Advance Math Model Questions Set 2 Practice Questions Answers Test with Solutions & More Shortcuts
Advance Math PRACTICE TEST [2 - EXERCISES]
Advance Math Model Questions Set 1
Advance Math Model Questions Set 2
Question : 6
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
Answer »Answer: (c)
(AAAA), (LL), HBD
P = ${5!}/{{9!}/{4!2!}} = {5! × 4! × 2!}/{9!}$
= ${24 × 2}/{9 × 8 × 7 × 6} = 1/{63}$
Question : 7
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
Answer »Answer: (a)
Points are formed when two lines cuts each others.
No. of ways $^{20}C_2 = {20!}/{2!18!} = {20 × 19}/2$ = 190
Question : 8
A class consists of 80 students, 25 of them are girls and 55 are boys. If 10 of them are rich and the remaining poor and also 20 of them are intelligent then the probability of selecting an intelligent rich girl is
a) ${25}/{128}$
b) $5/{512}$
c) $5/{128}$
d) None of these
Answer »Answer: (b)
Total 80, Girls = 25, Boys = 55
10 R, 70 P, 20 I
$1/4 × 1/8 × {25}/{80} = 5/{512}$
Question : 9
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
Answer »Answer: (a)
Six students $S_1 , S_2 , ........, S_6$ can be arranged round a circular table in 5 ! ways. Among these 6 students there are six vacant places, shown by dots (•) in which six teachers can sit in 6 ! ways.
Hence, number of arrangement = 5 ! × 6 !
Question : 10
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
Answer »Answer: (a)
It can be clearly established that the choices (a) , (c) and (d) may or may not be true . Statement (b) can never be true because every person cannot have a different number of acquaintances.
IMPORTANT quantitative aptitude EXERCISES
Advance Math Model Questions Set 2 Online Quiz
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