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Q. What is the coefficient of O2 when balancing the equation: C4H10 + O2 → CO2 + H2O? (2023)

A. 5
B. 6
C. 7
D. 8

Solution

The balanced equation is C4H10 + 6O2 → 4CO2 + 5H2O, so the coefficient of O2 is 6.

Correct Answer: B — 6

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Q. What is the coefficient of static friction if a block on a horizontal surface begins to slide at a force of 20 N and the normal force is 50 N?

A. 0.2
B. 0.4
C. 0.5
D. 0.6

Solution

The coefficient of static friction (μs) is given by μs = F/N, where F is the force and N is the normal force. Here, μs = 20 N / 50 N = 0.4.

Correct Answer: B — 0.4

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Q. What is the coefficient of variation if the mean is 50 and the standard deviation is 5?

A. 5%
B. 10%
C. 15%
D. 20%

Solution

Coefficient of Variation = (Standard Deviation / Mean) * 100 = (5 / 50) * 100 = 10%.

Correct Answer: B — 10%

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Q. What is the coefficient of variation if the mean is 50 and the standard deviation is 10?

A. 20%
B. 10%
C. 15%
D. 25%

Solution

Coefficient of variation = (Standard deviation / Mean) * 100 = (10 / 50) * 100 = 20%.

Correct Answer: A — 20%

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Q. What is the coefficient of x^0 in the expansion of (2x - 3)^5? (2022)

A. -243
B. 243
C. -81
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)

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

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 (3x - 4)^5?

A. -1024
B. 243
C. -243
D. 1024

Solution

The coefficient of x^0 is (-4)^5 = -1024.

Correct Answer: A — -1024

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Q. What is the coefficient of x^0 in the expansion of (x + 1/x)^8? (2021)

A. 28
B. 56
C. 70
D. 84

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^0 in the expansion of (x + 5)^3?

A. 125
B. 100
C. 75
D. 50

Solution

The coefficient of x^0 is C(3,0) * 5^3 = 1 * 125 = 125.

Correct Answer: A — 125

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Q. What is the coefficient of x^0 in the expansion of (x + 5)^5?

A. 3125
B. 625
C. 125
D. 25

Solution

The coefficient of x^0 is C(5,0) * 5^5 = 1 * 3125 = 3125.

Correct Answer: A — 3125

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Q. What is the coefficient of x^0 in the expansion of (x - 1)^5?

A. -1
B. 5
C. -5
D. 10

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^1 in the expansion of (x + 1)^10? (2021)

A. 10
B. 90
C. 100
D. 1

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 + 5)^6?

A. 30
B. 60
C. 90
D. 120

Solution

The coefficient of x^1 is C(6,1) * 5^5 = 6 * 3125 = 18750.

Correct Answer: C — 90

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Q. What is the coefficient of x^1 in the expansion of (x - 1)^5?

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

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)^6?

A. 15
B. 30
C. 45
D. 60

Solution

The coefficient of x^2 is C(6,2) * (2)^2 * (1)^4 = 15 * 4 = 60.

Correct Answer: B — 30

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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 - 1)^5? (2021)

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

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 (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^2 in the expansion of (3x - 4)^4?

A. 144
B. 216
C. 432
D. 576

Solution

The coefficient of x^2 is C(4,2) * (3)^2 * (-4)^2 = 6 * 9 * 16 = 864.

Correct Answer: C — 432

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Q. What is the coefficient of x^2 in the expansion of (3x - 4)^6?

A. 540
B. 720
C. 1080
D. 1440

Solution

The coefficient of x^2 is C(6,2) * (3)^2 * (-4)^(6-2) = 15 * 9 * 256 = 34560.

Correct Answer: C — 1080

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Q. What is the coefficient of x^2 in the expansion of (x + 1/2)^8?

A. 28
B. 56
C. 70
D. 84

Solution

The coefficient of x^2 is C(8,2) * (1/2)^2 = 28 * 1/4 = 7.

Correct Answer: C — 70

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Q. What is the coefficient of x^2 in the expansion of (x + 3)^5?

A. 45
B. 60
C. 75
D. 90

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?

A. 50
B. 100
C. 150
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 + 5)^7? (2021)

A. 21
B. 35
C. 105
D. 175

Solution

The coefficient of x^2 is given by 7C2 * 5^5 = 21 * 3125 = 65625.

Correct Answer: B — 35

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Q. What is the coefficient of x^2 in the expansion of (x - 1)^5?

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

Solution

The coefficient of x^2 is C(5,2) * (-1)^3 = 10 * (-1) = -10.

Correct Answer: A — -10

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

A. -40
B. -20
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^2 in the expansion of (x - 4)^6?

A. 240
B. 360
C. 480
D. 720

Solution

Using the binomial theorem, the coefficient of x^2 in (a + b)^n is given by nCk * a^(n-k) * b^k. Here, n=6, a=x, b=-4, and k=2. Thus, the coefficient is 6C2 * (1)^4 * (-4)^2 = 15 * 16 = 240.

Correct Answer: B — 360

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Q. What is the coefficient of x^3 in the expansion of (2x + 3)^5?

A. 90
B. 100
C. 120
D. 150

Solution

Using the binomial theorem, the coefficient of x^3 is given by C(5,3) * (2)^3 * (3)^(5-3) = 10 * 8 * 9 = 720.

Correct Answer: A — 90

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Major Competitive Exams

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