JEE Mains · Maths · STD 11- 2. Relation and Function
Let \(A = \{1, 2, 3, 4, 5, 6\}\). The number of one-one functions \(f: A \rightarrow A\) such that \(f(1) \geq 3\), \(f(3) \leq 4\) and \(f(2) + f(3) = 5\), is __________.
- A 70
- B 72
- C 78
- D 76
Answer & Solution
Correct Answer
(B) 72
Step-by-step Solution
Detailed explanation
Given \(A = \{1, 2, 3, 4, 5, 6\}\). Since \(f: A \rightarrow A\) is a one-one function, \(f(x)\) takes distinct values from \(A\) for each \(x \in A\). We are given the condition \(f(2) + f(3) = 5\). The possible pairs for \((f(2), f(3))\) from the set \(A\) are:…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(\mathrm{M}\) denote the median of the following frequency distribution then \(20\) \(M\) is equal to :
Class \(0-4\) \(4-8\) \(8-12\) \(12-16\) \(16-20\) Freq \(3\) \(9\) \(10\) \(8\) \(6\) JEE Mains 2024 Hard - Let a point A lie between the parallel lines \( L_{1} \) and \( L_{2} \) such that its distances from \( L_{1} \) and \( L_{2} \) are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC, where the points B and C lie on the lines \( L_{1} \) and \( L_{2} \) respectively, is:JEE Mains 2026 Easy
- The sum of all the real values of \(x\) satisfying the equation \({2^{\left( {x - 1} \right)\left( {{x^2} + 5x - 50} \right)}} = 1\) isJEE Mains 2017 Hard
- Two poles, \(\mathrm{AB}\) of length \(a\) metres and \(\mathrm{CD}\) of length \(\mathrm{a}+\mathrm{b}(\mathrm{b} \neq \mathrm{a})\) metres are erected at the same horizontal level with bases at \(\mathrm{B}\) and \(\mathrm{D} .\) If \(\mathrm{BD}=\mathrm{x}\) and \(\tan \angle\,ACB=\frac{1}{2}\), then:JEE Mains 2021 Hard
- The number of solutions of the equation \(|\cot x|=\cot x+\frac{1}{\sin x}\) in the interval \([0,2 \pi]\) isJEE Mains 2021 Hard
- Let \(\vec{a}=3 \hat{i}+\hat{j}-2 \hat{k}, \vec{b}=4 \hat{i}+\hat{j}+7 \hat{k}\) and \(\overrightarrow{\mathrm{c}}=\hat{\mathrm{i}}-3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}\) be three vectors. If a vectors \(\overrightarrow{\mathrm{p}}\) satisfies \(\overrightarrow{\mathrm{p}} \times \overrightarrow{\mathrm{b}}=\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{p}} \cdot \overrightarrow{\mathrm{a}}=0\), then \(\overrightarrow{\mathrm{p}} \cdot(\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}})\) is equal toJEE Mains 2024 Hard
More PYQs from JEE Mains
- Let \(\alpha\) and \(\beta\) be the roots of the equation \(\mathrm{x}^{2}-\mathrm{x}-1=0 .\) If \(\mathrm{p}_{\mathrm{k}}=(\alpha)^{\mathrm{k}}+(\beta)^{\mathrm{k}}, \mathrm{k} \geq 1,\) then which one of the following statements is not true?JEE Mains 2020 Hard
- A spherical iron ball of \(10 \;\mathrm{cm}\) radius is coated with a layer of ice of uniform thickness the melts at a rate of \(50\; \mathrm{cm}^{3} / \mathrm{min}\). When the thickness of ice is \(5 \;\mathrm{cm},\) then the rate (in \(\mathrm{cm} / \mathrm{min.}\) ) at which of the thickness of ice decreases, isJEE Mains 2020 Medium
- Let the smallest value of \(k \in \mathbb{N}\), for which the coefficient of \(x^3\) in \((1+x)^3 + (1+x)^4 + (1+x)^5 + \ldots + (1+x)^{99} + (1+kx)^{100}\), \(x \neq 0\), is \(\left(43n + \dfrac{101}{4}\right)\left(^{100}C_3\right)\) for some \(n \in \mathbb{N}\), be \(p\). Then the value of \(p + n\) is:JEE Mains 2026 Hard
- If \(\hat x,\,\hat y\) and \(\hat z\) are three unit vectors in three dimensional space , then the minimum value of \({\left| {\hat x + \hat y} \right|^2}\, + \,{\left| {\hat y + \hat z} \right|^2}\, + \,{\left| {\hat z + \hat x} \right|^2}\)JEE Mains 2014 Hard
- If \(a=\sin ^{-1}(\sin (5))\) and \(b=\cos ^{-1}(\cos (5))\), then \(a^2+b^2\) is equal toJEE Mains 2024 Medium
- The variance of the numbers \(8,21,34,47, \ldots, 320\) isJEE Mains 2025 Easy