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Q. What is the slope of the line perpendicular to the line 4x + 2y = 8?

A. -1/2
B. 1/2
C. 2
D. -2

Solution

The slope of the line is -2 (from y = -2x + 4). The slope of the perpendicular line is the negative reciprocal, which is 1/2.

Correct Answer: A — -1/2

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Q. What is the slope of the line perpendicular to the line 4x + 3y = 12?

A. -3/4
B. 4/3
C. 3/4
D. -4/3

Solution

The slope of the line 4x + 3y = 12 is -4/3. The slope of the perpendicular line is the negative reciprocal, which is 3/4.

Correct Answer: D — -4/3

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Q. What is the slope of the line perpendicular to the line 4x - 5y + 10 = 0? (2022)

A. 5/4
B. -4/5
C. 4/5
D. -5/4

Solution

The slope of the line is 4/5, so the slope of the perpendicular line is -5/4.

Correct Answer: B — -4/5

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Q. What is the slope of the line perpendicular to the line 4x - 5y = 10? (2022)

A. 5/4
B. -4/5
C. 4/5
D. -5/4

Solution

The slope of the line is 4/5, so the slope of the perpendicular line is -5/4.

Correct Answer: B — -4/5

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Q. What is the slope of the line perpendicular to the line 5x + 2y = 10?

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

Solution

The slope of the line is -5/2. The slope of the perpendicular line is the negative reciprocal, which is 2/5.

Correct Answer: A — -2/5

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Q. What is the slope of the line perpendicular to the line 7x - 2y + 3 = 0?

A. 1/2
B. -1/2
C. 2
D. -2

Solution

The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.

Correct Answer: B — -1/2

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Q. What is the slope of the line perpendicular to the line 7x - 2y = 14?

A. 1/7
B. -1/7
C. 2/7
D. -2/7

Solution

The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.

Correct Answer: B — -1/7

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Q. What is the slope of the line perpendicular to the line with slope 3?

A. -1/3
B. 1/3
C. 3
D. -3

Solution

Slope of perpendicular line = -1/m = -1/3.

Correct Answer: A — -1/3

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Q. What is the slope of the line perpendicular to the line y = -2x + 3?

A. -1/2
B. 1/2
C. 2
D. -2

Solution

The slope of the given line is -2. The slope of the perpendicular line is the negative reciprocal, which is 1/2.

Correct Answer: B — 1/2

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Q. What is the slope of the line perpendicular to the line y = -2x + 4?

A. 0.5
B. 2
C. -0.5
D. -2

Solution

The slope of the given line is -2. The slope of the perpendicular line is the negative reciprocal, which is 1/2.

Correct Answer: B — 2

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Q. What is the slope of the line perpendicular to the line y = -3x + 4?

A. 1/3
B. -1/3
C. 3
D. -3

Solution

The slope of the given line is -3. The slope of the perpendicular line is the negative reciprocal: 1/3.

Correct Answer: C — 3

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Q. What is the slope of the line perpendicular to the line y = 3x + 1? (2023)

A. -1/3
B. 1/3
C. 3
D. -3

Solution

Slope of perpendicular line = -1/(slope of original line) = -1/3.

Correct Answer: A — -1/3

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Q. What is the slope of the line represented by the equation 2x - 3y + 6 = 0?

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

Solution

Rearranging gives y = (2/3)x + 2, slope = 2/3.

Correct Answer: C — -2/3

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Q. What is the slope of the line represented by the equation 3x - 4y + 12 = 0?

A. 3/4
B. 4/3
C. -3/4
D. -4/3

Solution

Rearranging gives y = (3/4)x + 3. Slope = 3/4.

Correct Answer: C — -3/4

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Q. What is the slope of the line represented by the equation 4x - 2y + 8 = 0? (2021)

A. 2
B. 4
C. -2
D. -4

Solution

Rearranging gives y = 2x + 4, so slope = 2.

Correct Answer: C — -2

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Q. What is the slope of the line represented by the equation 5y - 10x = 20?

A. 2
B. 1
C. 0.5
D. 5

Solution

Rearranging to slope-intercept form: 5y = 10x + 20 => y = 2x + 4. The slope is 2.

Correct Answer: C — 0.5

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Q. What is the slope of the line represented by the equation y = 2x + 3?

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

Solution

The slope of the line in the equation y = mx + b is m, which is 2.

Correct Answer: B — 2

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Q. What is the slope of the line represented by the equation y = 3x + 2? (2021)

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

Solution

In the equation y = mx + b, m is the slope. Here, m = 3.

Correct Answer: A — 3

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Q. What is the slope of the line represented by the equation y = 3x + 4? (2022)

A. 3
B. 4
C. 1/3
D. 0

Solution

The slope of the line in the equation y = mx + b is m. Here, m = 3.

Correct Answer: A — 3

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Q. What is the slope of the line that passes through the points (0, 0) and (4, 8)?

A. 0
B. 1
C. 2
D. 4

Solution

The slope m = (8 - 0) / (4 - 0) = 2.

Correct Answer: C — 2

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Q. What is the slope of the line that passes through the points (4, 5) and (6, 9)?

A. 2
B. 3
C. 4
D. 1

Solution

The slope m = (9 - 5) / (6 - 4) = 4/2 = 2.

Correct Answer: A — 2

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Q. What is the slope of the lines represented by the equation 5x^2 - 10xy + 5y^2 = 0?

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

Solution

The equation can be factored to find the slopes, which are both 1.

Correct Answer: A — 1

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Q. What is the slope of the lines represented by the equation x^2 - 6xy + 9y^2 = 0?

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

Solution

Factoring gives (x - 3y)^2 = 0, indicating a double root, hence the slope is 3.

Correct Answer: A — 3

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Q. What is the slope of the tangent line to f(x) = x^2 + 2x at x = 1? (2023)

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

Solution

f'(x) = 2x + 2. At x = 1, f'(1) = 2(1) + 2 = 4.

Correct Answer: B — 3

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Q. What is the slope of the tangent line to the curve y = x^2 + 2x at the point (1, 3)?

A. 1
B. 2
C. 3
D. 4

Solution

The derivative y' = 2x + 2. At x = 1, y' = 2(1) + 2 = 4, which is the slope of the tangent line.

Correct Answer: B — 2

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Q. What is the slope of the tangent line to the curve y = x^2 + 2x at x = 1?

A. 3
B. 4
C. 2
D. 1

Solution

The derivative y' = 2x + 2. At x = 1, y' = 2(1) + 2 = 4.

Correct Answer: A — 3

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Q. What is the slope of the tangent line to the curve y = x^2 - 4x + 5 at x = 3? (2023)

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

Solution

The slope is given by f'(x) = 2x - 4. At x = 3, f'(3) = 2(3) - 4 = 2.

Correct Answer: C — 2

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Q. What is the slope of the tangent line to the curve y = x^2 at the point (1,1)? (2023)

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

Solution

The derivative y' = 2x; At x = 1, slope = 2(1) = 2.

Correct Answer: B — 2

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Q. What is the slope of the tangent line to the curve y = x^2 at the point (2, 4)?

A. 2
B. 4
C. 3
D. 1

Solution

The derivative y' = 2x. At x = 2, the slope is y'(2) = 2(2) = 4.

Correct Answer: A — 2

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Q. What is the slope of the tangent line to the curve y = x^2 at the point (3, 9)? (2020)

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

Solution

The derivative y' = 2x. At x = 3, y' = 2(3) = 6.

Correct Answer: B — 6

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Major Competitive Exams

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