Q. Find the coefficient of x^0 in the expansion of (2x - 3)^3.
-
A.
-27
-
B.
-24
-
C.
-18
-
D.
-12
Solution
The coefficient of x^0 is (-3)^3 = -27.
Correct Answer: A — -27
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Q. Find the coefficient of x^1 in the expansion of (x + 2)^5.
Solution
The coefficient of x^1 is C(5,1) * 2^4 = 5 * 16 = 80.
Correct Answer: B — 20
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Q. Find the coefficient of x^1 in the expansion of (x + 4)^3.
Solution
The coefficient of x^1 is C(3,1) * (4)^2 = 3 * 16 = 48.
Correct Answer: A — 12
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Q. Find the coefficient of x^2 in the expansion of (2x + 3)^6.
-
A.
540
-
B.
720
-
C.
810
-
D.
960
Solution
The coefficient of x^2 is given by 6C2 * (2)^2 * (3)^4 = 15 * 4 * 81 = 4860.
Correct Answer: A — 540
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Q. Find the coefficient of x^2 in the expansion of (2x - 3)^4.
Solution
Using the binomial theorem, the coefficient of x^2 in (2x - 3)^4 is given by 4C2 * (2)^2 * (-3)^2 = 6 * 4 * 9 = 216.
Correct Answer: C — 54
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Q. Find the coefficient of x^2 in the expansion of (3x - 4)^6.
-
A.
540
-
B.
720
-
C.
480
-
D.
360
Solution
The coefficient of x^2 is C(6,2) * (3)^2 * (-4)^4 = 15 * 9 * 256 = 34560.
Correct Answer: B — 720
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Q. Find the coefficient of x^2 in the expansion of (x + 4)^5. (2023)
-
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. Find the coefficient of x^2 in the expansion of (x - 5)^5.
-
A.
100
-
B.
150
-
C.
200
-
D.
250
Solution
The coefficient of x^2 is C(5,2) * (-5)^3 = 10 * (-125) = -1250.
Correct Answer: A — 100
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Q. Find the coefficient of x^3 in the expansion of (2x - 3)^4. (2022)
-
A.
-54
-
B.
-108
-
C.
108
-
D.
54
Solution
The coefficient of x^3 is C(4,3) * (2)^3 * (-3)^1 = 4 * 8 * (-3) = -96.
Correct Answer: B — -108
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Q. Find the coefficient of x^3 in the expansion of (2x - 3)^6.
-
A.
-540
-
B.
-720
-
C.
540
-
D.
720
Solution
The coefficient of x^3 is C(6,3)(2)^3(-3)^3 = 20 * 8 * (-27) = -4320.
Correct Answer: A — -540
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Q. Find the coefficient of x^3 in the expansion of (x + 1/2)^6.
Solution
The coefficient of x^3 is C(6,3) * (1/2)^3 = 20 * 1/8 = 2.5.
Correct Answer: B — 15
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Q. Find the coefficient of x^3 in the expansion of (x + 2)^6.
-
A.
80
-
B.
120
-
C.
160
-
D.
240
Solution
The coefficient of x^3 is C(6,3) * (2)^3 = 20 * 8 = 160.
Correct Answer: B — 120
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Q. Find the coefficient of x^3 in the expansion of (x - 1)^5.
Solution
The coefficient of x^3 is C(5,3) * (-1)^2 = 10.
Correct Answer: A — -10
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Q. Find the coefficient of x^3 in the expansion of (x - 1)^6.
-
A.
-20
-
B.
-15
-
C.
-10
-
D.
-6
Solution
The coefficient of x^3 is C(6,3) * (-1)^3 = 20 * (-1) = -20.
Correct Answer: A — -20
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Q. Find the coefficient of x^3 in the expansion of (x - 1)^7.
-
A.
-35
-
B.
-21
-
C.
-7
-
D.
-49
Solution
The coefficient of x^3 is given by 7C3 * (-1)^4 = 35.
Correct Answer: A — -35
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Q. Find the coefficient of x^3 in the expansion of (x - 2)^5.
-
A.
-40
-
B.
-80
-
C.
-60
-
D.
