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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 (5x + 2)^6? (2000) 2000

A. 600
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)^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^3 in the expansion of (x + 5)^8?

A. 2800
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)

A. -10
B. 10
C. 5
D. 15

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)^5?

A. 10
B. 20
C. 30
D. 40

Solution

The coefficient of x^3 is C(5,3) * (-2)^2 = 10 * 4 = 40.

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 + 3)^6?

A. 540
B. 720
C. 810
D. 960

Solution

The coefficient of x^4 is C(6,4) * (2)^4 * (3)^(6-4) = 15 * 16 * 9 = 2160.

Correct Answer: C — 810

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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 (2x - 3)^5?

A. 240
B. 300
C. 360
D. 420

Solution

The coefficient of x^4 is C(5, 4) * (2)^4 * (-3)^1 = 5 * 16 * (-3) = -240.

Correct Answer: C — 360

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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 (3x - 2)^5? (2021)

A. 90
B. 120
C. 150
D. 180

Solution

The coefficient of x^4 is given by 5C4 * (3)^4 * (-2)^1 = 5 * 81 * (-2) = -810.

Correct Answer: C — 150

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Q. What is the coefficient of x^4 in the expansion of (x + 1)^6?

A. 15
B. 20
C. 30
D. 35

Solution

The coefficient of x^4 is C(6,4) = 15.

Correct Answer: D — 35

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Q. What is the coefficient of x^4 in the expansion of (x + 1)^8? (2020)

A. 70
B. 56
C. 28
D. 8

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?

A. 15
B. 60
C. 90
D. 120

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^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 coefficient of x^5 in the expansion of (2x - 1)^6?

A. 32
B. 48
C. 64
D. 80

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 + 1/2)^10?

A. 252
B. 210
C. 120
D. 300

Solution

The coefficient of x^5 is C(10,5) * (1/2)^5 = 252 * 1/32 = 7.875.

Correct Answer: A — 252

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Q. What is the coefficient of x^5 in the expansion of (x + 2)^7?

A. 21
B. 42
C. 35
D. 28

Solution

The coefficient of x^5 is C(7,5)(2)^2 = 21 * 4 = 84.

Correct Answer: C — 35

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Q. What is the coefficient of x^5 in the expansion of (x + 2)^8?

A. 672
B. 1280
C. 960
D. 720

Solution

The coefficient of x^5 is C(8,5) * (2)^3 = 56 * 8 = 448.

Correct Answer: A — 672

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Q. What is the coefficient of x^5 in the expansion of (x + 3)^8?

A. 1680
B. 1440
C. 1260
D. 1080

Solution

Using the binomial theorem, the coefficient of x^5 in (x + 3)^8 is given by 8C5 * (3)^3 = 56 * 27 = 1512.

Correct Answer: A — 1680

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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^5 in the expansion of (x - 3)^7?

A. -21
B. -63
C. -126
D. -189

Solution

The coefficient of x^5 is C(7,5) * (-3)^2 = 21 * 9 = -189.

Correct Answer: B — -63

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Q. What is the coefficient of x^6 in the expansion of (2x - 1)^8? (2022)

A. -112
B. 112
C. 64
D. 128

Solution

The coefficient of x^6 is C(8,6) * (2)^6 * (-1)^2 = 28 * 64 = 1792.

Correct Answer: A — -112

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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)

A. 84
B. 126
C. 36
D. 54

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^6 in the expansion of (x + 5)^8?

A. 6720
B. 5600
C. 4480
D. 3360

Solution

The coefficient of x^6 is C(8,6) * (5)^2 = 28 * 25 = 700.

Correct Answer: A — 6720

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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 color of potassium permanganate (KMnO4)? (2021)

A. Colorless
B. Green
C. Purple
D. Yellow

Solution

Potassium permanganate (KMnO4) is known for its deep purple color.

Correct Answer: C — Purple

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Q. What is the color of the complex ion [Cu(H2O)6]2+?

A. Blue
B. Green
C. Yellow
D. Red

Solution

The complex ion [Cu(H2O)6]2+ is blue due to d-d transitions.

Correct Answer: A — Blue

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Major Competitive Exams

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