Find the number of all onto functions from the set {1,2,3,… ,n) to itself.
Find the number of all onto functions from the set {1,2,3,… ,n) to itself.
Solution and Explanation
Onto functions from the set {1, 2, 3, … ,n} to itself is simply a permutation on n symbols 1, 2, …, n.
Thus, the total number of onto maps from {1, 2, … , n} to itself is the same as the total number of permutations on n symbols 1, 2, …, n, which is n.
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
- (b) If $2x^2 - 5xy + y^3 = 76$, then find $\frac{dy}{dx}$.
- CBSE CLASS XII - 2025
- Differentiation
- “If you want to test a man’s character, give him power.” Analyse the theme of The Tiger King in the light of the above quote. (The Tiger King)
- A coil has 100 turns, each of area \( 0.05 \, \text{m}^2 \) and total resistance \( 1.5 \, \Omega \). It is inserted at an instant in a magnetic field of \( 90 \, \text{mT} \), with its axis parallel to the field. The charge induced in the coil at that instant is:
- CBSE CLASS XII - 2025
- Electromagnetic induction
- A 1 cm segment of a wire lying along the x-axis carries a current of 0.5 A along the \( +x \)-direction. A magnetic field \( \vec{B} = (0.4 \, \text{mT} \hat{j}) + (0.6 \, \text{mT} \hat{k}) \) is switched on. The force acting on the segment is:
- CBSE CLASS XII - 2025
- Magnetic Force on a Current-Carrying Wire
- Two wires of the same material and the same radius have their lengths in the ratio 2:3. They are connected in parallel to a battery which supplies a current of 15 A. Find the current through the wires.
- CBSE CLASS XII - 2025
- Current electricity