Let R be the relation in the set N given by R = {(a, b): a = b − 2, b > 6}. Choose the correct answer. (A) (2, 4) ∈ R (B) (3, 8) ∈R (C) (6, 8) ∈R (D) (8, 7) ∈ R
Let R be the relation in the set N given by R = {(a, b): a = b − 2, b > 6}. Choose the correct answer. (A) (2, 4) ∈ R (B) (3, 8) ∈R (C) (6, 8) ∈R (D) (8, 7) ∈ R
Solution and Explanation
R = {(a, b): a = b − 2, b > 6 }
Now, since b > 6, (2, 4) ∉ R
Also, as 3 ≠ 8 − 2, (3, 8) ∉ R
And, as 8 ≠ 7 − 2
∴ (8, 7) ∉ R
Now, consider (6, 8).
We have 8 > 6 and also, 6 = 8 − 2.
∴ (6, 8) ∈ R
The correct answer is C.
Top Questions on Relations and Functions
A school is organizing a debate competition with participants as speakers and judges. $ S = \{S_1, S_2, S_3, S_4\} $ where $ S = \{S_1, S_2, S_3, S_4\} $ represents the set of speakers. The judges are represented by the set: $ J = \{J_1, J_2, J_3\} $ where $ J = \{J_1, J_2, J_3\} $ represents the set of judges. Each speaker can be assigned only one judge. Let $ R $ be a relation from set $ S $ to $ J $ defined as: $ R = \{(x, y) : \text{speaker } x \text{ is judged by judge } y, x \in S, y \in J\} $.
- CBSE CLASS XII - 2025
- Mathematics
- Relations and Functions
During the festival season, a mela was organized by the Resident Welfare Association at a park near the society. The main attraction of the mela was a huge swing, which traced the path of a parabola given by the equation:\[ x^2 = y \quad \text{or} \quad f(x) = x^2 \]
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Relations and Functions
- Consider the function \( f : \mathbb{R} \rightarrow \mathbb{R} \), defined as \( f(x) = x^3 \). Assertion (A): \( f(x) \) is a one-one function. Reason (R): \( f(x) \) is a one-one function, if co-domain = range.
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Relations and Functions
- The cost and revenue functions are given as: \[ C(x) = 3x^2 + 5x + 200, \quad R(x) = 50x \] Find the number of items that should be sold to maximize the profit.
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Relations and Functions
- Let \( R \) be a relation defined by the teacher to plan the seating arrangement of students in pairs, where \( R = \{(x, y) : x, y \text{ are Roll Numbers of students such that } y = 3x \} \). List the elements of \( R \). Is the relation \( R \) reflexive, symmetric, and transitive? Justify your answer.
- CBSE CLASS XII - 2025
- Mathematics
- Relations and Functions
Questions Asked in CBSE CLASS XII exam
- Three batteries E1, E2, and E3 of emfs and internal resistances (4 V, 2 \(\Omega\)), (2 V, 4 \(\Omega\)) and (6 V, 2 \(\Omega\)) respectively are connected as shown in the figure. Find the values of the currents passing through batteries E1, E2, and E3.
- CBSE CLASS XII - 2025
- Kirchhoff's Laws
- A beam of light coming from a distant source is refracted by a spherical glass ball (refractive index 1.5) of radius 15 cm. Draw the ray diagram and obtain the position of the final image formed.
- A charge \( -6 \, \mu C \) is placed at the center B of a semicircle of radius 5 cm, as shown in the figure. An equal and opposite charge is placed at point D at a distance of 10 cm from B. A charge \( +5 \, \mu C \) is moved from point C to point A along the circumference. Calculate the work done on the charge.
- CBSE CLASS XII - 2025
- Electrostatics
- If $\tan^{-1} (x^2 - y^2) = a$, where $a$ is a constant, then $\frac{dy}{dx}$ is:
- CBSE CLASS XII - 2025
- Continuity and differentiability
- Kamala Das in ‘Keeping Quiet’ and Keats in ‘A Thing of Beauty’ depict nature as a source of inspiration and strength to man. Analyse both the poems in terms of the above perspective.
- CBSE CLASS XII - 2025
- Literature
Concepts Used:
Types of Relation
TYPES OF RELATION
Empty Relation
Relation is said to be empty relation if no element of set X is related or mapped to any element of X i.e, R = Φ.
Universal Relation
A relation R in a set, say A is a universal relation if each element of A is related to every element of A.
R = A × A.
Identity Relation
Every element of set A is related to itself only then the relation is identity relation.
Inverse Relation
Let R be a relation from set A to set B i.e., R ∈ A × B. The relation R-1 is said to be an Inverse relation if R-1 from set B to A is denoted by R-1
Reflexive Relation
If every element of set A maps to itself, the relation is Reflexive Relation. For every a ∈ A, (a, a) ∈ R.
Symmetric Relation
A relation R is said to be symmetric if (a, b) ∈ R then (b, a) ∈ R, for all a & b ∈ A.
Transitive Relation
A relation is said to be transitive if, (a, b) ∈ R, (b, c) ∈ R, then (a, c) ∈ R, for all a, b, c ∈ A
Equivalence Relation
A relation is said to be equivalence if and only if it is Reflexive, Symmetric, and Transitive.