JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of \(4-\)letter words, with or without meaning, each consisting of \(2\) vowels and \(2\) consonants, which can be formed from the letters of the word \(UNIVERSE\) without repetition is \(.........\).
- A \(431\)
- B \(430\)
- C \(432\)
- D \(487\)
Answer & Solution
Correct Answer
(C) \(432\)
Step-by-step Solution
Detailed explanation
\(UNIVERSE\) Vowels:\(E, I, U\) Consonants: \(N, V, R, S\) \(\rightarrow{ }^3 C _2 \times{ }^4 C _2 \times 4 !=3 \times 6 \times 24=432\)
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
- For positive integers \(n\), if \(4 a_n=\left(n^2+5 n+6\right)\) and \(S_n=\sum_{k=1}^n\left(\frac{1}{a_k}\right)\), then the value of \(507\ S_{2025}\) is :JEE Mains 2025 Medium
- Let the coefficients of three consecutive terms \(T_r, T_{r+1}\) and \(T_{r+2}\) in the binomial expansion of \((a+b)^{12}\) be in a G.P. and let \(p\) be the number of all possible values of \(r\). Let \(q\) be the sum of all rational terms in the binomial expansion of \((\sqrt[4]{3}+\sqrt[3]{4})^{12}\). Then \(\mathrm{p}+\mathrm{q}\) is equal to :JEE Mains 2025 Medium
- If \(x^{3} d y+x y d x=x^{2} d y+2 y d x ; y(2)=e\) and \(x\) \(>1,\) then \(y (4)\) is equal toJEE Mains 2020 Hard
- The number of ways in which \(5\) boys and \(3\) girls can be seated on a round table if a particular boy \(B_1\) and a particular girl \(G_1\) never sit adjacent to each other, isJEE Mains 2017 Hard
- The \(8^{\text {th }}\) common term of the series \(S _1=3+7+11+15+19+\ldots . .\) ; \(S _2=1+6+11+16+21+\ldots .\) is \(.......\).JEE Mains 2023 Medium
- If the variance of \(10\) natural numbers \(1,1,1, \ldots ., 1, k\) is less than \(10 ,\) then the maximum possible value of \(k\) is ...... .JEE Mains 2021 Hard
More PYQs from JEE Mains
- If the lengths of the sides of a triangle are in \(A.P.\) and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangleJEE Mains 2019 Hard
- A variable line \(\mathrm{L}\) passes through the point \((3,5)\) and intersects the positive coordinate axes at the points \(\mathrm{A}\) and \(\mathrm{B}\). The minimum area of the triangle \(\mathrm{OAB}\), where \(\mathrm{O}\) is the origin, is :JEE Mains 2024 Medium
- Let the relations \(R_1\) and \(R_2\) on the set \(\mathrm{X}=\{1,2,3, \ldots, 20\}\) be given by \(\mathrm{R}_1=\{(\mathrm{x}, \mathrm{y}): 2 \mathrm{x}-3 \mathrm{y}=2\}\) and \(\mathrm{R}_2=\{(\mathrm{x}, \mathrm{y}):-5 \mathrm{x}+4 \mathrm{y}=0\}\). If \(\mathrm{M}\) and \(\mathrm{N}\) be the minimum number of elements required to be added in \(R_1\) and \(R_2\), respectively, in order to make the relations symmetric, then \(\mathrm{M}+\mathrm{N}\) equalsJEE Mains 2024 Hard
- If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse isJEE Mains 2015 Hard
- If the fourth term in the binomial expansion of \(\left(\sqrt{\frac{1}{x^{1+\log _{10} x}}}+x^{\frac{1}{12}}\right)^{6}\) is equal to \(200\), and \(x > 1\), then the value of \(x\) isJEE Mains 2019 Hard
- In a class of \(140\) students numbered \(1\) to \(140\), all even numbered students opted Mathematics course, those whose number is divisible by \(3\) opted Physics course and those whose number is divisible by \(5\) opted Chemistry course. Then the number of students who did not opt for any of the three courses isJEE Mains 2019 Hard