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Q. What is the variance of the data set: 2, 4, 4, 4, 5, 5, 7, 9?

A. 2.5
B. 3.5
C. 4.5
D. 5.5

Solution

Mean = 5.0; Variance = [(2-5)^2 + (4-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (5-5)^2 + (7-5)^2 + (9-5)^2] / 8 = 2.5.

Correct Answer: A — 2.5

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Q. What is the variance of the following data set: {5, 7, 8, 9, 10}?

A. 2
B. 3
C. 4
D. 5

Solution

Mean = 7.8, Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²] / 5 = 3.

Correct Answer: B — 3

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Q. What is the variance of the following numbers: 1, 1, 1, 1, 1?

A. 0
B. 1
C. 2
D. 3

Solution

All values are the same, so variance = 0.

Correct Answer: A — 0

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Q. What is the variance of the following numbers: 1, 2, 3, 4, 5, 6? (2022)

A. 2.5
B. 3.5
C. 4.5
D. 5.5

Solution

Mean = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5. Variance = [(1-3.5)² + (2-3.5)² + (3-3.5)² + (4-3.5)² + (5-3.5)² + (6-3.5)²] / 6 = 2.92 (approx 2.5).

Correct Answer: A — 2.5

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Q. What is the variance of the following numbers: 2, 4, 4, 4, 5, 5, 7, 9?

A. 4
B. 6
C. 8
D. 10

Solution

Mean = 5. Variance = [(2-5)² + (4-5)² + (4-5)² + (4-5)² + (5-5)² + (5-5)² + (7-5)² + (9-5)²] / 8 = 6.

Correct Answer: B — 6

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Q. What is the variance of the following numbers: 5, 5, 5, 5? (2019)

A. 0
B. 1
C. 2
D. 3

Solution

All values are the same, so variance = 0.

Correct Answer: A — 0

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Q. What is the variance of the following numbers: 5, 7, 9, 11? (2020)

A. 4
B. 6
C. 8
D. 10

Solution

Mean = (5 + 7 + 9 + 11) / 4 = 8. Variance = [(5-8)² + (7-8)² + (9-8)² + (11-8)²] / 4 = 4.

Correct Answer: A — 4

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Q. What is the variance of the numbers: 1, 1, 1, 1, 1? (2023)

A. 0
B. 1
C. 2
D. 3

Solution

All values are the same, so variance = 0.

Correct Answer: A — 0

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Q. What is the variance of the numbers: 5, 5, 5, 5? (2023)

A. 0
B. 1
C. 2
D. 3

Solution

All values are the same, so variance = 0.

Correct Answer: A — 0

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Q. What is the vertex of the parabola defined by the equation y = -2(x - 1)^2 + 4?

A. (1, 4)
B. (1, -4)
C. (4, 1)
D. (-1, 4)

Solution

The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).

Correct Answer: A — (1, 4)

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Q. What is the vertex of the parabola given by the equation y = -2(x - 1)^2 + 4?

A. (1, 4)
B. (1, -4)
C. (4, 1)
D. (-1, 4)

Solution

The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).

Correct Answer: A — (1, 4)

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Q. What is the vertex of the parabola given by the equation y = 2x^2 - 4x + 1?

A. (1, -1)
B. (1, 0)
C. (2, 1)
D. (0, 1)

Solution

To find the vertex, use the formula x = -b/(2a). Here, a = 2, b = -4, so x = 1. Substitute x = 1 into the equation to find y = -1.

Correct Answer: A — (1, -1)

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Q. What is the vertex of the parabola represented by the equation y = -2(x - 1)^2 + 4?

A. (1, 4)
B. (1, -4)
C. (-1, 4)
D. (-1, -4)

Solution

The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).

Correct Answer: A — (1, 4)

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Q. What is the vertex of the parabola represented by the equation y = 2x^2 - 8x + 5?

A. (2, -3)
B. (2, -7)
C. (4, -3)
D. (4, -7)

Solution

The vertex can be found using x = -b/(2a) = 4. Substituting x = 4 into the equation gives y = -3.

Correct Answer: A — (2, -3)

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Q. What is the vertex of the parabola represented by the equation y = 3x^2 - 12x + 7? (2023)

A. (2, -5)
B. (2, -1)
C. (2, 1)
D. (2, 5)

Solution

The vertex can be found using x = -b/(2a). Here, x = 12/(2*3) = 2. Substituting x = 2 into the equation gives y = 3(2)^2 - 12(2) + 7 = -5.

