11. Relation between ${}^{n}{{C}_{r}}$ and ${}^{n}{{\operatorname{P}}_{r}}$ is
(A) ${}^{n}{{{P}}_{r}}$ = Â ${}^{n}{{C}_{r}}$
(B) ${}^{n}{{{P}}_{r}}$ =Â ${}^{n}{{C}_{n-r}}$
(C) ${}^{n}{{{P}}_{r}}$ = r! ${}^{n}{{C}_{r}}$
(D) ${}^{n}{{C}_{r}}$= r! x ${}^{n}{{{P
A. A
B. B
C. C
D. D
Correct Answer : C
12. In how many ways can 4 girls be seated on 10 different chairs in a row?
A. 3080
B. 720
C. 1080
D. 5040
Correct Answer : D
13. The number of different words that can be formed using all the letters of the word SPECIAL that begin with S and end with L is
A. 5!
B. 7!
C. 6!
D. 4!
Correct Answer : A
14. Number of ways of selecting 5 out of 7 persons is
(A) ${}^{7}{{P}_{5}}$ (B) ${}^{7}{{C}_{5}}$ (C)7! (D)5!
A. A
B. B
C. C
D. D
Correct Answer : B
15. Number of ways of arranging 3 persons in 8 distinct chairs is
(A) ${}^{8}{{P}_{3}}$
(B) ${}^{8}{{C}_{3}}$
(C)8!
(D) 3!
A. A
B. B
C. C
D. D
Correct Answer : A
16. The number of ways of forming a garland using 21 different flowers is
(A)20!
(B)21!
(C)21
(D)$\frac{20!}{2}$
A. A
B. B
C. C
D. D
Correct Answer : D
17. Number of even numbers can be formed using all the digits 1, 3, 5, 6, 7 is
A. 5!
B. 5
C. 4!
D. 0
Correct Answer : C
18. Number of odd numbers that can be formed using the digits 2, 4, 6, 8 is
A. 4!
B. 4
C. 1
D. 0
Correct Answer : D
19. Neha has 10 different chocolates. In how many ways can she give them to two of her friends?
A. 10!
B. 2¹â°
C. 10
D. 9
Correct Answer : B
20. How many arrangements can be made by using all the letters of the word ‘‘COMPLEX"?
A. 720
B. 5040
C. 2520
D. 40320
Correct Answer : B
21. Find the number of ways of arranging ail the letters of the word ARRANGE.
(A)7!
(B) $\frac{7!}{{{\left( 2! \right)}^{2}}}$
(C)$\frac{7!}{2!}$
(D)4! 7!
A. A
B. B
C. C
D. D
Correct Answer : B
22. The number of diagonals in a regular decagon is
A. 35
B. 45
C. 40
D. 50
Correct Answer : A
23. In how many ways can 6 letters be posted into 4 letterboxes?
(A)${{6}^{4}}$
(B)${}^{6}{{P}_{4}}$
(C) ${{4}^{6}}$
(D) ${}^{6}{{C}_{4}}$
A. A
B. B
C. C
D. D
Correct Answer : C
24. A set has 8 elements. How many non-empty subsets are there for the sot?
A. 256
B. 8
C. 255
D. 7
Correct Answer : C
25. In how many ways can we select two vertices in a hexagon?
A. 12
B. 10
C. 15
D. 16
Correct Answer : C
26. In a library there are 10 research scholars. In how many ways can we select 4 of them?
A. 200
B. 210
C. 160
D. 180
Correct Answer : B
27. In how many ways can 6 persons be seated around a circular table?
A. 720
B. 120
C. 24
D. 60
Correct Answer : B
28. Find the number of diagonals in a regular octagon.
A. 16
B. 20
C. 18
D. 12
Correct Answer : B
29. Find the number of ways in which 8 delegates can be arranged around a table for a meeting.
A. 420
B. 360
C. 600
D. 840
Correct Answer : D
30. Number of ways of arranging 5 persons in a row is
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