Binary Operations - Rajasthan Board (RBSE) STD 12 Science MATHS Questions

If a binary operation * is defined on the set Z of integers as a * b = 3a − b, then the value of (2 * 3) * 4 is:

Mark the correct alternative in the following question for the binary operation * on Z defined by a * b = a + b + 1, the identity element is:

0
-1
1
2

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Q 3M.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 $\triangle$

Commutative and associative without an identity.
Commutative but not associative with an identity.
Associative but not commutative without an identity.
Associative and commutative with an identity.

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Q 4M.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:

✓
$\frac{9}{8}$
B
$\frac{2}3$
C
$\frac{3}2$
D
None of these.

Answer: A.

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Q 5M.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:

$1$
$\frac{\text{a}-1}{\text{a}}$
$\frac{\text{a}}{\text{a}-1}$
$0$

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Q 62 Marks Questions2 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 72 Marks Questions2 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 82 Marks Questions2 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 92 Marks Questions2 Marks

Define a commutative binary operation on a set.

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Q 102 Marks Questions2 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 $a ^* b = ab^2.$
Here, $Z^+$ denotes the set of all non$-$negative integers.

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Q 113 Marks Question3 Marks

Construct the composition table for $\times _4$ on set $S = {0, 1, 2, 3}.$

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Q 123 Marks Question3 Marks

Write the composition table for the binary operation multiplication modulo $10 (\times _{10})$ on the set $S = \{2, 4, 6, 8\}.$

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Q 133 Marks Question3 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 Marks Question3 Marks

Let $A = R_0 \times R,$ where $R_0$ denote the set of all non$-$zero real numbers. A binary operation $'\odot'$ is defined on $A$ as follows :
$(a, b) \odot (c, d) = (ac, bc + d)$ for all $(a, b), (c, d) \in R_0 \times R.$
Find the identity element in $A.$

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Q 153 Marks Question3 Marks

QUESTION Let $R_0$ denote the set of all non$-$zero real numbers and let $A=R_0 \times R_0$. If $'\ ^*\ '$ is a binary operation on adefined by, $(a, b)^*(c, d)=(a c, b d)$ for all $(a, b),(c, d) \in A$ Show that $ '\ ^*\ '$ is both commutative and associative on $A.$

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Q 165 Marks Questions5 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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Q 175 Marks Questions5 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 185 Marks Questions5 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 195 Marks Questions5 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 205 Marks Questions5 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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Binary Operations question types

Binary Operations questions

Generate a Binary Operations paper free

$o$	$a$	$b$	$c$	$d$
$a$	$a$	$a$	$a$	$a$
$b$	$a$	$b$	$c$	$d$
$c$	$a$	$c$	$d$	$b$
$d$	$a$	$d$	$b$	$c$

$*$	$a$	$b$	$c$	$d$
$a$	$a$	$b$	$c$	$d$
$b$	$b$	$a$	$d$	$c$
$c$	$c$	$d$	$a$	$b$
$d$	$d$	$c$	$b$	$a$

$o$	$a$	$b$	$c$	$d$
$a$	$a$	$a$	$a$	$a$
$b$	$a$	$b$	$c$	$d$
$c$	$a$	$c$	$d$	$b$
$d$	$a$	$d$	$b$	$c$

$*$	$a$	$b$	$c$	$d$
$a$	$a$	$b$	$c$	$d$
$b$	$b$	$a$	$d$	$c$
$c$	$c$	$d$	$a$	$b$
$d$	$d$	$c$	$b$	$a$

Binary Operations MATHS - Binary Operations

Binary Operations question types

Binary Operations questions

Generate a Binary Operations paper free

$o$	$a$	$b$	$c$	$d$
$a$	$a$	$a$	$a$	$a$
$b$	$a$	$b$	$c$	$d$
$c$	$a$	$c$	$d$	$b$
$d$	$a$	$d$	$b$	$c$

$*$	$a$	$b$	$c$	$d$
$a$	$a$	$b$	$c$	$d$
$b$	$b$	$a$	$d$	$c$
$c$	$c$	$d$	$a$	$b$
$d$	$d$	$c$	$b$	$a$