JEE Main - Intersection and angles between lines Online Test (MCQ Quiz)

1. What is the point of intersection of the lines 2x + 3y - 5 = 0 and 3x - 4y + 1 = 0?

A) (11/17, 23/17) B) (17/11, 23/17) C) (11/17, 17/23) D) (23/17, 11/17)

2. Find the angle between the lines x + 2y + 1 = 0 and 2x - y + 3 = 0.

A) 0 degrees B) 30 degrees C) 45 degrees D) 90 degrees

3. The lines ax + by + c = 0 and dx + ey + f = 0 are perpendicular if:

A) ae + bd = 0 B) af + cd = 0 C) bf + ce = 0 D) ae - bd = 0

4. What is the condition for the lines ax + by + c = 0 and dx + ey + f = 0 to be parallel?

A) ae = bd B) af = cd C) bf = ce D) ae + bd = 0

5. Find the angle between the line y = (2 - sqrt(3))x + 5 and y = (2 + sqrt(3))x - 7.

A) 30 degrees B) 45 degrees C) 60 degrees D) 90 degrees

6. If the lines 3x - 2y + 5 = 0 and kx + 4y - 1 = 0 are parallel, find the value of k.

A) -6 B) 6 C) -3 D) 3

7. The angle between the lines y = m1x + c1 and y = m2x + c2 is given by:

8. Find the point of intersection of the lines represented by the equations: x + y = 5 and 2x - y = 4.

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

9. Two lines are perpendicular. If the slope of one line is 3, what is the slope of the other line?

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

10. The lines 5x + 2y - 7 = 0 and 4x + ky + 3 = 0 are perpendicular. Find the value of k.

A) 10/4 B) -10/4 C) 10 D) -10

11. Find the acute angle between the lines x - y + 1 = 0 and x + y - 2 = 0.

A) 0 degrees B) 30 degrees C) 45 degrees D) 60 degrees

12. What is the angle between the lines 3x - 4y = 5 and 4x + 3y = 7?

A) 0 degrees B) 30 degrees C) 60 degrees D) 90 degrees

13. If the lines x/a + y/b = 1 and x/c + y/d = 1 are parallel, then:

A) ad = bc B) ac = bd C) ab = cd D) ad + bc = 0

14. Find the point of intersection of the lines x = 5 and y = 3.

A) (5, 0) B) (0, 3) C) (5, 3) D) (3, 5)

15. The angle between the lines ax + by + c = 0 and dx + ey + f = 0 is given by:

16. Find the value of k such that the lines 2x + 3y - 1 = 0 and 4x + ky + 5 = 0 are parallel.

A) 6 B) 3 C) 2 D) 1

17. The lines x + 2y = 3 and 2x + 4y = 5 are:

A) Intersecting B) Parallel C) Coincident D) Perpendicular

18. Find the angle between the lines y = mx and y = -x/m.

A) 0 degrees B) 30 degrees C) 60 degrees D) 90 degrees

19. If the lines 2x + y - 3 = 0 and kx - 2y + 1 = 0 are perpendicular, find k.

A) 1 B) -1 C) 4 D) -4

20. What is the condition for the lines ax + by + c = 0 and dx + ey + f = 0 to be coincident?

A) a/d = b/e = c/f B) a/d = b/e != c/f C) ae = bd D) af = cd

21. Find the point of intersection of the lines x - y = 0 and x + y = 0.

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

22. Find the angle between the lines x cos(alpha) + y sin(alpha) = p and x sin(alpha) - y cos(alpha) = q.

A) 0 degrees B) 30 degrees C) 60 degrees D) 90 degrees

23. If the lines y = m1x + c1 and y = m2x + c2 are perpendicular, then:

A) m1m2 = 1 B) m1 + m2 = 0 C) m1m2 = -1 D) m1 / m2 = -1

24. Find the value of k if the lines 3x + 4y - 1 = 0 and 6x + 8y - 3 = 0 are parallel.

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

25. What is the angle between the line 2x - y + 5 = 0 and the x-axis?

A) arctan(2) B) arctan(-1/2) C) arctan(1/2) D) arctan(-2)

