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Mathematics - Three Dimensional Geometry

Practise 25 WBJEE previous year questions on Three Dimensional Geometry, compiled from papers spanning 2015 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 WBJEE tests.

Three Dimensional Geometry has been asked in 12 of the 18 years of WBJEE papers analysed (2009–2026), with 25 questions in all. 48% of them were easy, 40% moderate and 12% tough. Most of its questions came from 2024, with 3 questions that year. In the last three years (2024–2026) it had 6 questions across 3 papers, about 2 per paper.

The chapter's 4 topics are not weighted equally: Line and Plane (8 questions, 32%), Plane in Space (8 questions, 32%), and Direction Cosines and Direction Ratios (5 questions, 20%) have been asked the most. Line and Plane has also led over the last five years, with 3 questions. Plane in Space has produced the most tough questions (2).

  1. 1Intercepts of the plane on the coordinate axes respectively are2026Plane in Space
  2. 2Consider a square ABCD of diagonal length . The square is folded along the diagonal AC so that the plane of ABC is perpendicular to the plan2026Line in Space
  3. 3The straight line is2025Direction Cosines and Direction Ratios
  4. 4The plane is rotated through about its line of intersection with the plane . The equation of the plane in new position is2024Plane in Space
  5. 5If the relation between the direction ratios of two lines in are given by then the angle between the lines is ( , have their usual meaning)2024Line in Space
  6. 6Angle between two diagonals of a cube will be2024Line in Space
  7. 7If the distance between the plane \(a x-2 y+z=k\) and the plane containing the lines \( {x-1}{2}= {y-2}{3}= {z-3}{4}\) and \( {x-2}{3}= {y-32023Line and Plane
  8. 8The angle between a normal to the plane \(2 x-y+2 z-1=0\) and the X-axis is2023Line and Plane
  9. 9The line intersect the plane at the point2022Line and Plane
  10. 10The equation of the plane through the intersection of the planes and and parallel to the -axis is2022Plane in Space
  11. 11A line with positive direction cosines passes through the point and makes equal angle with co-ordinate axes. The line meets the plane at poi2021Line and Plane
  12. 12If from a point , perpendiculars and are drawn to and planes respectively, then the equation of the plane is2021Plane in Space
  13. 13The plane is rotated about its line of intersection with the plane through an angle . The equation changes to2021Plane in Space
  14. 14The equation of the plane through the point and parallel to the lines and is2020Line in Space
  15. 15The sine of the angle between the straight line and the plane is2020Line and Plane
  16. 16The direction ratios of the normal to the plane passing through the points (1,2,-3) ,(-1,-2,1) and parallel to is2019Direction Cosines and Direction Ratios
  17. 17The equation of the plane, which bisects the line joining the points (1,2,3) and (3,4,5) at right angles is2019Plane in Space
  18. 18A point lies on a line through and is parallel to the line If lies on the plane then segment PQ equals2018Line and Plane
  19. 19The foot of the perpendicular drawn from the point (1,8,4) on the line joining the point (0,-11,4) and (2,-3,1) is2018Direction Cosines and Direction Ratios
  20. 20The equation of the plane through (1,2,-3) and (2,-2,1) and parallel to -axis is2017Plane in Space
  21. 21Three lines are drawn from the origin with direction cosines proportional to (1,-1,1) (2,-3,0) and The three lines are2017Direction Cosines and Direction Ratios
  22. 22The cosine of the angle between any two diagonals of a cube is2016Direction Cosines and Direction Ratios
  23. 23A straight line joining the points (1,1,1) and (0,0,0) intersects the plane at2016Line and Plane
  24. 24Angle between the planes and is2016Plane in Space
  25. 25The value of for which the straight line may lie on the plane is2015Line and Plane

Frequently Asked Questions

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

This chapter includes 25 questions compiled from WBJEE papers spanning 2015 to 2026.

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

These are WBJEE 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 WBJEE Mathematics?

Three Dimensional Geometry has appeared in 12 of the 18 years of WBJEE papers covered here, with 25 questions across 12 papers - about 2 per paper it appears in.

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

Of the 25 questions analysed for this chapter, 48% are easy, 40% moderate and 12% tough. 2024 had the most, with 3 questions.

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

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

  • Line and Plane - 8 questions (32%)
  • Plane in Space - 8 questions (32%)
  • Direction Cosines and Direction Ratios - 5 questions (20%)
  • Plane in Space has produced the most tough questions (2).
6.Is Three Dimensional Geometry's weightage in WBJEE going up or down?

Across all 12 papers analysed, Three Dimensional Geometry has averaged about 2.1 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 2.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.