1. Which of the following is the general expression for the binomial theorem for a positive integer ?
A.
B.
C.
D.
Answer: B
2. What does Pascal's Triangle represent in relation to the binomial theorem?
A. The sum of the coefficients of terms.
B. The powers of terms in a binomial expansion.
C. The coefficients of the terms in a binomial expansion.
D. The number of terms in a binomial expansion.
Answer: C
3. In the expansion of , how many terms will there be?
A.
B.
C.
D.
Answer: B
4. In Pascal’s Triangle, what is the value of the coefficient for the term corresponding to in the expansion of ?
A.
B.
C.
D.
Answer: B
5. Which mathematician is most closely associated with the modern form of the binomial theorem for integral ?
A. Blaise Pascal
B. Michael Stifel
C. Pingla
D. Chu-shi-kie
Answer: A
6. Using the binomial theorem, what is the expansion of ?
A.
B.
C.
D.
Answer: A
7. What is the value of when ?
A.
B.
C.
D.
Answer: C
8. The sum of coefficients in the expansion of is given by:
A.
B.
C.
D.
Answer: B
9. The expansion of contains which of the following terms?
A.
B.
C.
D.
Answer: A
10. In the binomial expansion of , what is the sum of the indices of and in any term?
A. 1
B.
C.
D. 2
Answer: B
11. In the expansion , what is the sign of the third term?
A. Always positive
B. Always negative
C. Positive if is odd, negative if is even
D. Negative if is odd, positive if is even
Answer: D
12. The coefficient of in the expansion of is:
A. 5
B. 10
C. 15
D. 20
Answer: C
13. In , the middle term when is odd is:
A.
B.
C.
D. None of the above
Answer: D
14. If , then represents:
A. The number of terms in the expansion
B. The coefficient of the term in the expansion
C. The product of and
D. The constant term
Answer: B
15. The constant term in the expansion of is:
A. 5
B. 10
C. 20
D. 60
Answer: C
16. Which of the following represents the general term in ?
A.
B.
C.
D.
Answer: C
17. Using the binomial theorem, the value of can be simplified as:
A.
B.
C.
D.
Answer: A
18. How many terms are in the expansion of ?
A. 6
B. 21
C. 56
D. 120
Answer: B
19. In the binomial expansion, which term is the largest when ?
A. The first term
B. The last term
C. The middle term
D. Depends on the value of
Answer: C
20. For , which term has a positive coefficient?
A. All terms when is even
B. All terms when is odd
C. Alternate terms when is odd
D. Alternate terms when is even
Answer: D
21. The sum of the coefficients in the expansion of is given by:
A.
B.
C.
D. None of the above
Answer: B
22. What is the expansion of when ?
A. 8
B. 16
C. 32
D. 64
Answer: B
23. The term in has a coefficient of:
A. 5
B. 10
C. 15
D. 20
Answer: C
24. Which of these is NOT true for Pascal’s Triangle?
A. It contains the coefficients of .
B. It can be generated using the formula .
C. It has entries in row .
D. It is unrelated to the Binomial Theorem.
Answer: D
25. The coefficient of in is:
A. 15
B. -15
C. 20
D. -20
Answer: B
26. What is the binomial coefficient for the 5th term in ?
A.
B.
C.
D.
Answer: B
27. The expansion of will have how many terms?
A. 3
B. 4
C. 5
D. 6
Answer: C
28. In the binomial expansion of , the middle term exists when:
A. is odd
B. is even
C. is greater than 10
D. is odd
Answer: B
29. Using the binomial theorem, expanded gives the coefficient of as:
A. 10
B. 15
C. 20
D. 35
Answer: C
30. What is the expansion of ?
A.
B.
C.
D.
Answer: A
31. The coefficient of the last term in any binomial expansion is always:
A.
B.
C.
D.
Answer: A
32. If , the sum of the terms is:
A.
B.
C.
D.
Answer: A
33. The value of equals:
A.
