Q. What is the coefficient of x^7 in the expansion of (2x - 3)^8? (2022)
-
A.
-6720
-
B.
6720
-
C.
-3360
-
D.
3360
Solution
The coefficient of x^7 is C(8,7)(2)^7(-3)^1 = 8 * 128 * -3 = -3072.
Correct Answer: A — -6720
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Q. What is the constant term in the expansion of (2x^2 - 3/x)^5? (2020)
Solution
The constant term occurs when 2k - 5 = 0, k = 2. The term is C(5,2)(-3)^3(2^2) = 10 * -27 * 4 = -1080.
Correct Answer: A — -243
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Q. What is the sum of the coefficients in the expansion of (2 + 3)^4? (2022)
-
A.
81
-
B.
64
-
C.
100
-
D.
125
Solution
The sum of the coefficients is (2 + 3)^4 = 5^4 = 625.
Correct Answer: A — 81
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Q. What is the sum of the coefficients in the expansion of (x + 2)^5? (2021)
Solution
The sum of the coefficients is found by substituting x=1. So, (1 + 2)^5 = 3^5 = 243.
Correct Answer: B — 64
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Q. What is the term containing x^2 in the expansion of (3x - 4)^6?
-
A.
-1440
-
B.
720
-
C.
-720
-
D.
1440
Solution
The term containing x^2 is given by C(6,2) * (3x)^2 * (-4)^(6-2) = 15 * 9 * 256 = -1440.
Correct Answer: A — -1440
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Q. What is the term containing x^2 in the expansion of (x + 4)^6?
-
A.
240
-
B.
360
-
C.
480
-
D.
600
Solution
The term containing x^2 is given by C(6,2) * (4)^4 * (x)^2 = 15 * 256 * x^2 = 3840.
Correct Answer: C — 480
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Q. What is the term containing x^5 in the expansion of (2x + 3)^6?
-
A.
540
-
B.
720
-
C.
810
-
D.
900
Solution
The term containing x^5 occurs when k = 5. Using the binomial theorem, the term is C(6,5) * (2x)^5 * 3^1 = 6 * 32 * 3 = 576.
Correct Answer: B — 720
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Q. What is the term containing x^5 in the expansion of (2x - 3)^8?
-
A.
-6720
-
B.
6720
-
C.
-13440
-
D.
13440
Solution
The term containing x^5 occurs when k = 5. Using the binomial theorem, the term is C(8,5) * (2x)^5 * (-3)^3 = 56 * 32 * (-27) = -48384.
Correct Answer: A — -6720
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Q. What is the term independent of x in the expansion of (2x - 3)^8?
-
A.
-256
-
B.
256
-
C.
-512
-
D.
512
Solution
The term independent of x is given by C(8,4) * (2x)^4 * (-3)^4 = 70 * 16 * 81 = -256.
Correct Answer: A — -256
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Q. What is the term independent of x in the expansion of (3x - 2)^6?
Solution
The term independent of x occurs when k = 3. Using the binomial theorem, the term is C(6,3) * (3x)^3 * (-2)^(6-3) = 20 * 27 * -8 = -4320.
Correct Answer: C — 40
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Q. What is the value of (2 + 3)^3?
Solution
Using the binomial theorem, (2 + 3)^3 = C(3,0)(2)^3 + C(3,1)(2)^2(3) + C(3,2)(2)(3)^2 + C(3,3)(3)^3 = 8 + 36 + 54 + 27 = 125.
Correct Answer: B — 30
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Q. What is the value of (2 - 3)^5?
-
A.
-1
-
B.
-32
-
C.
-243
-
D.
-125
Solution
Using the binomial theorem, (2 - 3)^5 = (-1)^5 = -1.
Correct Answer: D — -125
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Q. What is the value of (3 - 2)^5 using the binomial theorem?
Solution
Using the binomial theorem, (3 - 2)^5 = 1^5 = 1.
Correct Answer: A — 1
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Q. What is the value of (x + 1)^5 when x = 2?
-
A.
32
-
B.
64
-
C.
128
-
D.
256
Solution
Using the binomial theorem, (x + 1)^5 = C(5,0)(2)^5 + C(5,1)(2)^4 + C(5,2)(2)^3 + C(5,3)(2)^2 + C(5,4)(2)^1 + C(5,5)(2)^0 = 32 + 80 + 80 + 40 + 10 + 1 = 243.
Correct Answer: C — 128
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Q. What is the value of the 3rd term in the expansion of (3x - 4)^5? (2020)
-
A.
-240
-
B.
240
-
C.
-180
-
D.
180
Solution
The 3rd term is C(5,2) * (3x)^3 * (-4)^2 = 10 * 27x^3 * 16 = -240.
Correct Answer: A — -240
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Q. What is the value of the 5th term in the expansion of (3x - 2)^6? (2023)
-
A.
-540
-
B.
540
-
C.
720
-
D.
360
Solution
The 5th term is given by C(6,4) * (3x)^4 * (-2)^2 = 15 * 81 * 4 = -4860.
Correct Answer: A — -540
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Q. What is the value of the coefficient of x^4 in the expansion of (x - 2)^6? (2023)
-
A.
-15
-
B.
-60
-
C.
-90
-
D.
-120
Solution
The coefficient of x^4 is C(6,4) * (-2)^2 = 15 * 4 = -60.
Correct Answer: B — -60
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Q. What is the value of the coefficient of x^5 in the expansion of (x + 1/2)^8?
-
A.
56
-
B.
112
-
C.
128
-
D.
64
Solution
The coefficient of x^5 is given by 8C5 * (1/2)^3 = 56 * 1/8 = 7.
Correct Answer: A — 56
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Q. What is the value of the coefficient of x^5 in the expansion of (x + 2)^7?
Solution
The coefficient of x^5 is given by 7C5 * (2)^2 = 21 * 4 = 84.
Correct Answer: C — 56
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Q. What is the value of the term containing x^4 in the expansion of (x + 1/2)^8? (2020)
Solution
The term containing x^4 is C(8,4) * (1/2)^4 = 70 * 1/16 = 4.375.
Correct Answer: A — 70
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Q. What is the value of the term containing x^5 in the expansion of (x + 1/2)^8? (2020)
Solution
The term containing x^5 is C(8,5)(1/2)^3 = 56 * 1/8 = 7.
Correct Answer: B — 56
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Q. What is the value of the term containing x^5 in the expansion of (x + 2)^8? (2020)
-
A.
112
-
B.
128
-
C.
256
-
D.
64
Solution
The term containing x^5 is C(8,5)(2)^3 = 56 * 8 = 448.
Correct Answer: B — 128
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