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Mathematics - Three Dimensional Geometry

Practise 479 MHTCET previous year questions on Three Dimensional Geometry, compiled from papers spanning 2007 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty MHTCET tests.

Three Dimensional Geometry has been asked in 16 of the 17 years of MHTCET papers analysed (2007–2026), with 479 questions in all. 46% of them were easy, 49% moderate and 5% tough. Most of its questions came from 2025, with 87 questions that year. In the last three years (2024–2026) it had 224 questions across 59 papers, about 3.8 per paper.

The chapter's 5 topics are not weighted equally: Line in Space (163 questions, 34%), Plane in Space (147 questions, 31%), and Line and Plane (73 questions, 15%) have been asked the most. Line in Space has also led over the last five years, with 119 questions. Line in Space has produced the most tough questions (9).

  1. 1If M denotes the midpoint of the line joining A and B , then the equation of the plane through M and perpendicular to AB is:20 Apr, 2026 (M)Basics of point in 3 dimension
  2. 2A plane meets the co-ordinate axes in A, B, C such that the centroid of the triangle ABC is the point , then the equation of the plane is,20 Apr, 2026 (M)Plane in Space
  3. 3The shortest distance between the lines and is20 Apr, 2026 (M)Line in Space
  4. 4The acute angle between the line and the plane is , then the value of are...20 Apr, 2026 (M)Line and Plane
  5. 5The Cartesian equations of the line passing through and parallel to the X-axis are ....20 Apr, 2026 (E)Line in Space
  6. 6Lines and intersect at point . If , then20 Apr, 2026 (E)Line in Space
  7. 7If the line joining points and is parallel to the line joining points and then the values of and are respectively20 Apr, 2026 (E)Direction Cosines and Direction Ratios
  8. 8If the perpendicular distance of the plane passing through the point and containing the line from origin is then ...20 Apr, 2026 (E)Plane in Space
  9. 9The symmetric form of the equation of the line , is19 Apr, 2026 (M)Line in Space
  10. 10If is the shortest distance between the lines and then is... ,(where denotes the greatest integer function.)19 Apr, 2026 (M)Line in Space
  11. 11From a point P , perpendiculars PA and PB are drawn to XY plane and ZX plane respectively. If O is the origin, then the equation of plane OA19 Apr, 2026 (M)Basics of point in 3 dimension
  12. 12The plane cuts the axes at the points A, B, C then the area of triangle ABC is19 Apr, 2026 (M)Plane in Space
  13. 13A line passing through the points and meets the XY plane and the YZ plane at points A and B respectively. The distance AB is equal to...19 Apr, 2026 (E)Line in Space
  14. 14Let is the equation of a plane and the line having direction ratios is parallel to the plane, then the value of b is...19 Apr, 2026 (E)Plane in Space
  15. 15The shortest distance between the lines and is...19 Apr, 2026 (E)Line in Space
  16. 16If are the direction angles of the line and , then the value of is...19 Apr, 2026 (E)Direction Cosines and Direction Ratios
  17. 17The perpendicular distance from the origin to the plane containing the points and is...(in units)19 Apr, 2026 (E)Plane in Space
  18. 18If the plane cuts coordinate axes at A, B and C, then the volume of tetrahedron OABC (where O is the origin) is ......cubic units.18 Apr, 2026 (M)Plane in Space
  19. 19The coordinates of the point of intersection of the lines and are...18 Apr, 2026 (M)Line in Space
  20. 20If the plane , where and are parameters, intersects coordinate axes at points , and then ...18 Apr, 2026 (M)Plane in Space
  21. 21The acute angle between the -plane and the plane passing through the point and parallel to the vectors with direction ratios and is...18 Apr, 2026 (M)Plane in Space
  22. 22The line passes through the point and is parallel to the plane . If line intersects the line , then equation of the line is...18 Apr, 2026 (M)Line in Space
  23. 23The acute angle between the lines and is18 Apr, 2026 (E)Line in Space
  24. 24The angle between the line and the plane is18 Apr, 2026 (E)Line and Plane
  25. 25If the equation of a plane passing through , and parallel to the z axis, is , then18 Apr, 2026 (E)Plane in Space
  26. 26The angle between a diagonal and one of its edges of a cube is ...................17 Apr, 2026 (M)Direction Cosines and Direction Ratios
  27. 27If the lines and intersect each other and is collinear to , then the values of and are17 Apr, 2026 (M)Line in Space
  28. 28If for some the lines and are coplanar, then line passes through the point17 Apr, 2026 (M)Line in Space
  29. 29If is the angle between the lines and , then17 Apr, 2026 (M)Line in Space
  30. 30If the distance of point from the line passing through the point , and parallel to the vector is , then17 Apr, 2026 (E)Line in Space
  31. 31If A and B are the feet of the perpendiculars drawn from to planes and , then the equation of the plane passing through the points A, B and 17 Apr, 2026 (E)Basics of point in 3 dimension
  32. 32The sum of the coordinates of one of the points on the line which is at a distance of 3 units from the point is ...17 Apr, 2026 (E)Line in Space
  33. 33The angle between the line and the plane is17 Apr, 2026 (E)Line in Space
  34. 34The equation of the perpendicular line from the point to the line is17 Apr, 2026 (E)Line in Space
  35. 35The vector equation of the line whose cartesian equations are16 Apr, 2026 (M)Line in Space
  36. 36If the product of the distances of the point (1, 2, 3) from the origin and the plane is 7, then the value of k is16 Apr, 2026 (M)Basics of point in 3 dimension
  37. 37The lines and are16 Apr, 2026 (M)Line in Space
  38. 38The direction ratios of the normal to the plane passing through (1, 0, 0), (0, 1, 0) which makes an angle of measure with the plane are....16 Apr, 2026 (M)Plane in Space
  39. 39The lines and are coplanar if16 Apr, 2026 (M)Line in Space
  40. 40The values of p and q so that the line joining the points (7, p, 2) and (q, -2, 5) may be parallel to the line joining the points (2, -3, 5)16 Apr, 2026 (E)Direction Cosines and Direction Ratios
  41. 41If is the distance of point (2, 5, 10) from the plane containing the lines and , then16 Apr, 2026 (E)Plane in Space
  42. 42The vector equation of plane in parametric form, passing through the points (-1, 2, 0), (2, 2, -1) and parallel to the line is16 Apr, 2026 (E)Plane in Space
  43. 43If the lines and are perpendicular to each other then the value of is ...16 Apr, 2026 (E)Line in Space
  44. 44If a unit vector makes angles with , with and with , then a value of is equal to...15 Apr, 2026 (M)Direction Cosines and Direction Ratios
  45. 45The equation of the plane containing the lines and is15 Apr, 2026 (M)Plane in Space
  46. 46The direction cosines of a line which is perpendicular to the lines and are...15 Apr, 2026 (M)Direction Cosines and Direction Ratios
  47. 47For the line , identify the incorrect statement among the following.15 Apr, 2026 (M)Line in Space
  48. 48If the lines and are perpendicular to each other, then the value of m is ...15 Apr, 2026 (M)Line in Space
  49. 49The distance of the point from the plane measured parallel to the line is15 Apr, 2026 (E)Line and Plane
  50. 50The equation of the plane passing through the point and perpendicular to the planes and is15 Apr, 2026 (E)Plane in Space

