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3d Geometry Questions

Practice 88 3d Geometry questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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88
Total Questions
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0
Easy
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79
Medium
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9
Hard
Practice by Exam:Mathematics(70)Quantitative Aptitude(12)Reasoning(2)Logical Reasoning(1)Quantitative Aptitude@NUM: 54(1)Quantitative Aptitude@NUM: 52(1)Mental Ability and Reasoning(1)

About 3D Geometry — practice questions, PYQs & concepts

3D Geometry is a frequently-tested topic on Mathematics, Quantitative Aptitude, Reasoning. ExamTest.live currently lists 88 3D Geometry questions spanning previous-year papers from 2026 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

3D Geometry weight in competitive exams

Across our 3D Geometry question bank, the largest sources are Mathematics (70), Quantitative Aptitude (12), Reasoning (2), Logical Reasoning (1) and Quantitative Aptitude@NUM: 54 (1). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 0 easy 3D Geometry questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
  • Time yourself: Every question shows the average solve time so you can benchmark your speed against other students.
  • Read every explanation: Even on questions you got right — the explanation often surfaces a faster approach you can reuse.

All 3d Geometry Questions(1–88 of 88)

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Q1mediummcqMathematicsMathematics Mock Test - 52026
14% accuracy
What is the perpendicular distance from the point to the line ?
Q2mediummcqMathematicsMathematics Mock Test - 102026
8% accuracy
The lines and are perpendicular to each other, if:
Q3hardmcqMathematicsMathematics Mock Test - 102026
0% accuracy
The equation of a plane passing through the line of intersection of the planes and and at a distance from the point is . The value of is:
Q4mediummcqMathematicsMathematics Mock Test - 102026
8% accuracy
Let the line lie in the plane . The value of is:
Q5mediummcqMathematicsMathematics Mock Test - 102026
0% accuracy
The triangle formed by the points and is:
Q6mediummcqMathematicsMathematics Mock Test - 102026
8% accuracy
The ratio in which the line segment joining the points and is divided by the -plane is:
Q7mediummcqQuantitative AptitudeSSC CGL2026
33% accuracy
If the curved surface area of a right circular cone is 10010 sq cm and its slant height is 91 cm, find its total surface area.
Q8mediummcqQuantitative AptitudeSSC CGL2026
33% accuracy
A triangular prism has 9 edges. How many vertices does it have?
Q9mediummcqLogical ReasoningCompetitive Exam2026
0% accuracy
If you have a regular dodecahedron and you slice it in half along a plane that passes through the centres of opposite faces, what is the shape of the cross-section?
Q10mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
A straight line with direction cosines is:
Q11mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
Find the shortest distance between the lines and .
Q12mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
Find the image of the point in the plane .
Q13mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
How many balls of radius 3cm can be made by melting a bigger ball of diameter 48cm?
Q14mediummcqMathematicsMathematics Mock Test - 42026
100% accuracy
If the lines and lie on the same plane, then:
Q15mediummcqMathematicsMathematics Mock Test - 42026
100% accuracy
Find the distance between the straight line and the plane .
Q16mediummcqMathematicsMathematics Mock Test - 42026
100% accuracy
The plane makes an angle with the X-axis. The value of is equal to:
Q17mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
If is the acute angle between the diagonals of a cube, then which one of the following is correct?
Q18mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
If a line has direction ratios , then what is the sum of the squares of its direction cosines?
Q19mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
