1. In how many ways "PROBATIONARY" can be written such that the vowels are always together ?
A. 2 * 7!*5!
B. 8!
C. 2 * 8!*5!
D. 8! / 2!
E. 7!
2. What is the probability that the number selected from the set {1,2,3,.......50} is a multiple of 3 or 6 ?
A. 12/25
B. 8/25
C. 4/25
D. 16/25
E. None of these
3. A bag contains 4 black and 6 white balls. 2 balls are drawn at randomn. Find the probability that atleast one of them is black ?
A. 1/3
B. 2/3
C. 3/4
D. 3/5
E. None of these
4. A bag contains 20 tickets numbered from 1-20. 2 tickets are drawn at randomn. Find the probability that both numbers are prime ?
A. 16/95
B. 15/95
C. 14/95
D. 17/95
E. None of these
5. A bag contains 3 red, 6 white and 7 black balls. Two balls are drawn at random. What is the probability that both are black ?
A. 9/40
B. 7/40
C. 11/40
D. 13/40
E. None of these
6. 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. 200
B. 180
C. 190
D. 220
E. 230
7. A boy has 3 library tickets and 8 books of his interest are there in the library. Out of these 8, he does not want to borrow Chemistry Part II, unless Chemistry Part I is also borrowed. The number of ways in which he can choose the three books to be borrowed is ?
A. 42
B. 40
C. 41
D. 45
E. 44
8. In a football championship, 153 matches were played. Every two teams played one match with each other. The number of teams, participating in the championship were ?
A. 20
B. 22
C. 16
D. 18
E. None of these
9. How many motor vehicle registration number plates can be formed with the digits 1, 2, 3, 4, 5 (no digits being repeated) if it is given that registration number can have 1 to 5 digits ?
A. 320
B. 325
C. 350
D. 315
E. None of these
10. If a team of four persons is to be selected from 8 males and 8 females, then in how many ways can the selections be made to include at least one male ?
A. 1750
B. 1500
C. 1450
D. 1600
E. None of these
ANSWERS
1. Vowels in the word PROBATIONARY are O, A, I, O, A
Now keeping them together and treating them as one word.
No. of ways of writting that will be = 8!
Now the vowel group its self can be written in = (5!/2!*2!)
Thus, total ways of writing PROBATIONARY is = (8!*5!)/(2!*2!) = 2*7!*5!
2. Multiples of 3 are {3,6,.......,48} = 16 numbers
Multiples of 6 are {6,12,18,...48} = 8 numbers
Now, as multiples of 6 are already included in multiples of 3.
Thus, no. of favorable cases are = 16
Required Probability = 16/50 = 8/25
3. Total ways of selecting 2 balls from 10 = 10C2 = 45
No. of ways of selecting 2 white balls from 6 white balls = 6C2 = 15
No. of favorable cases are = total ways - no. of ways of selecting no black ball or in other words 2 white balls
= 45 - 15 = 30
Required Probability = 30/45 = 2/3
4. Total prime no.s from 1-20 = 8
Total ways of selecting 2 tickets from 20 = 20C2 = 190
No. of ways of selecting two prime no.s from 8 = 8C2 = 28
Required Probability = 28/190 = 14/95.
5. The reqd. probability is 7C2 / 16C2 = 7/40.
6.
7. Number of Ways = No Chemistry or Chemistry I alone or Chemistry I and
Chemistry II
= 6C3 + 6C2 + 6C1 = 20 + 15 + 6 = 41.
8.
9. If number is 1 digit number, Number of ways= 5.
If number is 2 digit number, Number of ways=5×4=20
If 3 digit number, Number of ways= 5×4×3= 60
If 4 digit number, Number of ways=5×4×3×2=120
If 5 digit number, Number of ways=5×4×3×2×1=120.
By adding these we get the sum as 325.
10. If we subtract the cases in which all are females, we will be left with the cases where atleast one male is selected.
Therefore, the total ways in which 4 members can be selected from 16 = 16C4
and total ways in which 4 females can be selected = 8C4.
So required ways to select at least one male is 16C4 - 8C4 = 1750.
