Binary Operations - Maharashtra Board STD 12 Maths Questions - Vidyadip

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

MCQ

Solve the Following Question.(2 Marks)

Solve the Following Question.(3 Marks)

Solve the Following Question.(5 Marks)

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 1MCQ1 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 $\triangle$

A
Commutative and associative without an identity.
B
Commutative but not associative with an identity.
C
Associative but not commutative without an identity.
✓
Associative and commutative with an identity.

Answer: D.

View full solution →

Q 2MCQ1 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.

View full solution →

Q 3MCQ1 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:

A
$1$
B
$\frac{\text{a}-1}{\text{a}}$
C
$\frac{\text{a}}{\text{a}-1}$
✓
$0$

Answer: D.

View full solution →

Q 4MCQ1 Mark

The number of commutative binary operation that can be defined on a set of $2$ elements is:

A
$8$
B
$6$
C
$4$
✓
$2$

Answer: D.

View full solution →

Q 5MCQ1 Mark

On the set $Q^+$ of all positive rational numbers a binary operation $*$ is defined by $\text{a}*\text{b}=\frac{\text{ab}}2\forall\text{ a, b}\in \text{Q}^+$. The inverse of $8$ is:

A
$\frac{1}{8}$
✓
$\frac{1}2$
C
$2$
D
$4$

Answer: B.

View full solution →

Q 6Solve the Following Question.(2 Marks)2 Marks

Define a binary operation on a set.

View full solution →

Q 7Solve the Following Question.(2 Marks)2 Marks

The binary operation *: R × R → R is defined as a * b = 2a + b. Find (2 * 3) * 4.

View full solution →

Q 8Solve the Following Question.(2 Marks)2 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.

View full solution →

Q 9Solve the Following Question.(2 Marks)2 Marks

Write the composition table for the binary operation $\times _5$ (multiplication modulo $5$) on the set $S = {0, 1, 2, 3, 4}$.

View full solution →

Q 10Solve the Following Question.(2 Marks)2 Marks

Let * be a binary operation on set of integers I, defined by a * b = 2a + b − 3. Find the value of 3 * 4.

View full solution →

Q 11Solve the Following Question.(3 Marks)3 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.

View full solution →

Q 12Solve the Following Question.(3 Marks)3 Marks

Construct the composition table for $\times _5$ on $Z_5 = {0, 1, 2, 3, 4}$.

View full solution →

Q 13Solve the Following Question.(3 Marks)3 Marks

For the binary operation $\times _7 $ on the set $S = \{1, 2, 3, 4, 5, 6\},$ compute $3^{−1} \times _7 4.$

View full solution →

Q 14Solve the Following Question.(3 Marks)3 Marks

The binary operation * is defined by $\text{a}\ ^*\ \text{b}=\frac{\text{ab}}{7}$ on the set Q of all rational numbers. Show that * is associative.

View full solution →

Q 15Solve the Following Question.(3 Marks)3 Marks

For the binary operation multiplication modulo $10 (\times _{10})$ defined on the set $S = \{1, 3, 7, 9\},$ write the inverse of $3.$

View full solution →

Q 16Solve the Following Question.(5 Marks)5 Marks

Let S be the set of all real numbers except -1 and let '*' be an operation defined by a * b = a + b + ab for all a, b ∈ S. Determine whether '*' is a binary operation on S. If yes, check its commutativity and associativity. Also, solve the equation (2 * x) * 3 = 7.

View full solution →

Q 17Solve the Following Question.(5 Marks)5 Marks

Let S be the set of all rational numbers except 1 and * be defined on S by a * b = a + b - ab, for all a, b ∈ S.
Prove that:

* is a binary operation on S.
* is commutative as well as associative.

View full solution →

Q 18Solve the Following Question.(5 Marks)5 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.

View full solution →

Q 19Solve the Following Question.(5 Marks)5 Marks

Let A =R×R and * be a binary operation on A defined by,
(a, b) * (c, d) = (a + c, b + d).
Show that * is commutative and associative. Find the binary element for * on A, if any.

View full solution →

Q 20Solve the Following Question.(5 Marks)5 Marks

Define a binary operation * on the set {0, 1, 2, 3, 4, 5} as:
$\text{a}\times\text{b}=\begin{cases}\text{a + b},&\text{if }\text{a + b}<6\\\text{a + b}-6,&\text{if }\text{a + b}\geq6\end{cases}$
Show that 0 is the identity for this operation and each element a ≠ 0 of the set is invertible with 6 − a being the inverse of a.

View full solution →

Browse all question groups ↑

Generate a Binary Operations paper free

Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.

Generate Paper Free All Maths chapters