The length of the perpendicular drawn from the origin to the plane is:
Q20mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Find the angle between the pair of lines and .
Q21mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Find the Cartesian equation of the plane which passes through the point and is perpendicular to the line with direction ratios ?
Q22mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Determine the coordinates of the foot of the perpendicular drawn from the origin to the plane .
Q23mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Which of the following is NOT a known factor to uniquely determine a plane?
Q24mediummcqQuantitative AptitudeStaff Selection Commission2026
0% accuracy
A solid metallic sphere of radius 4.2 cm is melted and recast into a right circular cylinder of radius 6 cm. What is the height (in cm) of the cylinder (correct to one decimal place)?
Q25hardmcqMathematicsAIEEE 20042026
0% accuracy
A line makes the same angle with each of the and axes. If the angle which it makes with -axis, is such that then equals
Q26hardmcqMathematicsAIEEE 20042026
0% accuracy
Distance between two parallel planes and is
Q27hardmcqMathematicsAIEEE 20042026
0% accuracy
A line with direction cosines proportional to meets each of the lines and The co-ordinates of each of the point of intersection are given by
Q28hardmcqMathematicsAIEEE 20042026
0% accuracy
If the straight lines and with parameters and respectively, are co-planar then equals
Q29hardmcqMathematicsAIEEE 20042026
0% accuracy
The intersection of the spheres and is the same as the intersection of one of the sphere and the plane
Q30mediummcqMathematicsAIEEE 20062026
0% accuracy
The two lines ; and are perpendicular to each other if:
Q31mediummcqMathematicsAIEEE 20062026
0% accuracy
The image of the point in the plane is:
Q32mediummcqQuantitative AptitudeStaff Selection Commission2026
100% accuracy
A dodecahedron has 20 vertices. How many edges does it have?
Q33mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Determine the coordinates of the point where the line through the points and crosses the -plane.
Q34mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
If is the equation of the line passing through and , then is:
Q35mediummcqQuantitative AptitudeCompetitive Exam2026
A sphere of radius is melted and made into a cone of height . Find the diameter of the cone.
Q36mediummcqMathematicsMathematics Mock Test - 112026
Consider a plane passing through the points , and . Which one of the following points lies on this plane?
Q37mediummcqMathematicsMathematics Mock Test - 112026
Consider the plane passing through the points , and . What are the direction ratios of the normal to the plane?
Q38mediummcqMathematicsMathematics Mock Test - 112026
The number of straight lines that are equally inclined to the three-dimensional coordinate axes is:
Q39mediummcqMathematicsMathematics Mock Test - 82026
The ratio in which the plane divides the line joining the points and is:
Q40mediummcqMathematicsMathematics Mock Test - 112026
Let be a line that is perpendicular to the plane and passes through the point . The point on the line that is nearest to the -axis is:
Q41mediummcqQuantitative Aptitude@NUM: 54Competitive Exam2026
A rectangle of length and breadth is rotated about its shorter side to form a cylinder. What is the volume (in ) of the cylinder so generated? (Take )
Q42hardmcqMathematicsCompetitive Exams2026
A plane intersects a regular tetrahedron in such a way that the intersection forms an equilateral triangle. How many such planes can do this?
Q43mediummcqQuantitative AptitudeSSC CGL2026
If a cone of radius 10.5cm and height 12cm is melted and constructed into a cylinder of the same radius, what will be the height of this cylinder?
Q44mediummcqQuantitative AptitudeStaff Selection Commission2026
If a cylinder of radius 7cm and height 9cm is melted and constructed into a cone of the same radius, what will be the height of this cone?
Q45mediummcqQuantitative AptitudeStaff Selection Commission2026
If the length of the diagonal of a cube is 16
3

