JEE Main 2026 Apr 6 Shift 1, Mathematics Q7: Combinations

JEE Main2026Apr 6, Shift 1Mathematics

The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is:

A
$2670$
B
$2840$
C
$2920$
D
$3600$

Solution

The distinct vowels available in INCONSEQUENTIAL are ${I, E, O, A, U}$ ( $5$ letters) and the distinct consonants are ${N, C, S, Q, T, L}$ ( $6$ letters).

Choose $2$ vowels: $(2 5) = 10$ ways. Choose $2$ consonants: $(2 6) = 15$ ways. Arrange the $4$ chosen letters: $4! = 24$ ways.

Total $= 10 \times 15 \times 24 = 3600$ .

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JEE Main 2026 Apr 6 Shift 1, Mathematics Q7: Combinations

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