{a}*\text{b}=\frac{\text{ab}}3\forall\text{ a, b}\in \text{Q}^+$. The inverse of 4 * 6 is:

  1. $\frac{9}{8}$

  2. $\frac{2}3$

  3. $\frac{3}2$

  4. None of these.

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Q 4M.C.Q (1 Marks)1 Mark
Let * be a binary operation defined on set Q − {1} by the rule a * b = a + b − ab. Then, the identify element for * is:
  1. $1$
  2. $\frac{\text{a}-1}{\text{a}}$
  3. $\frac{\text{a}}{\text{a}-1}$
  4. $0$
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Q 62 Marks2 Marks
Is * defined on the set {1, 2, 3, 4, 5} by a * b = LCM of a and b a binary operation? Justify your answer.
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Q 72 Marks2 Marks
Let * be a binary operation on set of integers I, defined by a * b = 2a + b − 3. Find the value of 3 * 4.
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Q 82 Marks2 Marks
Determine whether the following operations define a binary operation on the given set or not:
'*' on N defined by a * b = a + b - 2 for all $\text{a, b}\in\text{N.}$
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Q 92 Marks2 Marks
Determine whether the following operations define a binary operation on the given set or not:

$'\odot'$ on N defined by $\text{a}\odot\text{b}=\text{a}^{\text{b}}+\text{b}^{\text{a}}$ for all $\text{a, b}\in\text{N.}$

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Q 102 Marks2 Marks
Determine whether or not the definition of * given below gives a binary operation. In the event that * is not a binary operation give justification of this.
On R, define * by a * b = a + 4b2
Here, Z+ denotes the set of all non-negative integers.
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Q 113 Marks3 Marks
Write the composition table for the binary operation multiplication modulo 10 (×10) on the set S = {2, 4, 6, 8}.
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Q 123 Marks3 Marks
On the set Q of all ration numbers if a binary operation * is defined by $\text{a}\ ^*\ \text{b}=\frac{\text{ab}}{5},$ prove that * is associative on Q.
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Q 133 Marks3 Marks
Check the commutativity and associativity of the following binary operations:
'*' on R defined by a * b = a + b - 7 for all a, b ∈ R.
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Q 143 Marks3 Marks
Let A = R0 × R, where R0 denote the set of all non-zero real numbers. A binary operation '⊙' is defined on A as follows:
(a, b) ⊙ (c, d) = (ac, bc + d) for all (a, b), (c, d) ∈ R0 × R.
Find the identity element in A.
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Q 164 Marks4 Marks
Consider the binary operation * and o defined by the following tables on set S = {a, b, c, d}.
o
a
b
c
d
a
a
a
a
a
b
a
b
c
d
c
a
c
d
b
d
a
d
b
c
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Q 174 Marks4 Marks
On R − {1}, a binary operation * is defined by a * b = a + b − ab. Prove that * is commutative and associative. Find the identity element for * on R − {1}. Also, prove that every element of R − {1} is invertible.
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Q 184 Marks4 Marks
Check the commutativity and associativity of the following binary operations:
'*' on N defined by a * b = gcd(a, b) for all a, b ∈ N.
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Q 194 Marks4 Marks
Consider the binary operation * and o defined by the following tables on set S = {a, b, c, d}.
*
a
b
c
d
a
a
b
c
d
b
b
a
d
c
c
c
d
a
b
d
d
c
b
a
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Q 204 Marks4 Marks
Check the commutativity and associativity of the following binary operations:
'*' on Q defined by $\text{a}\ ^*\ \text{b}=\frac{\text{ab}}{4}$ for all a, b ∈ Q.
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