B.
C.
D.
Answer: A
34. Which of the following expansions is correct?
A.
B.
C.
D.
Answer: B
35. Which is a correct property of binomial coefficients?
A.
B.
C.
D.
Answer: B
36. The expansion of has which of the following coefficients for ?
A. 4
B. 5
C. 6
D. 8
Answer: C
37. The binomial coefficient is always equal to:
A.
B.
C.
D.
Answer: C
38. If is expanded, the coefficients of all terms:
A. Are always positive
B. Alternate between positive and negative
C. Depend on being odd or even
D. Are always negative
Answer: B
39. In the expansion of , the ratio of the coefficients of the terms and is:
A.
B.
C.
D.
Answer: A
40. The expansion of has how many terms?
A. 3
B. 4
C. 5
D. 6
Answer: B
41. In , the term independent of in the expansion of is:
A.
B.
C.
D.
Answer: A
42. The coefficient of in the expansion of is:
A. 6
B. 10
C. 15
D. 20
Answer: C
43. In the binomial expansion , what happens to the coefficients as approaches ?
A. They increase
B. They decrease
C. They first increase and then decrease
D. They remain constant
Answer: C
44. The expansion of gives the 3rd term as:
A.
B.
C.
D.
Answer: B
45. In , the total number of positive terms is:
A.
B.
C.
D.
Answer: A
46. The value of is:
A. 35
B. 28
C. 21
D. 15
Answer: A
47. Which term of is ?
A. 2nd term
B. 3rd term
C. 4th term
D. 5th term
Answer: C
48. If , the sum of the odd coefficients is:
A.
B.
C.
D. None of the above
Answer: A
49. Which of the following is the third term in the expansion of ?
A.
B.
C.
D.
Answer: D
50. In Pascal's Triangle, the sum of the elements in the 6th row is:
A. 16
B. 32
C. 64
D. 128
Answer: C
51. The coefficient of in is:
A. 10
B. 15
C. 20
D. 35
Answer: D
52. If is expanded, the coefficients of the -th and -th terms are:
A. Equal
B. Opposite
C. Add up to
D. Multiply to
Answer: A
53. The coefficient of in the expansion of is:
A. 80
B. 120
C. 160
D. 200
Answer: C
54. The binomial theorem for holds true for:
A. All values of
B. Only for positive integers
C. Only for
D. Only for
Answer: B
55. The number of terms in the expansion of is:
A. 12
B. 15
C. 20
D. 25
Answer: C
56. The coefficient of in is:
A. 10
B. 15
C. 20
D. 30
Answer: C
57. The coefficient of the term independent of in is:
A. 15
B. 20
C. 25
D. 30
Answer: A
58. Which of the following is the sum of coefficients in the expansion of ?
A. 8
B. 16
C. 64
D. 256
Answer: D
59. The expansion contains how many terms?
A. 5
B. 6
C. 7
D. 8
Answer: B
60. If the coefficient of in is 12, then is:
A. 2
B. 3
C. 4
D. 6
Answer: C
61. The binomial coefficient equals:
A.
B.
C.
D.
Answer: B
62. In , the total number of coefficients is:
A.
B.
C.
D.
Answer: A
63. Which term of is ?
A. 4th term
B. 5th term
C. 6th term
D. 7th term
Answer: B
64. The coefficient of in is:
A. 60
B. 80
C. 100
D. 120
Answer: D
65. In , if , the sum of all terms is:
A.
B.
C.
D.
Answer: B
66. The middle term in is:
A.
B.
C.
D.
Answer: A
67. If , the coefficient of is:
A.
B.
C.
D.
Answer: A
68. The coefficient of in is:
A.
B.
C.
D.
Answer: B
69. In , the coefficient of is:
A. -15
B. 15
C. -20
D. 20
Answer: D
70. The number of terms in the expansion of is:
A. 15
B. 21
C. 25
D. 35
Answer: B
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