Correct Answer: A — (2, -5)

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Q. What is the vertex of the parabola represented by the equation y = x² - 4x + 3? (2022)

A. (2, -1)
B. (2, 1)
C. (1, 2)
D. (3, 0)

Solution

The vertex can be found using the formula x = -b/2a. Here, x = 2, and substituting back gives y = -1.

Correct Answer: A — (2, -1)

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Q. What is the vertex of the parabola represented by the equation y = x² - 6x + 8? (2023)

A. (3, -1)
B. (3, -5)
C. (2, -4)
D. (2, -2)

Solution

The vertex can be found using the formula x = -b/2a = 6/2 = 3. Substituting x = 3 into the equation gives y = -1.

Correct Answer: A — (3, -1)

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Q. What is the vertex of the quadratic function f(x) = 2x^2 - 8x + 5? (2021)

A. (2, -3)
B. (2, -7)
C. (4, -3)
D. (4, -7)

Solution

The vertex can be found using x = -b/(2a). Here, x = 8/(2*2) = 2. Substituting x = 2 into f(x) gives f(2) = -3, so the vertex is (2, -3).

Correct Answer: A — (2, -3)

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Q. What is the vertex of the quadratic function f(x) = 2x^2 - 8x + 6?

A. (2, -2)
B. (2, 2)
C. (4, -2)
D. (4, 2)

Solution

The vertex can be found using the formula x = -b/(2a), which gives x = 2. Substituting x back into the function gives the y-coordinate.

Correct Answer: A — (2, -2)

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Q. What is the viscosity of water at 20°C?

A. 0.001 Pa·s
B. 0.01 Pa·s
C. 0.1 Pa·s
D. 1 Pa·s

Solution

The viscosity of water at 20°C is approximately 0.001 Pa·s.

Correct Answer: A — 0.001 Pa·s

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Q. What is the voltage across a 10 ohm resistor carrying a current of 0.5 A?

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

Solution

Using Ohm's law, V = I * R = 0.5 A * 10 Ω = 5 V.

Correct Answer: A — 5 V

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Q. What is the voltage across a 10Ω resistor carrying a current of 2A? (2022)

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

Solution

Using Ohm's law, V = I * R = 2A * 10Ω = 20V.

Correct Answer: B — 10V

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Q. What is the voltage across a 10Ω resistor carrying a current of 3A? (2022)

A. 30V
B. 20V
C. 10V
D. 15V

Solution

Using Ohm's law, V = IR = 3A * 10Ω = 30V.

Correct Answer: A — 30V

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Q. What is the voltage across a 12Ω resistor carrying a current of 1.5A? (2023)

A. 18V
B. 12V
C. 6V
D. 24V

Solution

Using Ohm's law, V = IR = 1.5A * 12Ω = 18V.

Correct Answer: A — 18V

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Q. What is the voltage across a 12Ω resistor carrying a current of 3A? (2023)

A. 36V
B. 24V
C. 12V
D. 18V

Solution

Using Ohm's law, V = IR = 3A * 12Ω = 36V.

Correct Answer: A — 36V

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Q. What is the voltage across a 5Ω resistor carrying a current of 3A? (2023)

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

Solution

Using Ohm's law, V = IR = 3A * 5Ω = 15V.

Correct Answer: A — 15V

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Q. What is the voltage across a 5Ω resistor if a current of 3A flows through it? (2020)

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

Solution

Using Ohm's law, V = IR = 3A * 5Ω = 15V.

Correct Answer: A — 15V

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Q. What is the voltage drop across a 10Ω resistor carrying a current of 2A? (2019)

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

Solution

Using Ohm's law, V = I * R = 2A * 10Ω = 20V.

Correct Answer: B — 10V

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Q. What is the voltage drop across a 3 ohm resistor carrying a current of 2 A?

A. 3 V
B. 6 V
C. 9 V
D. 12 V

Solution

Using Ohm's law, V = I * R = 2 A * 3 ohms = 6 V.

Correct Answer: B — 6 V

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Q. What is the voltage drop across a 3Ω resistor carrying a current of 4A? (2019)

A. 6V
B. 8V
C. 12V
D. 15V

Solution

Using Ohm's law, V = I * R = 4A * 3Ω = 12V.

Correct Answer: C — 12V

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Major Competitive Exams

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