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
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
- Edge of a variable cube increases at the rate of 5 cm/s. The rate at which the surface area of the cube increases when the edge is 2 cm long is :
- CBSE CLASS XII - 2025
- Mathematics
- Relations and Functions
Questions Asked in CBSE CLASS XII exam
Rupal, Shanu and Trisha were partners in a firm sharing profits and losses in the ratio of 4:3:1. Their Balance Sheet as at 31st March, 2024 was as follows:
(i) Trisha's share of profit was entirely taken by Shanu.
(ii) Fixed assets were found to be undervalued by Rs 2,40,000.
(iii) Stock was revalued at Rs 2,00,000.
(iv) Goodwill of the firm was valued at Rs 8,00,000 on Trisha's retirement.
(v) The total capital of the new firm was fixed at Rs 16,00,000 which was adjusted according to the new profit sharing ratio of the partners. For this necessary cash was paid off or brought in by the partners as the case may be.
Prepare Revaluation Account and Partners' Capital Accounts.- CBSE CLASS XII - 2025
- Partnership Accounts
On the basis of the following hypothetical data, calculate the percentage change in Real Gross Domestic Product (GDP) in the year 2022 – 23, using 2020 – 21 as the base year.
Year Nominal GDP Nominal GDP (Adjusted to Base Year Price) 2020–21 3,000 5,000 2022–23 4,000 6,000 - CBSE CLASS XII - 2025
- National Income Accounting
- Determine those values of $x$ for which $f(x) = \frac{2}{x} - 5$, $x \ne 0$ is increasing or decreasing.
- CBSE CLASS XII - 2025
- Functions
- Analyse how freedom is curbed in the context of Franz in ‘The Last Lesson’ and Saheb in ‘Lost Spring’.
- CBSE CLASS XII - 2025
- The Last Lesson
- Altima Ltd. invited applications for 2,00,000 equity shares of ₹ 10 at a premium of ₹ 4 per share. Amount payable:
On application and allotment – ₹ 7 (incl. ₹ 1 premium)
On first and final call – Balance.
Applications received for 2,40,000 shares. 30,000 rejected. Manvi allotted 4,000 shares failed to pay first and final call. Her shares were forfeited. These were reissued at ₹ 4 per share fully paid-up.
Pass journal entries in the books of Altima Ltd.- CBSE CLASS XII - 2025
- Accounting for Share Capital