26. Find the point of intersection of the lines x + 2y = 1 and 3x + 4y = -1.

A) (-3, 2) B) (3, -2) C) (-2, 3) D) (2, -3)

27. The lines ax + by + c = 0 and dx + ey + f = 0 are parallel if:

A) ae = bd B) ae + bd = 0 C) af = cd D) bf = ce

28. Find the angle between the lines y = x and y = -x.

A) 0 degrees B) 30 degrees C) 45 degrees D) 90 degrees

29. If the lines 5x - 2y + 1 = 0 and kx + 4y - 3 = 0 are perpendicular, find k.

A) 8 B) -8 C) 10 D) -10

30. Find the point of intersection of the lines x - 2y = 5 and 2x + 3y = 1.

A) (17/7, -4/7) B) (17/7, 4/7) C) (-17/7, 4/7) D) (17/7, -4/7)

31. The lines x + 2y + 3 = 0 and 2x + 4y + 5 = 0 are:

A) Intersecting B) Parallel C) Coincident D) Perpendicular

32. Find the acute angle between the lines y = (sqrt(3) - 1)x and y = (sqrt(3) + 1)x.

A) 30 degrees B) 45 degrees C) 60 degrees D) 90 degrees

33. If the lines 2x - 3y + 1 = 0 and kx + 6y - 5 = 0 are parallel, find k.

A) 4 B) -4 C) 3 D) -3

34. What is the angle between the lines x + sqrt(3)y = 1 and sqrt(3)x + y = 2?

A) 0 degrees B) 30 degrees C) 60 degrees D) 90 degrees

35. Find the point of intersection of the lines 3x + 2y = 7 and x - y = 1.

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

36. If the lines ax + by + c = 0 and dx + ey + f = 0 are perpendicular, then:

A) ae + bd = 0 B) ad + be = 0 C) af + cd = 0 D) bf + ce = 0

37. Find the angle between the line y = 2x + 3 and y = -x/2 + 1.

A) 0 degrees B) 30 degrees C) 60 degrees D) 90 degrees

38. The lines x + y = 1 and 2x + 2y = 3 are:

A) Intersecting B) Parallel C) Coincident D) Perpendicular

39. Find the value of k if the lines 5x - 3y + 2 = 0 and 10x - 6y + k = 0 are coincident.

A) 4 B) -4 C) 2 D) -2

40. Find the point of intersection of the lines x + y - 1 = 0 and x - y + 1 = 0.

A) (0, 1) B) (1, 0) C) (0, 0) D) (1, 1)

41. The angle between the lines ax + by + c = 0 and x-axis is given by:

A) tan(theta) = -a/b B) tan(theta) = b/a C) tan(theta) = -b/a D) tan(theta) = a/b

42. If the lines y = m1x + c1 and y = m2x + c2 are parallel, then:

A) m1 = m2 B) m1 = -m2 C) m1m2 = 1 D) m1m2 = -1

43. Find the point of intersection of the lines 2x + y = 5 and x + y = 3.

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

44. The lines x/3 + y/4 = 1 and x/6 + y/8 = 1 are:

A) Intersecting B) Parallel C) Coincident D) Perpendicular

45. Find the angle between the lines x + y = 1 and x - y = 1.

A) 0 degrees B) 30 degrees C) 45 degrees D) 90 degrees

46. If the lines 3x + 2y - 1 = 0 and kx - 4y + 5 = 0 are perpendicular, find k.

A) 6 B) -6 C) 8 D) -8

47. Find the point of intersection of the lines 4x + 3y = 1 and x - y = 2.

A) (-1, 5/3) B) (1, -1) C) (1, -1/3) D) (-1, 1)

48. The lines x = 5 and y = x are:

A) Intersecting B) Parallel C) Coincident D) Perpendicular

49. Find the angle between the lines 2x + 3y = 5 and 3x - 2y = 7.

A) 0 degrees B) 30 degrees C) 60 degrees D) 90 degrees

Intersection and angles between lines - Online Test

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