1. The value of $n$ when $^{11}P_n = 11 \cdot 10 \cdot 9$ is:
2. factorial form of $n(n^2-1)=?$
3. Number of words that can be formed from the letters of the word "PLANE'' using all letters at a time is equal to:
4. The value of $4! \cdot 0! \cdot 1!$ is
5. ${}^nC_r + {}^nC_{r-1}=?$
6. In how many ways a cricket team of 11 players out of 15 can be selected if the captain must be included in each way:
7. ${}^nC_r$ is valid only if
8. $(n - 1)(n - 2)(n - 3) \ldots (n - r + 1) = ?$
9. Factorial form of $n(n - 1)(n - 2) = ?$
10. $n$ different objects taken all at a time can be arranged in:
11. From $A=\{1,3,5,7,9\}$ and $B=\{2,4,6,8\}$ if a Cartesian product $A \times B$ is chosen, then number of ways that $a+b=9$;
12. The expression $\frac{(n - 1)!(n - 2)!}{(n!)^2}$ reduced to
13. The number of ways in which $r$ letters can be posted in n-letter boxes in a town in;
14. If ${}^{15}C_{3r}={}^{15}C_{r+3}$ then value of $r$ is:
15. The number of permutations of the word "ANAMA" is:
16. If $r = n$, then $^nP_r$ equals:
17. $\frac{n!}{r!(n-r)!}$ is equal to:
18. A student has to answer 10 out of 12 questions in an examination such that he must be choose at least 4 from first 5 questions. The nature of choice is:
19. If $n$ is a positive integer, then factorial of $n$ is denoted by ---
21. The factorial form of $\frac{10.9}{2.1}$ is
22. $\frac{^nP_r}{r!}$ is equal to:
23. Let $A=\{1,2,3,...,20\}$ Find the number of ways that the integer chosen is a prime number.
24. $^nP_r$ is equal to (where $n > 0$, $r > 0$):
25. If $^nC_r = ^nC_q$, which of the following must be true:
26. The value of permutation $^{20}P_3$ is:
27. The total number of 6-digit numbers in which all the odd and only odd digit appear is
28. If $3{}^nP_3={}^nP_4$ then value of n is:
29. If $^nC_5 = ^nC_4$, then $n$ is equal to:
30. ${}^nC_{n-r}$ is equal to:
31. If $n$ is a negative integer then $n!$ is
32. The value of $n$ if $^nC_{10} = \frac{12 \times 11}{2!}$:
33. Circular permutation of $n$ non-living things is given by:
34. ${}^nC_{r}={}^nC_{n-r}$ is useful when
35. Factorial notation was introduced by
36. Number of ways of arrangements of the word $\textbf{GARDEN}$
37. If ${}^nC_4={}^nC_{10}$ then value of $n$ is;
38. The product of r consecutive positive numbers in divisible by:
39. The value of $\frac{4!}{0!}$ is
40. Factorial form $\frac{(n+1)(n)(n - 1)}{3 \cdot 2 \cdot 1}$ is
41. Number of ways of arranging 5 keys in a circular ring is:
42. 5 persons can be seated at a round table in how many ways?
44. ${}^nC_r \times r!$=________?
45. If $r=n$, ${}^nC_r$ is equal to ________
