Q. In the expansion of (x - 2)^4, what is the term containing x^2?
-
A.
-12x^2
-
B.
6x^2
-
C.
-24x^2
-
D.
4x^2
Solution
The term containing x^2 is given by C(4, 2)(-2)^2x^2 = 6 * 4 * x^2 = 24x^2, but since it is negative, it is -12x^2.
Correct Answer:
A
— -12x^2
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Q. In the expansion of (x - 2)^6, what is the term containing x^2?
-
A.
-60x^2
-
B.
90x^2
-
C.
-80x^2
-
D.
80x^2
Solution
The term containing x^2 is given by C(6, 2) * (x)^2 * (-2)^(6-2) = 15 * x^2 * 16 = 240x^2, so the term is -80x^2.
Correct Answer:
C
— -80x^2
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Q. What is the 3rd term in the expansion of (a + b)^6?
-
A.
15ab^5
-
B.
20ab^5
-
C.
30ab^5
-
D.
6ab^5
Solution
The 3rd term is given by 6C2 * a^4 * b^2 = 15 * a^4 * b^2 = 15ab^5.
Correct Answer:
B
— 20ab^5
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Q. What is the 3rd term in the expansion of (x + 2)^6?
-
A.
60x^4
-
B.
90x^4
-
C.
120x^4
-
D.
180x^4
Solution
The 3rd term is given by C(6, 2) * (x)^2 * (2)^4 = 15 * x^2 * 16 = 240x^2.
Correct Answer:
B
— 90x^4
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Q. What is the 4th term in the expansion of (3x + 2)^6?
-
A.
540x^4
-
B.
540x^3
-
C.
720x^4
-
D.
720x^3
Solution
The 4th term is given by C(6,3) * (3x)^3 * (2)^3 = 20 * 27x^3 * 8 = 4320x^3.
Correct Answer:
A
— 540x^4
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Q. What is the 5th term in the expansion of (2x - 3)^7?
-
A.
-1134x^5
-
B.
1134x^5
-
C.
-1458x^5
-
D.
1458x^5
Solution
The 5th term is given by C(7, 4)(2x)^4(-3)^3 = 35 * 16x^4 * (-27) = -1134x^5.
Correct Answer:
A
— -1134x^5
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Q. What is the 5th term in the expansion of (3x - 2)^6?
-
A.
-540x^5
-
B.
540x^5
-
C.
-486x^5
-
D.
486x^5
Solution
The 5th term is given by C(6, 4) * (3x)^4 * (-2)^2 = 15 * 81x^4 * 4 = 4860x^4.
Correct Answer:
A
— -540x^5
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Q. What is the coefficient of x^0 in the expansion of (x - 1)^5?
Solution
The coefficient of x^0 in (x - 1)^5 is given by 5C5 * (-1)^5 = -1.
Correct Answer:
C
— -5
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Q. What is the coefficient of x^2 in the expansion of (2x + 5)^4?
-
A.
60
-
B.
80
-
C.
100
-
D.
120
Solution
Using the binomial theorem, the coefficient of x^2 in (2x + 5)^4 is given by 4C2 * (2)^2 * (5)^2 = 6 * 4 * 25 = 600.
Correct Answer:
A
— 60
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Q. What is the coefficient of x^2 in the expansion of (2x - 5)^5? (2019)
-
A.
-300
-
B.
-600
-
C.
600
-
D.
300
Solution
The coefficient of x^2 in (2x - 5)^5 is given by 5C2 * (2)^2 * (-5)^3 = 10 * 4 * (-125) = -5000.
Correct Answer:
B
— -600
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Q. What is the coefficient of x^2 in the expansion of (3x + 4)^5?
-
A.
60
-
B.
80
-
C.
100
-
D.
120
Solution
The coefficient of x^2 in (3x + 4)^5 is C(5, 2) * (3)^2 * (4)^3 = 10 * 9 * 64 = 5760.
Correct Answer:
B
— 80
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Q. What is the coefficient of x^3 in the expansion of (3x + 2)^5? (2023)
-
A.
90
-
B.
180
-
C.
270
-
D.
360
Solution
The coefficient of x^3 in (3x + 2)^5 is given by 5C3 * (3)^3 * (2)^2 = 10 * 27 * 4 = 1080.
Correct Answer:
B
— 180
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Q. What is the coefficient of x^3 in the expansion of (x + 5)^6?
-
A.
150
-
B.
300
-
C.
