Question

Question 1

Consider the system of congruences x ≡ 19 (mod 23), x ≡ 8 (mod 29). The smallest positive solution to this system is......

Question 2

Out of 8 consonants and 5 vowels, the number of words of 2 consonants and 2 vowels can be formed is .......

Question 3

In a group of 7 men and 8 women, a committee with 5 people is to be selected. The number of ways to form this committee so that at least two women are selected is......

Question 4

The number of ways to re-arrange the letters in ASSISTANTS in such a way that all occurrences of vowels are side by side, and all occurrences of consonants are side by side is.....

Question 5

Ten students are going to take four different course. Each student takes exactly one course. The number of ways for these students to take these courses such that every course is taken by at least one student is.....

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Answer 1