Q56 / 150 · MHT CET 2026 (17 April Shift 1) · Mathematics
The number of arrangements of the letters in the word SOLAPUR, so that consonants and vowels are placed alternately is
- A$100$
- B$129$
- Correct answerC$144$
- D$121$
Solution
The word SOLAPUR consists of 7 letters.
The vowels are O, A, U (3 vowels).
The consonants are S, L, P, R (4 consonants).
Since consonants and vowels must be placed alternately and there are 4 consonants and 3 vowels, the arrangement must start and end with a consonant. The only possible pattern is C V C V C V C, where C represents a consonant and V represents a vowel.
The 4 consonants can be arranged in the 4 alternate positions in $4!$ ways.
The 3 vowels can be arranged in the 3 remaining alternate positions in $3!$ ways.
Total number of arrangements is $4! \times 3!$.
$24 \times 6 = 144$
The vowels are O, A, U (3 vowels).
The consonants are S, L, P, R (4 consonants).
Since consonants and vowels must be placed alternately and there are 4 consonants and 3 vowels, the arrangement must start and end with a consonant. The only possible pattern is C V C V C V C, where C represents a consonant and V represents a vowel.
The 4 consonants can be arranged in the 4 alternate positions in $4!$ ways.
The 3 vowels can be arranged in the 3 remaining alternate positions in $3!$ ways.
Total number of arrangements is $4! \times 3!$.
$24 \times 6 = 144$
Hence, the correct answer is option: 'C'.