Frequently Asked Questions

1.How many questions are available for Three Dimensional Geometry?

This chapter includes 479 questions compiled from MHTCET papers spanning 2007 to 2026.

2.Are these questions only from MHTCET, or from other exams too?

These are MHTCET questions specifically for the Three Dimensional Geometry chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Three Dimensional Geometry an important chapter for MHTCET Mathematics?

Three Dimensional Geometry has appeared in 16 of the 17 years of MHTCET papers covered here, with 479 questions across 106 papers - about 5 per paper it appears in.

4.What is the difficulty level of Three Dimensional Geometry questions in MHTCET?

Of the 479 questions analysed for this chapter, 46% are easy, 49% moderate and 5% tough. 2025 had the most, with 87 questions.

5.Which topics in Three Dimensional Geometry should I focus on?

These topics have carried the most weightage in Three Dimensional Geometry:

  • Line in Space - 163 questions (34%)
  • Plane in Space - 147 questions (31%)
  • Line and Plane - 73 questions (15%)
  • Line in Space has produced the most tough questions (9).
6.Is Three Dimensional Geometry's weightage in MHTCET going up or down?

Across all 106 papers analysed, Three Dimensional Geometry has averaged about 4.5 questions per paper. In the last three years (2024–2026), that average has fallen, at about 3.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.