Advance Math Model Questions Set 2 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Question : 1

Six teachers and six students have to sit round a circular table such that there is a teacher between any two students. The number of ways in which they can sit is

a) 5 ! × 6 !

b) 5 ! × 5 !

c) 6 ! × 6 !

d) None of these

Question : 2

Twenty-seven persons attend a party. Which one of the following statements can never be true ?

a) Each person in the party has a different number of acquaintances

b) There is a person in the party who has an odd number of acquaintances

c) There is a person in the party who is acquainted with all the twenty-six others

d) In the party, there is no set of three mutual acquaintances

Question : 3

A bag has 13 red, 14 green and 15 white balls, $p_1$ is the probability of drawing exactly 2 white balls when four balls are drawn. Then the number of balls of each colour are doubled. Let $p_2$ be the probability of drawing 4 white balls when 8 ball are drawn, then

a) $p_1 > p_2$

b) $p_1 < p_2$

c) $p_1 = p_2$

d) None

Question : 4

If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, the number of points in which they intersect each other is

a) 190

b) 250

c) 220

d) 120

Question : 5

The alphabets of word ALLAHABAD are arranged at random. The probability that in the words so formed, all identical alphabets are found together, is

a) $16/17$

b) $5!/9!$

c) $1/63$

d) None of these

Question : 6

A man and his wife appear for an interview for two posts. The probability of the husband's selection is $1/7$ and that of the wife's selection is $1/5$ . The probability that only one of them will be selected is

a) $4/{35}$

b) $6/{35}$

c) $6/7$

d) $2/7$