1st Year Mathematics Chapter 6 Test6. Permutation and Combination

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

1. In how many ways 6 women and 5 men be seated in a row such that male and female occupy alternate seats ?
   1. 11 !
   2. 30 !
   3. 6 ! 5 !
   4. 6 ! 5 ! 2 !
2. 10! = ?
   1. 5! + 5!
   2. 8! + 2!
   3. 10! + 0!
   4. None of these
3. In a Chinese restaurant 4 different dishes of rice, 5 different dishes of chicken and 7 different types of salads are available.In how many ways a person can select his meal ?
   1. 140
   2. 150
   3. 16
   4. 14
4. How many lines can be drawn through 21 points on a circle ?
   1. 310
   2. 210
   3. 410
   4. 570
5. 10 persons want to sit at a round table .In how many ways they can be seated , if 3 persons insist on sitting together ?
   1. 5040
   2. 30240
   3. 10080
   4. 2520
6. If $18C_r = 18C_{r+2}$ then $rC_5 = ?$
   1. 24
   2. 56
   3. 72
   4. 120
7. Ten students are participating in a race .In how many ways can the first 3 prizes be won ?
   1. 920
   2. 680
   3. 820
   4. 720
8. How many odd numbers less than 1000 can be formed by using the digits 0 , 2 , 5 , 7 ? ( repetition of digits is allowed )
   1. 52
   2. 32
   3. 22
   4. 42
9. ${}^n C_r :{}^n C_{r +1} = ?$
   1. $$\frac{n+1}{r+1}$$
   2. $$\frac{r+1}{n-r}$$
   3. $$\frac{n}{r+1}$$
   4. $$\frac{r+1}{n+r}$$
10. How many numbers can be formed from 1 , 2 , 3 , 4 , 5 , if even digit occupy even places .(each digit used at once )
    1. 72
    2. 48
    3. 24
    4. 12