AP EAMCET · Maths · Permutation Combination
The number of ways of arranging all the letters of the word PERFECTION such that there must be exactly two consonants between any two vowels is
- A \(4!+6!\)
- B \(3!+6!\)
- C \(2!3!6!\)
- D \(\frac{6!}{4!}\)
Answer & Solution
Correct Answer
(C) \(2!3!6!\)
Step-by-step Solution
Detailed explanation
Vowels: E, E, I, O (4 letters, E repeats 2 times) Consonants: P, R, F, C, T, N (6 distinct letters) Arrangement pattern (V=Vowel, C=Consonant): VCCVCCVCCV Ways to arrange vowels: \( \frac{4!}{2!} \) Ways to arrange consonants: \( 6! \) Total ways:…
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
- The equation \((2 p-3) x^2+2 p x y-y^2=0\) represents a pair of distinct linesAP EAMCET 2025 Medium
- A box contains 4 black, 2 white and 6 red balls. Another box contains 3 black and 5 white balls. Throwing an unbiassed die, a ball is drawn from the first box if either 1 or 2 appears on the die-otherwise a ball is drawn from the second box. If the drawn ball is black then the probability that 2 appeared on the die isAP EAMCET 2017 Easy
- The number of distinct positive integers can be formed using \(0,1,2,3\) where each integer used at most once is equal toAP EAMCET 2021 Easy
- \(\int \frac{\sqrt{\cot x}}{\sin x \cos x} d x=-f(x)+c \Rightarrow f(x)\)AP EAMCET 2004 Easy
- A square is formed by the lines \(x=0, y=0\), \(x=1, y=1\). Then, the equations of its diagonals will beAP EAMCET 2020 Easy
- \(\lim _{x \rightarrow \infty}\left[\sqrt{x^2+2 x-1}-x\right]\) is equal to :AP EAMCET 2006 Easy
More PYQs from AP EAMCET
- If \(\triangle A B C\) is right angled at \(A\), then \(r_2+r_3\) is equal toAP EAMCET 2002 Hard
- \(\mathrm{z}_1, \mathrm{z}_2, \mathrm{z}_3\) represent the vertices \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) of a triangle ABC respectively in the Argand plane. If \(\left|z_1-z_2\right|=\sqrt{25-12 \sqrt{3}},\left|\frac{z_1-z_3}{z_2-z_3}\right|=\frac{3}{4}\) and \(\underline{\mathrm{ACB}}=30^{\circ}\), then the area (in sq. units) of that traingle isAP EAMCET 2025 Hard
- For \(a \in \mathrm{R}-\{0\}\), if \(a \cos x+a \sin x+a=2 K+1\) has a solution, then \(K\) lies in the intervalAP EAMCET 2024 Medium
- If the magnitude of the vector product of the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) with a unit vector along the sum of the vectors \(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}\) and \(\lambda \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) is equal to \(\sqrt{2}\), then the value of ' \(\lambda\) ' isAP EAMCET 2020 Medium
- Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be any three non coplanar vectors. If \(m\), \(n\) are scalars such that \(\vec{a}+\vec{b}=m \vec{d}-\vec{c}\) and \(\vec{b}+\vec{c}=n \vec{a}-\vec{d}\), then \(3 \vec{a}+2 \vec{b}+2 \vec{c}+\vec{d}=\)AP EAMCET 2023 Medium
- Which one of the following solutions of compounds show highest osmotic pressure? \(\left(A B, A B_2\right.\) and \(A_2 B_3\) are ionic compounds)AP EAMCET 2017 Medium