Mathematics · JEE

Three Dimensional Geometry Mock Test for JEE

31+ syllabus-aligned questions available

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A Three Dimensional Geometry JEE mock test on Goodmarks lets you attempt 31+ timed MCQs with instant feedback. Use it to benchmark speed, accuracy, and readiness for JEE Main Mathematics.

Simulate exam conditions with a Three Dimensional Geometry mock test. Attempt 31+ timed MCQs, check your score instantly, and review every solution to close gaps before the real exam.

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36+ important formulas for Three Dimensional Geometry

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Subtopics in Three Dimensional Geometry

View Three Dimensional Geometry formula sheet — 36+ JEE formulas

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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

In three dimensions, the coordinate axes of a rectangular cartesian coordinate system are

Q5MathsUnit 11: Three Dimensional Geometry

The equation of the plane passing through the intersection of the planes

\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{6}

and

\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}+\boldsymbol{4} \boldsymbol{z}+\boldsymbol{5}=

0,

and the point (1,1,1) is

Q6MathsUnit 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})

Q7MathsUnit 11: Three Dimensional Geometry

\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-1} \& \frac{x-1}{k}=

\frac{\boldsymbol{y}-\boldsymbol{4}}{\boldsymbol{2}}=\frac{\boldsymbol{z}-\boldsymbol{5}}{\boldsymbol{2}}

are coplanar then

\mathbf{k}=?

Q8MathsUnit 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}

Q9MathsUnit 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

Q10MathsUnit 11: Three Dimensional Geometry

If the points

(x, y,-3),(2,0,-1)

and (4,2,3) lies on a straight line, then what are the values of

x

and

y

respectively?

Q11MathsUnit 11: Three Dimensional Geometry

The direction ratios of the joining

A(1,2,1)

and (2,1,2) are

Q12MathsUnit 11: Three Dimensional Geometry

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

Q13MathsUnit 11: Three Dimensional Geometry

The equation of a plane passing through the point

A(2,-3,7)

and making equal intercepts on the axes, is?

Q14MathsUnit 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

Q15MathsUnit 11: Three Dimensional Geometry

z_{1}

and

z_{2}

are

z

co-ordinates of the points of trisection of the segment joining the points

\boldsymbol{A}(\mathbf{2}, \mathbf{1}, \mathbf{4}), \boldsymbol{B}(-\mathbf{1}, \mathbf{3}, \mathbf{6})

then

z_{1}+z_{2}=

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Frequently asked questions

How long should a Three Dimensional Geometry mock test take?

For a topic-level test, aim for 20–30 minutes. For a full subject mock, allow 60–90 minutes to mirror JEE timing.

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Aim for 70%+ accuracy initially, then push toward 85%+ as your exam date approaches. Review explanations for every wrong answer.

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