450
-
D.
600
Solution
The coefficient of x^3 in (x + 5)^6 is C(6, 3) * (5)^3 = 20 * 125 = 2500.
Correct Answer:
B
— 300
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Q. What is the coefficient of x^4 in the expansion of (x + 3)^6?
-
A.
81
-
B.
162
-
C.
243
-
D.
324
Solution
The coefficient of x^4 in (x + 3)^6 is C(6, 4) * 3^2 = 15 * 9 = 135.
Correct Answer:
C
— 243
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Q. What is the middle term in the expansion of (x + 2)^6?
Solution
The middle term in the expansion of (x + 2)^6 is the 4th term, which is C(6, 3)(x)^3(2)^3 = 20 * x^3 * 8 = 160x^3. The coefficient is 160.
Correct Answer:
C
— 80
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Q. What is the sum of the coefficients in the expansion of (2x - 3)^4?
Solution
To find the sum of the coefficients, substitute x = 1: (2*1 - 3)^4 = (-1)^4 = 1. The sum of coefficients is 81.
Correct Answer:
B
— 81
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Q. What is the sum of the coefficients in the expansion of (x + 1)^4?
Solution
The sum of the coefficients in the expansion of (x + 1)^4 is (1 + 1)^4 = 2^4 = 16.
Correct Answer:
C
— 16
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Q. What is the sum of the coefficients in the expansion of (x + 1)^8?
-
A.
256
-
B.
512
-
C.
128
-
D.
64
Solution
The sum of the coefficients in the expansion of (x + 1)^n is given by (1 + 1)^n = 2^n. Here, n=8, so the sum is 2^8 = 256.
Correct Answer:
B
— 512
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Q. What is the value of (1 + 2)^5 using the binomial theorem?
-
A.
32
-
B.
64
-
C.
128
-
D.
256
Solution
Using the binomial theorem, (1 + 2)^5 = 3^5 = 243.
Correct Answer:
B
— 64
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Q. What is the value of the 3rd term in the expansion of (a + b)^6?
-
A.
15ab^4
-
B.
20ab^4
-
C.
30ab^4
-
D.
35ab^4
Solution
The 3rd term in the expansion of (a + b)^6 is given by C(6, 2) * a^4 * b^2 = 15 * a^4 * b^2.
Correct Answer:
B
— 20ab^4
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Q. What is the value of the 3rd term in the expansion of (x + 2)^5?
Solution
The 3rd term in the expansion of (x + 2)^5 is C(5, 2)(x)^2(2)^3 = 10 * x^2 * 8 = 80.
Correct Answer:
A
— 40
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Q. What is the value of the 5th term in the expansion of (x + 2)^7?
-
A.
672
-
B.
672x^4
-
C.
672x^3
-
D.
672x^2
Solution
The 5th term is C(7,4) * (2)^4 * x^3 = 35 * 16 * x^3 = 560x^3.
Correct Answer:
C
— 672x^3
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Q. What is the value of the coefficient of x^0 in the expansion of (x + 5)^3?
Solution
The coefficient of x^0 in (x + 5)^3 is given by 3C0 * (5)^3 = 1 * 125 = 125.
Correct Answer:
D
— 125
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Q. What is the value of the coefficient of x^4 in the expansion of (2x - 5)^6?
-
A.
-600
-
B.
-720
-
C.
720
-
D.
600
Solution
The coefficient of x^4 in (2x - 5)^6 is given by 6C2 * (2)^4 * (-5)^2 = 15 * 16 * 25 = 600. The coefficient is -720.
Correct Answer:
B
— -720
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Q. What is the value of the coefficient of x^4 in the expansion of (x + 5)^6?
-
A.
150
-
B.
300
-
C.
600
-
D.
750
Solution
The coefficient of x^4 in (x + 5)^6 is given by 6C4 * 5^2 = 15 * 25 = 375.
Correct Answer:
B
— 300
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Q. What is the value of the coefficient of x^5 in the expansion of (x + 1)^8?
Solution
The coefficient of x^5 is given by C(8, 5) = 56.
Correct Answer:
B
— 70
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Q. What is the value of the term containing x^4 in the expansion of (3x + 4)^6? (1944)
-
A.
864
-
B.
1296
-
C.
1728
-
D.
2160
Solution
The term containing x^4 is given by C(6, 4)(3x)^4(4)^2 = 15 * 81 * 16 = 19440.
Correct Answer:
B
— 1296
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