Exams › JEE Advanced › Maths

Let S be a set containing n > 0 elements. If B_r denotes the number of binary relations on S and B_f denotes the number of functions from S to S, express B_r and B_f in terms of n.

1. n² and 2(n+1)²
2. n³ and n^(n+1)
3. n and n^(n+6)
4. 2^(n²) and nⁿ

Correct answer: 2^(n²) and nⁿ

Solution

S x S has n² elements so the number of binary relations (subsets) is 2^(n²); each element has n possible images so the number of functions is nⁿ.

Related JEE Advanced Maths questions

• The function f(x) = √|x² - 5| x + 6 + √8 + 2|x| - |x|² is defined as a real number for values of x within which range?
• The relation x² = xy can be described as:
• Consider the function f: R → R given by f(x) = (e^x - e^(-x)) / (e^x + e^(-x)). Which of the following statements is accurate?
• Consider the functions f(x) = max {1 + sin(x), 1 - cos(x)} for x in the interval [0, 2π], and g(x) = max {1, |x - 1|} for x belonging to the set of real numbers. Which of the following is true?
• Given f(x + f(y)) = f(x) + y, x, y ∈ R. Find f(1000).
• Find the range of fog(x) = f(g(x)) = f(4x(1 − x)).

⚔️ Practice JEE Advanced Maths free + battle 1v1 →