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Previous year question hub

Three Dimensional Geometry - Algebra - Mathematics Previous Year Questions

Practice Three Dimensional Geometry - Algebra - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

11Papers
10Years
23Questions
1Topics

Three Dimensional Geometry question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Three Dimensional Geometry. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 23 100%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 23 100%

Subject weightage

Top subjects by unique question coverage.

Mathematics
23 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
23 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Three Dimensional Geometry
23 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

VITEEE 2025
2 Qs
WB JEE 2025
1 Qs
WB JEE 2024
3 Qs
WB JEE 2023
2 Qs
WB JEE 2022
2 Qs
WB JEE 2021
4 Qs
WB JEE 2020
2 Qs
WB JEE 2019
2 Qs
WB JEE 2018
2 Qs
WB JEE 2017
2 Qs
WB JEE 2016
1 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
VITEEE 202520252View paper
WB JEE 202520251View paper
WB JEE 202420243View paper
WB JEE 202320232View paper
WB JEE 202220222View paper
WB JEE 202120214View paper
WB JEE 202020202View paper
WB JEE 201920192View paper
WB JEE 201820182View paper
WB JEE 201720172View paper
WB JEE 201620161View paper

All Three Dimensional Geometry previous year questions

Practice every matching question in batches of 20, with every available option.

1
2016 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2016
The cosine of the angle between any two diagonals of a cube is
A
\({1 \over 3}\)
B
\({1 \over 2}\)
C
\({2 \over 3}\)
D
\({1 \over {\sqrt 3 }}\)
Open complete paper
2
2017 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2017
Three lines are drawn from the origin O with direction cosines proportional to (1, \(-\)1, 1), (2, \(-\)3, 0) and (1, 0, 3). The three lines are
A
not coplanar
B
coplanar
C
perpendicular to each other
D
coincident
Open complete paper
3
2017 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2017
The equation of the plane through (1, 2, \(-\)3) and (2, \(-\)2, 1) and parallel to X-axis is
A
y \(-\) z + 1 = 0
B
y \(-\) z \(-\) 1 = 0
C
y + z \(-\) 1 = 0
D
y + z + 1 = 0
Open complete paper
4
2018 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2018
A point P lies on a line through Q(1, \(-\)2, 3) and is parallel to the line \({x \over 1} = {y \over 4} = {z \over 5}\). If P lies on the plane 2x + 3y \(-\) 4z + 22 = 0, then segment PQ equals
A
\(\sqrt {42}\) units
B
\(\sqrt {32}\) units
C
4 units
D
5 units
Open complete paper
5
2018 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2018
The foot of the perpendicular drawn from the point (1, 8, 4) on the line joining the point (0, \(-\)11, 4) and (2, \(-\)3, 1) is
A
(4, 5, 2)
B
(\(-\)4, 5, 2)
C
(4, \(-\)5, 2)
D
(4, 5, \(-\)2)
Open complete paper
6
2019 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2019
The direction ratios of the normal to the plane passing through the points (1, 2, \(-\)3), (\(-\)1, \(-\)2, 1) and parallel to \({{x - 2} \over 2} = {{y + 1} \over 3} = {z \over 4}\) is
A
(2, 3, 4)
B
(14, \(-\)8, \(-\)1)
C
(\(-\)2, 0, \(-\)3)
D
(1, \(-\)2, \(-\)3)
Open complete paper
7
2019 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2019
The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles is
A
x + y + z = 0
B
x + y \(-\) z = 9
C
x + y + z = 9
D
x + y \(-\) z + 9 = 0
Open complete paper
8
2020 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2020
The sine of the angle between the straight line \({{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}\) and the plane \(2x - 2y + z = 5\) is
A
\({{2\sqrt 3 } \over 5}\)
B
\({{\sqrt 2 } \over {10}}\)
C
\({4 \over {5\sqrt 2 }}\)
D
\({{\sqrt 5 } \over 6}\)
Open complete paper
9
2020 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2020
The equation of the plane through the point \((2, - 1, - 3)\) and parallel to the lines

