nCr Definitions and Properties

Q.

If ${}^{56}{P}_{r+6}:{}^{54}{P}_{r+3}$ = 30800:1, then r =

1. 31

2. 51

3. 40

4. 41

Q. If P(n, 5) = 20P (n, 3), then n =

1. 4
2. 6
3. 8
4. 2

Q. The value of ${\sum }_{r=1}^{10}r{.}^r{P}_r$ =

1. 11!
2. 11! - 1
3. 11! + 1
4. 11! - 11

Q. From a group of persons the number of ways of selecting 5 persons is equal to that of 8 persons. The number of persons in the group is

1. 13
2. 18
3. 40
4. 21

Q. The digit at units place of the sum $(1!{)}^2+(2!{)}^2+(3!{)}^2+.....+(20009{)}^2$

1. 5
2. 0
3. 1
4. 7

Q. If P (10, r) = 5040, then r =

1. 2
2. 4
3. 6
4. 8

Q. If ${}^n{C}_{r-1}=36,{}^n{C}_r=84and{}^n{C}_{r+1}=126$ then r is

1. 1
2. 2
3. 3
4. none of these

Q. The value of the expression ${}^{47}{C}_4+{\sum }_{j=1}^5{}^{52-j}{C}_3$ is

1. $Noneofthese$
2. ${}^{47}{C}_5$
3. ${}^{52}{C}_5$
4. ${}^{52}{C}_4$

Q.

If ${}^{56}{P}_{r+6}:{}^{54}{P}_{r+3}$ = 30800:1, then r =

1. 41

2. 31

3. 51

4. 40

Q. The value of ${\sum }_{r=1}^{10}r{.}^r{P}_r$ =

1. 11!
2. 11! - 1
3. 11! + 1
4. 11! - 11