## Infosys P&C Questions with Solutions

1. How many 4 digit numbers contain number 2.
a. 3170
b. 3172
c. 3174
d. 3168
Ans: D
Sol: Total number of 4 digit numbers are 9000 (between 1000 and 9999).
We find the numbers without any two in them. So total numbers are 8 x 9 x 9 x 9 = 5832 So numbers with number two in them = 9000 – 5832 = 3168

2. How many three digit numbers ABC are formed where at least two of the three digits are same.
a. 252
b. 260
c. 213
d. 226
Ans: a
Sol: Total 3 digit numbers = 9 x 10 x 10 = 900
Total number of 3 digit numbers without repetition = 9 x 9 x 8 = 648
So a number of three digit numbers with at least one digit repeats = 900 – 648=252

3. In a cycle race, there are 5 persons named as J,K,L,M,N participated for 5 positions so that in how many number of ways can M finishes always before N?
a. 70
b. 60
c. 80
d. 22
Ans: b
Sol: Total number of ways in which 5 persons can finish is 5! = 120 (there are no ties) Now in half of these ways M can finish before N.

4. There are 16 people, they divide into four groups, now from those four groups select a team of three members, such that no two members of the team should belong to the same group.
a.112
b.234
c.256
d.214
Ans: c
Sol: We can select any three of the 4 groups in 4 C 3
ways. Now from each of these groups, we can select 1 person in 4 ways. So total ways = 4 x 4 x 4 x 4 = 256

5. 7 people have to be selected from 12 men and 3 women, Such that no two women can come together. In how many ways we can select them?
a. 2772
b. 2773
c. 2775
d. 2134
Ans: 2772
Sol: We can select only one woman, and remaining 6 from men. So 12 C 6 × 3 C 1 = 2772

6. Tennis players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
a. 210
b. 123
c. 250
d. 215
Ans: a
Sol: We can select two teams out of 15 in 15 C 2 ways. So each team plays with other teams once. Now to play two games, we have to conduct 15 C 2 x 2 = 210 games.

7. Find the no of ways in which 6 toffees can be distributed over 5 different people namely A,B,C,D,E.
a. 3
b. 4
c. 6
d. 5
Ans : d
Sol: We assume that all the toffees are similar. Then Number of ways are ( n + r −1) C r −1
HereA+B+C+D+E=6
Here r = 5, n = 6
Number of ways = 6+5−1 C 5−1 = 10 C 4 = 210.
If all the toffees are different, then each toffee can be distributed to any of the five. So total ways are 5

8. A shop has 4 shelves, 3 wardrobes, 2 chairs and 7 tables for sale. You have to buy a. 1 shelf
b. 1 wardrobe
c. either 1 chair or 1 table
How many selections can be made?
a. 110
b. 109
c. 108
d. 107
Ans : c
Sol:
The way to answer this question
4 C 1 × 3 C 1 × 2 C 1 + 4 C 1 × 3 C 1 × 7 C 1 = 108

9. How many ways can one arrange the word EDUCATION such that relative positions of vowels and consonants remain same?
a. 2880
b. 2180
c. 2670
d. 2560
Ans: a
Sol: The word EDUCATION is a 9 letter word with none of the letters repeating
The vowels occupy 3,5,7th & 8th position in the word & remaining five positions are occupied by consonants
As the relative position of the vowels & consonants in any arrangement should remain the same as in the word EDUCATION. The four vowels can be arranged in 3rd,5th,7th & 8th position in 4! ways.
similarly, the five consonants can be arranged in 1st , 2nd, 4th, 6th & 9th position in 5! ways Hence the total number of ways = 5!×4!=120×24=2880

10. There are 8 digits and 5 alphabets.In how many ways can you form an alphanumeric word using 3 digits and 2 alphabets?
a. 33190
b. 33210
c. 41200
d. 43200
Ans: d
Sol:
Select 3 digits from 8 digits i. e. 8 C 3 ways
And also select 2 alphabets from 5 alphabets i.e., 5 C 2 ways
Now to form an alphanumeric word of 5 characters we have to arrange the 5 selected digits. So the answer is . 8 C 3
× 5 C 2 × 5! = 43200