Mathematics · JEE

Three Dimensional Geometry Previous Year Questions for JEE

16+ syllabus-aligned questions available

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Goodmarks offers 16+ JEE-style PYQs for Three Dimensional Geometry with detailed solutions. While official past papers rotate yearly, our bank covers the same concepts, difficulty, and question formats tested in JEE Mathematics.

Previous year questions are the fastest way to understand how Three Dimensional Geometry is tested in JEE. Practise 16+ exam-pattern MCQs modelled on JEE Main and Advanced, with full solutions for every question.

Subtopics in Three Dimensional Geometry

Coordinates of a point in space, the distance between two points, section formula
Direction ratios and direction cosines and the angle between two intersecting lines
Equation of a line; Skew lines, the shortest distance between them and its equation

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Q1MathsUnit 11: Three Dimensional Geometry

The plane

\boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\boldsymbol{z}-\boldsymbol{6}=\mathbf{0}

and the line

\frac{x}{1}=\frac{y}{2}=\frac{z}{3}

are related as

Q2MathsUnit 11: Three Dimensional Geometry

Statement-1: The point

\boldsymbol{A}(\mathbf{3}, \mathbf{1}, \boldsymbol{6})

is the mirror image of the point

B(1,3,4)

in the plane

\boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5}

Statement-2: The plane

\boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5}

bisects the line segment joining

\boldsymbol{A}(\boldsymbol{3}, \mathbf{1}, \boldsymbol{6})

and

\boldsymbol{B}(\mathbf{1}, \boldsymbol{3}, \boldsymbol{4})

Q3MathsUnit 11: Three Dimensional Geometry

How many cubes each of surface area

24 c m^{2}

can be made out of a cube of edge measure

1 \mathrm{m} ?

Q4MathsUnit 11: Three Dimensional Geometry

Find the equation of the plane through the points

\boldsymbol{A}(\mathbf{2}, \mathbf{2}-\mathbf{1}), \boldsymbol{B}(\mathbf{3}, \mathbf{4}, \mathbf{2})

and

\boldsymbol{C}(\boldsymbol{7}, \boldsymbol{0}, \boldsymbol{6})

Q5MathsUnit 11: Three Dimensional Geometry

The shortest distance between the lines

\frac{\boldsymbol{x}-\mathbf{5}}{\mathbf{4}}=\frac{\boldsymbol{y}-\mathbf{7}}{-\mathbf{5}}=\frac{\boldsymbol{z}+\mathbf{3}}{-\mathbf{5}}

and

\frac{\boldsymbol{x}-\mathbf{8}}{\mathbf{4}}=

\frac{y-7}{-5}=\frac{z-5}{-5}

Q6MathsUnit 11: Three Dimensional Geometry

\operatorname{Let} \boldsymbol{A}(\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\mathbf{5} \hat{\boldsymbol{k}}) \boldsymbol{B}(-\hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+2 \hat{\boldsymbol{k}})

and

C(\lambda \hat{i}+5 \hat{j}+\mu \hat{k})

are vertices of

a

triangle and its median through

A

is equally inclined to the positive directions of the axes. The value of

\lambda+

\mu

is equal to

Q7MathsUnit 11: Three Dimensional Geometry

The ratio of the volume and surface area of a sphere of unit radius:

Q8MathsUnit 11: Three Dimensional Geometry

The projection of the line segment joining (0,0,0) and (5,2,4) on the line whose direction ratios are 2,-3,6 is

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Frequently asked questions

Why practise PYQs for Three Dimensional Geometry?

PYQs reveal recurring concepts, common traps, and the difficulty level JEE expects. Solving them builds exam temperament and time management.

Does Goodmarks have actual JEE past papers?

Our bank includes exam-style MCQs aligned with JEE Main Mathematics syllabus for Three Dimensional Geometry, covering the same topics as previous year papers.

How should I use PYQs for Three Dimensional Geometry?

Solve timed sets, review every explanation, note weak subtopics, then revisit with focused practice on Goodmarks.

Are PYQ solutions step-by-step?

Yes. Every question includes the correct answer and a detailed explanation showing the reasoning.