-100
Solution
The coefficient of x^3 is C(5,3) * (-2)^2 = 10 * 4 = 40.
Correct Answer: A — -40
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Q. Find the coefficient of x^3 in the expansion of (x - 3)^5.
-
A.
-135
-
B.
-90
-
C.
-60
-
D.
-45
Solution
The coefficient of x^3 is C(5,3) * (-3)^2 = 10 * 9 = -90.
Correct Answer: A — -135
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Q. Find the coefficient of x^4 in the expansion of (2x - 3)^5.
-
A.
-240
-
B.
-360
-
C.
-480
-
D.
-600
Solution
The coefficient of x^4 is C(5,4) * (2)^4 * (-3)^1 = 5 * 16 * (-3) = -240.
Correct Answer: A — -240
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Q. Find the coefficient of x^4 in the expansion of (2x - 3)^6.
-
A.
540
-
B.
720
-
C.
810
-
D.
900
Solution
The coefficient of x^4 is C(6,4) * (2)^4 * (-3)^2 = 15 * 16 * 9 = 2160.
Correct Answer: A — 540
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Q. Find the coefficient of x^4 in the expansion of (3x + 2)^5. (2022)
-
A.
240
-
B.
360
-
C.
480
-
D.
600
Solution
The coefficient of x^4 is C(5,4)(3)^4(2)^1 = 5 * 81 * 2 = 810.
Correct Answer: B — 360
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Q. Find the coefficient of x^4 in the expansion of (3x - 2)^6.
-
A.
540
-
B.
720
-
C.
810
-
D.
960
Solution
Using the binomial theorem, the coefficient of x^4 in (3x - 2)^6 is given by 6C4 * (3)^4 * (-2)^2 = 15 * 81 * 4 = 4860.
Correct Answer: C — 810
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Q. Find the coefficient of x^4 in the expansion of (x + 1)^6.
Solution
The coefficient of x^4 is C(6,4) * 1^2 = 15.
Correct Answer: B — 20
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Q. Find the coefficient of x^4 in the expansion of (x + 1)^8.
Solution
The coefficient of x^4 is C(8, 4) = 70.
Correct Answer: A — 70
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Q. Find the coefficient of x^4 in the expansion of (x + 2)^6.
Solution
The coefficient of x^4 is C(6,4) * (2)^2 = 15 * 4 = 60.
Correct Answer: B — 30
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Q. Find the coefficient of x^4 in the expansion of (x + 3)^6.
-
A.
81
-
B.
162
-
C.
243
-
D.
729
Solution
The coefficient of x^4 is C(6,4) * (3)^2 = 15 * 9 = 135.
Correct Answer: C — 243
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Q. Find the coefficient of x^4 in the expansion of (x + 5)^7.
-
A.
210
-
B.
1260
-
C.
1750
-
D.
2450
Solution
The coefficient of x^4 is given by C(7,4) * 5^3 = 35 * 125 = 4375.
Correct Answer: B — 1260
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Q. Find the coefficient of x^4 in the expansion of (x - 1)^5.
Solution
The coefficient of x^4 is C(5,4) * (-1)^1 = 5 * (-1) = -5.
Correct Answer: C — -10
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Q. Find the coefficient of x^4 in the expansion of (x - 5)^6.
-
A.
150
-
B.
200
-
C.
250
-
D.
300
Solution
The coefficient of x^4 is given by C(6,4) * (-5)^2 = 15 * 25 = 375.
Correct Answer: B — 200
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Q. Find the coefficient of x^5 in the expansion of (2x - 3)^6. (2022)
-
A.
-540
-
B.
540
-
C.
-720
-
D.
720
Solution
The coefficient of x^5 is C(6,5) * (2)^5 * (-3)^1 = 6 * 32 * (-3) = -576.
Correct Answer: A — -540
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Q. Find the coefficient of x^5 in the expansion of (2x - 3)^7. (2023)
-
A.
168
-
B.
252
-
C.
336
-
D.
504
Solution
The coefficient of x^5 is C(7,5) * (2)^5 * (-3)^2 = 21 * 32 * 9 = 6048.
Correct Answer: B — 252
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