\({{x - 1} \over 2} = {{y + 2} \over 3} = {z \over { - 4}}\) and \({x \over 2} = {{y - 1} \over { - 3}} = {{z - 2} \over 2}\) is
A
\(8x + 14y + 13z + 37 = 0\)
B
\(8x - 14y - 13z - 37 = 0\)
C
\(8x - 14y - 13z + 37 = 0\)
D
\(x + 2y + 2z + 6 = 0\)
Open complete paper
10
2021 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2021
If from a point P(a, b, c), perpendicular PA and PB are drawn to YZ and ZX-planes respectively, then the equation of the plane OAB is
A
bcx + cay + abz = 0
B
bcx + cay \(-\) abz = 0
C
bcx \(-\) cay + abz = 0
D
bcx \(-\) cay \(-\) abz = 0
Open complete paper
11
2021 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2021
A plane meets the co-ordinate axes t the points A, B, C respectively such a way that the centroid of \(\Delta\)ABC is (1, r, r2) for some real r. If the plane passes through the point (5, 5, \(-\)12) then r =
A
\({3 \over 2}\)
B
4
C
\(-\) 4
D
\(-\) \({3 \over 2}\)
Open complete paper
12
2021 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2021
The plane lx + my = 0 is rotated about its line of intersection with the plane z = 0 through an angle \(\alpha\). The equation changes to
A
\(lx + my \pm \tan \alpha \sqrt {{l^2} + {m^2}} = 0\)
B
\(lx + my \pm z\tan \alpha \sqrt {{l^2} + {m^2} + 1} = 0\)
C
\(lx + my \pm z\tan \alpha \sqrt {{l^2} + 1} = 0\)
D
\(lx + my \pm z\tan \alpha \sqrt {{l^2} + {m^2}} = 0\)
Open complete paper
13
2021 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2021
A line with positive direction cosines passes through the point P(2, \(-\)1, 2) and makes equal angle with co-ordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals.
A
1 unit
B
\(\sqrt 2\) unit
C
\(\sqrt 3\) unit
D
2 unit
Open complete paper
14
2022 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2022

The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y \(-\) z + 4 = 0 and parallel to the x-axis is

A
y + 3z + 6 = 0
B
y + 3z \(-\) 6 = 0
C
y \(-\) 3z + 6 = 0
D
y \(-\) 3z \(-\) 6 = 0
Open complete paper
15
2022 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2022

The line \(x - 2y + 4z + 4 = 0\), \(x + y + z - 8 = 0\) intersect the plane \(x - y + 2z + 1 = 0\) at the point

A
\(( - 2,5,1)\)
B
\((2, - 5,1)\)
C
\((2,5, - 1)\)
D
\((2,5,1)\)
Open complete paper
16
2023 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2023

If the distance between the plane \(\alpha x - 2y + z = k\) and the plane containing the lines \({{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}\) and \({{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}\) is \(\sqrt 6\), then \(|k|\) is

A
36
B
12
C
6
D
\(2\sqrt 3\)
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17
2023 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2023

The angle between a normal to the plane \(2x - y + 2z - 1 = 0\) and the X-axis is

A
\({\cos ^{ - 1}}{2 \over 3}\)
B
\({\cos ^{ - 1}}{1 \over 5}\)
C
\({\cos ^{ - 1}}{3 \over 4}\)
D
\({\cos ^{ - 1}}{1 \over 3}\)
Open complete paper
18
2024 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2024

Angle between two diagonals of a cube will be

A
\(\cos ^{-1}\left(\frac{1}{3}\right)\)
B
\(\sin ^{-1}\left(\frac{1}{3}\right)\)
C
\(\frac{\pi}{2}-\cos ^{-1}\left(\frac{1}{3}\right)\)
D
\(\frac{\pi}{2}-\sin ^{-1}\left(\frac{1}{3}\right)\)
Open complete paper
19
2024 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2024

If the relation between the direction ratios of two lines in \(\mathbb{R}^3\) are given by

$$l+\mathrm{m}+\mathrm{n}=0,2 l \mathrm{~m}+2 \mathrm{mn}-l \mathrm{n}=0$$

then the angle between the lines is (\(l, \mathrm{~m}, \mathrm{n}\) have their usual meaning)

A
\(\frac{\pi}{6}\)
B
\(\frac{2 \pi}{3}\)
C
\(\frac{\pi}{2}\)
D
\(\frac{\pi}{4}\)
Open complete paper
20
2024 · Mathematics · Algebra · Three Dimensional Geometry
WB JEE 2024

The plane \(2 x-y+3 z+5=0\) is rotated through \(90^{\circ}\) about its line of intersection with the plane \(x+y+z=1\). The equation of the plane in new position is

A
\(3 x+9 y+z+17=0\)
B
\(3 x+9 y+z=17\)
C
\(3 x-9 y-z=17\)
D
\(3 x+9 y-z=17\)
Open complete paper

Showing 20 of 23 questions