​
cm, what is its lateral surface area (in sq cm)?
Q46mediummcqMental Ability and ReasoningUP Police Assistant Operator Exam2026
When a cube is sliced by a plane perpendicular to one of its body diagonals passing through its midpoint, what is the shape of the resulting cross-section?
Q47mediummcqQuantitative Aptitude@NUM: 52SSC CGL2026
How many spherical balls each of radius can be made out of a solid metallic cube of edge ? (Take )
Q48mediummcqQuantitative AptitudeCompetitive Exam2026
Find the maximum length of a rod, that can be placed in a room of dimension 12m×12m×14m.
Q49mediummcqQuantitative AptitudeCompetitive Exam2026
How many cubes of length 50 cm can be accommodated in a container of 5 m in length, 2 m in width and 5 m in height?
Q50mediummcqMathematicsMathematics Mock Test - 112026
Let be the plane passing through the intersection of planes and . If the plane contains the origin, then the equation of the plane is:
Q51mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
Six solid cubes, each of side , are melted to form a rectangular solid of base area . The lateral surface area (in ) of the resulting solid is:
Q52mediummcqReasoningCompetitive Exam2026
When a cylinder is sliced by a plane parallel to its height and passing through the center, what is the shape of the cross-section?
Q53mediummcqReasoningCompetitive Exam2026
A regular dodecahedron is sliced by a plane passing through two opposite edges and not through any vertices. What is the shape of the cross-section?
Q54mediummcqMathematicsMathematics Mock Test - 112026
Three vertices of a parallelogram are , and . The coordinates of the fourth vertex are:
Q55hardmcqMathematicsCompetitive Exams2026
A cylinder is intersected by a plane inclined at an angle of to its axis. What is the shape of the resulting cross-section?
Q56mediummcqMathematicsMathematics Mock Test - 112026
If the coordinates of and are and , then the projections of the line segment on the coordinate axes are:
Q57mediummcqMathematicsMathematics Mock Test - 112026
A line joining the points and is perpendicular to a plane. Then the coefficients of and in the equation of the plane are respectively:
Q58mediummcqMathematicsMathematics Mock Test - 112026
The reflection of the origin in the plane is:
Q59mediummcqMathematicsAIEEE2026
A line in three-dimensional space makes angles and with the positive -axis and the positive -axis respectively. If makes an acute angle with the positive -axis, then equals:
Q60mediummcqMathematicsAIEEE2026
The plane cuts the sphere in a circle of radius:
Q61mediummcqMathematicsAIEEE2026
The angle between the lines and is:
Q62mediummcqMathematicsAIEEE2026
The distance between the line and the plane is:
Q63mediummcqMathematicsAIEEE2026
If the angle between the line and the plane is such that , then the value of is:
Q64mediummcqMathematicsAIEEE-CBSE-ENG-032026
Two systems of rectangular axes have the same origin. If a plane cuts them at distances and from the origin, then:
Q65mediummcqMathematicsAIEEE-CBSE-ENG-032026
The radius of the circle in which the sphere is cut by the plane is:
Q66mediummcqMathematicsAIEEE-CBSE-ENG-032026
The shortest distance from the plane to the sphere is:
Q67mediummcqMathematicsAIEEE-CBSE-ENG-032026
The two lines , and , will be perpendicular, if and only if:
Q68mediummcqMathematicsAIEEE-CBSE-ENG-032026
A tetrahedron has vertices at , , and . Then the angle between the faces and will be:
Q69mediummcqMathematicsAIEEE-CBSE-ENG-032026
The lines and are coplanar if:
Q70mediummcqMathematicsAIEEE2026
The line passing through the points and crosses the -plane at the point . Then:
Q71mediummcqMathematicsAIEEE2026
If the straight lines and intersect at a point, then the integer is equal to:
Q72mediummcqMathematicsAIEEE 20092026
Let the line lies in the plane . Then equals:
Q73mediummcqMathematicsAIEEE2026
Statement-1: The point is the mirror image of the point in the plane .Statement-2: The plane bisects the line segment joining and .
Q74mediummcqMathematicsAIEEE2026
If the plane passes through the midpoint of the line joining the centres of the spheres and , then equals:
Q75hardmcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
If the angle between the line and the plane is , then equals:
Q76mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
Statement-1 : The point is the mirror image of the point in the line .Statement-2 : The line bisects the line segment joining and .
Q77mediummcqMathematicsAIEEE 20122026
If the lines and intersect, then is equal to:
Q78mediummcqMathematicsAIEEE 20122026
An equation of a plane parallel to the plane and at a unit distance from the origin is:
Q79mediummcqMathematicsJEE Main2026
Distance between two parallel planes and is:
Q80mediummcqMathematicsJEE Main2026
If the lines and are coplanar, then can have:
Q81mediummcqMathematicsMathematics Mock Test - 32026
The line with direction ratios is inclined with the -axis at an angle of:
Q82mediummcqMathematicsMathematics Mock Test - 32026
The lines and are:
Q83mediummcqMathematicsMathematics Mock Test - 32026
What is the cosine of the angle between the planes and ?
Q84mediummcqMathematicsMathematics Mock Test - 82026
Determine the vector equation for the line, given the Cartesian equation is ?
Q85mediummcqMathematicsMathematics Mock Test - 82026
Determine the vector equation of the plane passing through the intersection of the planes and , and through the point ?
Q86mediummcqMathematicsMathematics Mock Test - 82026
Determine the direction cosines of the unit vector perpendicular to the plane passing through the origin?
Q87mediummcqMathematicsMathematics Mock Test - 82026
If the plane is parallel to the line , then the value of is:
Q88mediummcqMathematicsMathematics Mock Test - 82026
If from a point , perpendiculars and are drawn to the and planes respectively, then the equation of the plane (where is the origin) is:

Frequently Asked Questions

How many 3d Geometry questions are on ExamTest.live?▼
We have 88 3d Geometry questions spread across 1 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
Are 3d Geometry MCQs free?▼
Yes. All 3d Geometry questions, answers, and explanations on ExamTest.live are completely free. No account or subscription required.
Which exams include 3d Geometry questions?▼
3d Geometry questions are commonly asked in Mathematics, Quantitative Aptitude, Reasoning, Logical Reasoning, Quantitative Aptitude@NUM: 54. You can filter by exam using the links above.
How do I practice 3d Geometry questions effectively?▼
Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.