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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Q. Find the coefficient of x^5 in the expansion of (2x - 3)^8.
-
A.
-6720
-
B.
6720
-
C.
-3360
-
D.
3360
Solution
The coefficient of x^5 is C(8,5) * (2)^5 * (-3)^3 = 56 * 32 * (-27) = -6720.
Correct Answer: A — -6720
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Q. Find the coefficient of x^5 in the expansion of (x + 1)^7.
Solution
The coefficient of x^5 is C(7,5) = 21.
Correct Answer: C — 35
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Q. Find the coefficient of x^5 in the expansion of (x + 2)^7.
Solution
The coefficient of x^5 is C(7,5) * 2^2 = 21 * 4 = 84.
Correct Answer: C — 56
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Q. Find the constant term in the expansion of (3x - 4/x)^5.
Solution
The constant term occurs when the power of x is zero. The term is given by 5C2 * (3x)^2 * (-4/x)^3 = 10 * 9 * (-64) = -5760.
Correct Answer: A — -64
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Q. Find the constant term in the expansion of (x - 2/x)^6. (2022)
Solution
The constant term occurs when the power of x is zero. Setting 6 - 2k = 0 gives k = 3. The term is C(6,3)(-2)^3 = -64.
Correct Answer: A — -64
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Q. Find the term containing x^3 in the expansion of (x - 1)^5.
Solution
The term containing x^3 is C(5,3) * x^3 * (-1)^2 = 10 * x^3 * 1 = 10.
Correct Answer: C — -10
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Q. Find the term independent of x in the expansion of (x^2 - 2x + 3)^4. (2022)
Solution
The term independent of x occurs when the powers of x cancel out. The term is 81.
Correct Answer: A — 81
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Q. Find the term independent of x in the expansion of (x^2 - 3x + 1)^5. (2023)
Solution
The term independent of x occurs when the powers of x cancel out. The term is C(5,2)(-3)^2(1)^3 = 45.
Correct Answer: A — -15
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Q. Find the term independent of x in the expansion of (x^2 - 4x + 4)^4. (2020)
Solution
The expression can be rewritten as (x - 2)^4. The term independent of x occurs when k = 4, which gives us (-2)^4 = 16.
Correct Answer: C — 256
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Q. Find the value of (3 + 2)^3 using the binomial theorem.
Solution
Using the binomial theorem, (3 + 2)^3 = C(3,0) * 3^3 * 2^0 + C(3,1) * 3^2 * 2^1 + C(3,2) * 3^1 * 2^2 + C(3,3) * 3^0 * 2^3 = 27 + 54 + 36 + 8 = 125.
Correct Answer: B — 27
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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^0?
Solution
The coefficient of x^0 is given by 4C4 * (2x)^0 * (3)^4 = 1 * 81 = 81.
Correct Answer: A — 81
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Q. In the expansion of (2x + 5)^3, what is the coefficient of x?
Solution
The coefficient of x is given by 3C1 * (2)^1 * (5)^2 = 3 * 2 * 25 = 150.
Correct Answer: B — 45
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Q. In the expansion of (2x - 5)^5, what is the coefficient of x^2? (2021)
-
A.
-300
-
B.
-600
-
C.
600
-
D.
300
Solution
The coefficient of x^2 is C(5,2) * (2)^2 * (-5)^3 = 10 * 4 * (-125) = -5000.
Correct Answer: A — -300
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Q. In the expansion of (2x - 5)^5, what is the coefficient of x^3? (2021)
-
A.
150
-
B.
300
-
C.
450
-
D.
600
Solution
The coefficient of x^3 is C(5,3) * (2)^3 * (-5)^2 = 10 * 8 * 25 = 2000.
Correct Answer: C — 450
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Q. In the expansion of (2x - 5)^6, what is the coefficient of x^2? (2021)
-
A.
-150
-
B.
-300
-
C.
300
-
D.
150
Solution
The coefficient of x^2 is C(6,2) * (2)^2 * (-5)^4 = 15 * 4 * 625 = -37500.
Correct Answer: A — -150
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Q. In the expansion of (2x - 5)^6, what is the coefficient of x^3? (2020)
-
A.
