Q. What is the 3rd term in the expansion of (x + 4)^6? (2020)
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A.
240x^4
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B.
360x^4
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C.
480x^4
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D.
600x^4
Solution
The 3rd term is C(6,2) * (4)^2 * (x)^4 = 15 * 16 * x^4 = 240x^4.
Correct Answer: B — 360x^4
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Q. What is the 4th term in the expansion of (2x - 3)^6? (2020)
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A.
-540
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B.
540
-
C.
-720
-
D.
720
Solution
The 4th term is C(6,3) * (2x)^3 * (-3)^3 = 20 * 8x^3 * -27 = -540.
Correct Answer: A — -540
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Q. What is the 5th term in the expansion of (2 + 3x)^6? (2023)
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A.
486
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B.
540
-
C.
729
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D.
810
Solution
The 5th term is given by 6C4 * (2)^(6-4) * (3x)^4 = 15 * 4 * 81x^4 = 4860x^4.
Correct Answer: B — 540
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Q. What is the 5th term in the expansion of (3x - 2)^7? (2023)
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A.
-1680x^3
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B.
1680x^3
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C.
-2520x^3
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D.
2520x^3
Solution
The 5th term is given by C(7,4) * (3x)^4 * (-2)^3 = 35 * 81 * (-8) = -1680x^3.
Correct Answer: A — -1680x^3
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Q. What is the coefficient of x^0 in the expansion of (2x - 3)^5? (2022)
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A.
-243
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B.
243
-
C.
-81
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D.
81
Solution
The constant term is C(5,5)(-3)^5 = -243.
Correct Answer: A — -243
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Q. What is the coefficient of x^0 in the expansion of (3x + 2)^5? (2022)
Solution
The coefficient of x^0 is C(5,5) * (3x)^0 * (2)^5 = 1 * 32 = 32.
Correct Answer: C — 64
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Q. What is the coefficient of x^0 in the expansion of (x + 1/x)^8? (2021)
Solution
The coefficient of x^0 occurs when k=4, which gives us 8C4 = 70.
Correct Answer: C — 70
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Q. What is the coefficient of x^1 in the expansion of (x + 1)^10? (2021)
Solution
The coefficient of x^1 is C(10,1)(1)^9 = 10.
Correct Answer: A — 10
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Q. What is the coefficient of x^1 in the expansion of (x - 1)^5?
Solution
The coefficient of x^1 is given by 5C1 * (-1)^4 = 5 * 1 = 5.
Correct Answer: A — -5
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Q. What is the coefficient of x^2 in the expansion of (2x - 1)^5? (2021)
Solution
The coefficient of x^2 is C(5,2) * (2)^2 * (-1)^3 = 10 * 4 * (-1) = -40.
Correct Answer: B — 20
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Q. What is the coefficient of x^2 in the expansion of (x + 3)^5?
Solution
The coefficient of x^2 is given by 5C2 * (3)^3 = 10 * 27 = 270.
Correct Answer: A — 45
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Q. What is the coefficient of x^2 in the expansion of (x + 4)^5?
-
A.
80
-
B.
100
-
C.
120
-
D.
160
Solution
The coefficient of x^2 is C(5,2) * 4^3 = 10 * 64 = 640.
Correct Answer: A — 80
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Q. What is the coefficient of x^2 in the expansion of (x + 5)^4?
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A.
50
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B.
100
-
C.
150
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D.
200
Solution
The coefficient of x^2 is C(4,2) * (5)^2 = 6 * 25 = 150.
Correct Answer: B — 100
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Q. What is the coefficient of x^2 in the expansion of (x - 2)^5?
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A.
-40
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B.
-20
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C.
20
-
D.
40
Solution
The coefficient of x^2 is given by 5C2 * (-2)^3 = 10 * (-8) = -80.
Correct Answer: A — -40
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Q. What is the coefficient of x^3 in the expansion of (5x + 2)^6? (2000) 2000
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A.
600
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B.
720
-
C.
800
-
D.
900
Solution
The coefficient of x^3 is C(6,3) * (5)^3 * (2)^3 = 20 * 125 * 8 = 20000.
Correct Answer: B — 720
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Q. What is the coefficient of x^3 in the expansion of (x + 5)^8?
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A.
2800
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B.
3360
-
C.
4000
-
D.
4200
Solution
The coefficient of x^3 is given by 8C3 * (5)^5 = 56 * 3125 = 175000.
Correct Answer: B — 3360
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Q. What is the coefficient of x^3 in the expansion of (x - 1)^5? (2022)
Solution
The coefficient of x^3 is C(5,3)(-1)^2 = 10.
Correct Answer: A — -10
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Q. What is the coefficient of x^3 in the expansion of (x - 2)^6?
-
A.
-80
-
B.
-120
-
C.
-240
-
D.
-720
Solution
The coefficient of x^3 is C(6,3) * (-2)^3 = 20 * (-8) = -160.
Correct Answer: B — -120
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Q. What is the coefficient of x^4 in the expansion of (2x + 5)^6? (2022)
-
A.
150
-
B.
300
-
C.
600
-
D.
450
Solution
The coefficient of x^4 is C(6,4) * (2)^4 * (5)^2 = 15 * 16 * 25 = 600.
Correct Answer: D — 450
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Q. What is the coefficient of x^4 in the expansion of (3x + 2)^6?
-
A.
540
-
B.
720
-
C.
810
-
D.
900
Solution
The coefficient of x^4 is C(6,4) * (3)^4 * (2)^2 = 15 * 81 * 4 = 4860.
Correct Answer: B — 720
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Q. What is the coefficient of x^4 in the expansion of (x + 1)^8? (2020)
Solution
The coefficient of x^4 is C(8,4) = 70.
Correct Answer: B — 56
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Q. What is the coefficient of x^4 in the expansion of (x + 2)^6?
Solution
The coefficient of x^4 is given by 6C4 * (2)^2 = 15 * 4 = 60.
Correct Answer: C — 90
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Q. What is the coefficient of x^5 in the expansion of (2x - 1)^6?
Solution
The coefficient of x^5 is C(6,5) * (2)^5 * (-1)^1 = 6 * 32 * (-1) = -192.
Correct Answer: D — 80
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Q. What is the coefficient of x^5 in the expansion of (x + 4)^7? (2020)
-
A.
672
-
B.
6720
-
C.
1680
-
D.
840
Solution
The coefficient of x^5 is C(7,5) * (4)^2 = 21 * 16 = 336.
Correct Answer: C — 1680
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Q. What is the coefficient of x^6 in the expansion of (x + 3)^8? (2020)
-
A.
56
-
B.
84
-
C.
112
-
D.
128
Solution
The coefficient of x^6 is C(8,6) * (3)^2 = 28 * 9 = 252.
Correct Answer: B — 84
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Q. What is the coefficient of x^6 in the expansion of (x + 3)^9? (2020)
Solution
The coefficient of x^6 is C(9,6)(3)^3 = 84 * 27 = 2268.
Correct Answer: B — 126
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Q. What is the coefficient of x^7 in the expansion of (2x - 3)^8? (2022)
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A.
-6720
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B.
6720
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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 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
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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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