Class 11 Mathematics

1. The slope of a line passing through points (x₁, y₁) and (x₂, y₂) is given by:

• A. (y₂ - y₁) / (x₂ - x₁)
• B. (x₂ - x₁) / (y₂ - y₁)
• C. (y₂ + y₁) / (x₂ + x₁)
• D. (y₁ - x₁) / (y₂ - x₂)

2. What is the slope of a line parallel to the x-axis?

• A. 0
• B. 1
• C. Undefined
• D. -1

3. The slope of a line perpendicular to the x-axis (parallel to y-axis) is:

• A. Undefined
• B. 0
• C. 1
• D. -1

4. Two non-vertical lines with slopes m₁ and m₂ are perpendicular if and only if:

• A. m₁ · m₂ = -1
• B. m₁ = m₂
• C. m₁ + m₂ = 0
• D. m₁ · m₂ = 1

5. Two lines with slopes m₁ and m₂ are parallel if and only if:

• A. m₁ = m₂
• B. m₁ · m₂ = -1
• C. m₁ + m₂ = 0
• D. m₁ · m₂ = 1

6. The equation of a line in slope-intercept form is:

• A. y = mx + c
• B. x/a + y/b = 1
• C. y - y₁ = m(x - x₁)
• D. Ax + By + C = 0

7. The equation of a line in intercept form with x-intercept 'a' and y-intercept 'b' is:

• A. x/a + y/b = 1
• B. ax + by = 1
• C. x/b + y/a = 1
• D. a/x + b/y = 1

8. The equation of a line passing through (x₁, y₁) with slope m is:

• A. y - y₁ = m(x - x₁)
• B. x - x₁ = m(y - y₁)
• C. y + y₁ = m(x + x₁)
• D. y = m(x - x₁)

9. The slope of the line 3x - 4y + 10 = 0 is:

• A. 3/4
• B. -3/4
• C. 4/3
• D. -4/3

10. The distance of a point (x₁, y₁) from the line Ax + By + C = 0 is:

• A. |Ax₁ + By₁ + C| / √(A² + B²)
• B. (Ax₁ + By₁ + C) / (A + B)
• C. |Ax₁ + By₁| / √(A² + B²)
• D. |Ax₁ - By₁ + C| / (A² + B²)

11. Distance between two parallel lines Ax + By + C₁ = 0 and Ax + By + C₂ = 0 is:

• A. |C₁ - C₂| / √(A² + B²)
• B. |C₁ + C₂| / √(A² + B²)
• C. |C₁ - C₂| / (A² + B²)
• D. (C₁ - C₂) / √(A + B)

12. Find the slope of the line passing through (3, -2) and (-1, 4):

• A. -3/2
• B. 3/2
• C. -2/3
• D. 2/3

13. Acute angle θ between two lines with slopes m₁ and m₂ is given by:

• A. tan θ = |(m₂ - m₁) / (1 + m₁m₂)|
• B. tan θ = (m₁ + m₂) / (1 - m₁m₂)
• C. tan θ = (m₂ - m₁) / (1 - m₁m₂)
• D. cos θ = |(m₂ - m₁) / (1 + m₁m₂)|

14. What is the equation of the x-axis?

• A. y = 0
• B. x = 0
• C. x + y = 0
• D. y = 1

15. What is the equation of the y-axis?

• A. x = 0
• B. y = 0
• C. x + y = 1
• D. x = 1

16. The equation of a line parallel to 2x + 3y + 5 = 0 is of the form:

• A. 2x + 3y + k = 0
• B. 3x - 2y + k = 0
• C. 2x - 3y + k = 0
• D. 3x + 2y + k = 0

17. The equation of a line perpendicular to 2x + 3y + 5 = 0 is of the form:

• A. 3x - 2y + k = 0
• B. 2x + 3y + k = 0
• C. 2x - 3y + k = 0
• D. 3x + 2y + k = 0

18. Distance between parallel lines 3x - 4y + 7 = 0 and 3x - 4y + 2 = 0 is:

• A. 1
• B. 5
• C. 9/5
• D. 1/5

19. If points (a, 0), (0, b) and (x, y) are collinear, then:

• A. x/a + y/b = 1
• B. x/a - y/b = 1
• C. ax + by = 1
• D. a/x + b/y = 1

20. Distance of the origin (0,0) from the line 4x + 3y - 12 = 0 is:

• A. 12/5
• B. 5/12
• C. 12
• D. 7/5

21. The x-intercept and y-intercept of line 2x - 3y = 6 are respectively:

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

22. Find inclination of line whose slope is 1:

• A. 45°
• B. 30°
• C. 60°
• D. 90°

23. Inclination of line with slope -1/√3 is:

• A. 150°
• B. 120°
• C. 135°
• D. 30°

24. Equation of line passing through origin and having slope m is:

• A. y = mx
• B. y = mx + c
• C. x = my
• D. x + y = m

25. Line passing through (1, 2) and perpendicular to x - 2y + 1 = 0 is:

• A. 2x + y - 4 = 0
• B. 2x - y = 0
• C. x + 2y - 5 = 0
• D. x - 2y + 3 = 0

26. Area of triangle formed by lines x = 0, y = 0, and x/a + y/b = 1 is:

• A. 1/2 |ab|
• B. |ab|
• C. 1/4 |ab|
• D. 2|ab|

27. Line x - y + 2 = 0 makes an angle with the positive direction of x-axis equal to:

• A. 45°
• B. 135°
• C. 60°
• D. 30°

28. Two lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are coincident if:

• A. a₁/a₂ = b₁/b₂ = c₁/c₂
• B. a₁/a₂ = b₁/b₂ ≠ c₁/c₂
• C. a₁ a₂ + b₁ b₂ = 0
• D. a₁ b₂ - a₂ b₁ = 1

29. Midpoint of line segment joining (2, 4) and (6, 8) lies on which line?

• A. x + y = 10
• B. x - y = 2
• C. 2x - y = 1
• D. x + 2y = 8

30. Intersecting point of lines x + y = 5 and x - y = 1 is:

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