In how many different ways can the letters of the word RUMOUR be arranged?

Answer: Option 3 The word 'LEADING' has 7 different letters. When the vowels EAI are always together, they can be supposed to form one letter. Then, we have to arrange the letters...

Answer: Option 4 In the word 'CORPORATION', we treat the vowels OOAIO as one letter. Thus, we have CRPRTN (OOAIO). This has 7 (6 + 1) letters of which R occurs 2...

Answer: Option 3 There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants. Let us mark these positions as under: (1) (2) (3) (4)...

Answer: Option 3 In the word 'MATHEMATICS', we treat the vowels AEAI as one letter. Thus, we have MTHMTCS (AEAI). Now, we have to arrange 8 letters, out of which M occurs...

Answer: Option 2 The word 'OPTICAL' contains 7 different letters. When the vowels OIA are always together, they can be supposed to form one letter. Then, we have to arrange the letters...

Answer: Option 4 The given word contains 7 letters out of which E is taken 2 times and all other letters are different . ∴ Required number of ways $$\eqalign{ & = \frac{{7!}}{{2!}}...

Answer: Option 5 The given 6 letters, all different. ∴ Required number of ways $$\eqalign{ & {}^6{P_6} = 6! \cr & = {6 \times 5 \times 4 \times 3 \times 2 \times 1} \cr &...

Answer: Option 2 The word ‘TRANSPIRATION’ has 13 letters in which each of T, R, A, N and I has come two times We have to arrange TT RR NN PS...

Answer: Option 2 Keeping the vowels (AIA) together, we have CPTL (AIA). We treat (AIA) as 1 letter. Thus, we have to arrange 5 letters. These can be arranged in 5! = (5...

Answer: Option 3 The given words contains 8 letters of which E is taken 2 times. ∴ Required number of ways$$\eqalign{ & = \frac{{8!}}{{2!}} \cr & = \frac{{8 \times 7 \times 6 \times...