Mathematics for Competitive Exam Success

Mathematics

3D Geometry Applications of Derivatives Binomial Theorem Circles Complex Numbers Conic Sections Coordinate Geometry Differential Equations Differentiation Integration Limits & Continuity Matrices & Determinants Permutations & Combinations Probability Quadratic Equations Sequences & Series Sets & Relations Straight Lines Trigonometry Vector Algebra

Q. What is the volume of a cube with side length 4 units? (2020)

A. 16
B. 64
C. 32
D. 48

Solution

Volume = side³ = 4³ = 64 cubic units.

Correct Answer: B — 64

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Q. What is the volume of a cylinder with radius 2 and height 5? (2023)

A. 20π
B. 10π
C. 15π
D. 25π

Solution

Volume = πr²h = π(2²)(5) = 20π cubic units.

Correct Answer: A — 20π

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Q. What is the volume of a cylinder with radius 3 units and height 5 units? (2021)

A. 45π
B. 30π
C. 15π
D. 9π

Solution

Volume = πr²h = π(3²)(5) = 45π cubic units.

Correct Answer: A — 45π

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Q. What is the volume of a sphere with radius 5 units? (2021)

A. 500/3π
B. 125/3π
C. 100/3π
D. 200/3π

Solution

Volume = (4/3)πr³ = (4/3)π(5)³ = (4/3)π(125) = 500/3π cubic units.

Correct Answer: A — 500/3π

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Q. What is the x-intercept of the line 5x - 2y + 10 = 0?

A. -2
B. 2
C. 0
D. 5

Solution

Setting y = 0 in the equation gives 5x + 10 = 0, thus x = -2.

Correct Answer: B — 2

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Q. What is the x-intercept of the line 6x - 2y = 12?

A. 2
B. 3
C. 4
D. 6

Solution

Setting y = 0 in the equation gives 6x = 12, thus x = 2. The x-intercept is 2.

Correct Answer: B — 3

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Q. What is the y-intercept of the line 2x - 3y + 6 = 0? (2023)

A. 2
B. 3
C. -2
D. -3

Solution

Rearranging gives y = (2/3)x + 2; y-intercept = 2

Correct Answer: A — 2

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Q. What is the y-intercept of the line 3x - 2y = 6? (2020) 2020

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

Solution

Setting x = 0, we get -2y = 6, so y = -3.

Correct Answer: A — 3

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Q. What is the y-intercept of the line 3x - 4y = 12? (2023)

A. 3
B. 4
C. 0
D. 12

Solution

Setting x = 0, we get -4y = 12, so y = -3.

Correct Answer: A — 3

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Q. What is the y-intercept of the line 4x + 5y - 20 = 0?

A. 4
B. 5
C. 20
D. 0

Solution

Setting x = 0 in the equation gives 5y = 20, thus y = 4. The y-intercept is 4.

Correct Answer: B — 5

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Q. Which of the following equations has roots that are both negative? (2022)

A. x² + 4x + 4 = 0
B. x² - 4x + 4 = 0
C. x² + 2x + 1 = 0
D. x² - 2x + 1 = 0

Solution

The equation x² + 4x + 4 = 0 has roots -2 and -2, which are both negative.

Correct Answer: A — x² + 4x + 4 = 0

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Q. Which of the following is the conjugate of the complex number 2 - 3i? (2020)

A. 2 + 3i
B. 2 - 3i
C. 3 - 2i
D. 3 + 2i

Solution

The conjugate of a complex number a + bi is a - bi. Thus, the conjugate of 2 - 3i is 2 + 3i.

Correct Answer: A — 2 + 3i

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Q. Which of the following is the conjugate of the complex number 5 - 3i? (2020)

A. 5 + 3i
B. 5 - 3i
C. -5 + 3i
D. -5 - 3i

Solution

The conjugate of a complex number a + bi is a - bi. Thus, the conjugate of 5 - 3i is 5 + 3i.

Correct Answer: A — 5 + 3i

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Q. Which of the following lines is perpendicular to the line y = 3x + 1?

A. y = -1/3x + 2
B. y = 3x - 1
C. y = 1/3x + 1
D. y = -3x + 1

Solution

The slope of the given line is 3. The slope of a line perpendicular to it is -1/3.

Correct Answer: A — y = -1/3x + 2

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Q. Which of the following points lies on the line 4x - 5y + 20 = 0?

A. (5, 0)
B. (0, 4)
C. (4, 0)
D. (0, -4)

Solution

Substituting (0, -4) into the equation gives 4(0) - 5(-4) + 20 = 0, which is true.

Correct Answer: D — (0, -4)

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Mathematics

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