-600
-
B.
-720
-
C.
720
-
D.
600
Solution
The coefficient of x^3 is C(6,3)(2)^3(-5)^3 = 20 * 8 * -125 = -20000.
Correct Answer: B — -720
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Q. In the expansion of (3x - 2)^6, what is the coefficient of x^4? (2022)
-
A.
540
-
B.
810
-
C.
729
-
D.
486
Solution
The coefficient of x^4 is given by 6C4 * (3)^4 * (-2)^2 = 15 * 81 * 4 = 4860.
Correct Answer: A — 540
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Q. In the expansion of (3x - 4)^4, what is the coefficient of x^2? (2023)
-
A.
-144
-
B.
-216
-
C.
216
-
D.
144
Solution
The coefficient of x^2 is C(4,2)(3)^2(-4)^2 = 6 * 9 * 16 = -864.
Correct Answer: B — -216
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Q. In the expansion of (x + 3)^4, what is the coefficient of x^3? (2023)
Solution
The coefficient of x^3 is C(4,3) * (3)^1 = 4 * 3 = 12.
Correct Answer: A — 36
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Q. In the expansion of (x - 1)^5, what is the coefficient of x^3?
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 3rd term in the expansion of (2x + 3)^4?
-
A.
108x^2
-
B.
216x^2
-
C.
324x^2
-
D.
432x^2
Solution
The 3rd term is given by C(4,2) * (2x)^2 * (3)^2 = 6 * 4x^2 * 9 = 216x^2.
Correct Answer: B — 216x^2
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Q. What is the 3rd term in the expansion of (2x + 5)^6? (2000)
-
A.
600x^4
-
B.
1500x^4
-
C.
1800x^4
-
D.
2000x^4
Solution
The 3rd term is given by C(6,2) * (2x)^2 * (5)^4 = 15 * 4 * 625 = 37500.
Correct Answer: B — 1500x^4
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Q. What is the 3rd term in the expansion of (2x - 3)^5? (2022)
-
A.
-90x^3
-
B.
90x^3
-
C.
-60x^3
-
D.
60x^3
Solution
The 3rd term is C(5,2) * (2x)^3 * (-3)^2 = 10 * 8x^3 * 9 = -720x^3.
Correct Answer: A — -90x^3
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Q. What is the 3rd term in the expansion of (x + 2)^5? (2021)
Solution
The 3rd term is given by C(5,2) * (x)^3 * (2)^2 = 10 * x^3 * 4 = 40.
Correct Answer: C — 60
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Q. What is the 3rd term in the expansion of (x + 2)^8? (2022)
-
A.
112
-
B.
128
-
C.
256
-
D.
64
Solution
The 3rd term is given by 8C2 * (2)^2 * (x)^6 = 28 * 4 * x^6 = 112x^6.
Correct Answer: A — 112
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Q. What is the 3rd term in the expansion of (x + 3)^4? (2023)
-
A.
36x^2
-
B.
54x^2
-
C.
72x^2
-
D.
108x^2
Solution
The 3rd term is C(4,2) * (3)^2 * (x)^2 = 6 * 9 * x^2 = 54x^2.
Correct Answer: B — 54x^2
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Q. What is the 3rd term in the expansion of (x + 3)^5? (2023)
-
A.
45
-
B.
90
-
C.
135
-
D.
180
Solution
The 3rd term is C(5,2) * (3)^2 * (x)^3 = 10 * 9 * x^3 = 90.
Correct Answer: B — 90
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Q. What is the 3rd term in the expansion of (x + 3)^7? (2023)
-
A.
189
-
B.
441
-
C.
729
-
D.
1024
Solution
The 3rd term is C(7,2) * (3)^2 * (x)^5 = 21 * 9 * x^5 = 189.
Correct Answer: B — 441
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Q. What is the 3rd term in the expansion of (x + 4)^5? (2023)
-
A.
80x^3
-
B.
160x^3
-
C.
240x^3
-
D.
320x^3
Solution
The 3rd term is given by C(5,2) * (4)^2 * (x)^3 = 10 * 16 * x^3 = 160x^3.
Correct Answer: C — 240x^3
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