My Cart
Your Cart 0

    Your cart is empty.

  • Total (Amount) ₹0.00
Previous year question hub

3D Geometry - Algebra - Mathematics Previous Year Questions

Practice 3D Geometry - Algebra - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

34Papers
24Years
46Questions
1Topics

3D Geometry question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for 3D Geometry. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 28 60.9%
Hard 9 19.6%
Easy 7 15.2%
Not classified 2 4.3%

Question type distribution

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

Multiple Choices 40 87%
Subjective 4 8.7%
Numerical Answer Type (NAT) 2 4.3%

Subject weightage

Top subjects by unique question coverage.

Mathematics
46 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
46 Qs

Subtopic coverage

Top subtopics inside this exact selection.

3D Geometry
46 Qs

Paper coverage

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

JEE ADVANCED 2025 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2024 PAPER 1 ONLINE
2 Qs
JEE ADVANCED 2024 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2023 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2022 PAPER 1 ONLINE
2 Qs
JEE ADVANCED 2020 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2020 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2019 PAPER 1 OFFLINE
2 Qs
JEE ADVANCED 2019 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2018 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2016 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2016 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 1 OFFLINE
2 Qs
JEE ADVANCED 2014 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2013 PAPER 1 OFFLINE
2 Qs
JEE ADVANCED 2013 PAPER 2 OFFLINE
2 Qs
IIT JEE 2012 PAPER 2 OFFLINE
2 Qs
IIT JEE 2012 PAPER 1 OFFLINE
1 Qs
IIT JEE 2010 PAPER 1 OFFLINE
2 Qs
IIT JEE 2010 PAPER 2 OFFLINE
1 Qs
IIT JEE 2009 PAPER 1 OFFLINE
1 Qs
IIT JEE 2009 PAPER 2 OFFLINE
1 Qs
IIT JEE 2008 PAPER 1 OFFLINE
1 Qs
IIT JEE 2008 PAPER 2 OFFLINE
1 Qs
IIT JEE 2007 PAPER 2 OFFLINE
1 Qs
IIT JEE 2006
2 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2004
2 Qs
IIT JEE 2004 SCREENING
1 Qs
IIT JEE 2003 SCREENING
1 Qs
IIT JEE 1996
1 Qs
IIT JEE 1994
2 Qs
IIT JEE 1983
2 Qs
IIT JEE 1978
1 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
JEE ADVANCED 2025 PAPER 1 ONLINE20251View paper
JEE ADVANCED 2024 PAPER 1 ONLINE20242View paper
JEE ADVANCED 2024 PAPER 2 ONLINE20241View paper
JEE ADVANCED 2023 PAPER 1 ONLINE20231View paper
JEE ADVANCED 2022 PAPER 1 ONLINE20222View paper
JEE ADVANCED 2020 PAPER 1 OFFLINE20201View paper
JEE ADVANCED 2020 PAPER 2 OFFLINE20201View paper
JEE ADVANCED 2019 PAPER 1 OFFLINE20192View paper
JEE ADVANCED 2019 PAPER 2 OFFLINE20191View paper
JEE ADVANCED 2018 PAPER 1 OFFLINE20181View paper
JEE ADVANCED 2016 PAPER 1 OFFLINE20161View paper
JEE ADVANCED 2016 PAPER 2 OFFLINE20161View paper
JEE ADVANCED 2015 PAPER 1 OFFLINE20152View paper
JEE ADVANCED 2014 PAPER 1 OFFLINE20141View paper
JEE ADVANCED 2013 PAPER 1 OFFLINE20132View paper
JEE ADVANCED 2013 PAPER 2 OFFLINE20132View paper
IIT JEE 2012 PAPER 1 OFFLINE20121View paper
IIT JEE 2012 PAPER 2 OFFLINE20122View paper
IIT JEE 2010 PAPER 1 OFFLINE20102View paper
IIT JEE 2010 PAPER 2 OFFLINE20101View paper
IIT JEE 2009 PAPER 1 OFFLINE20091View paper
IIT JEE 2009 PAPER 2 OFFLINE20091View paper
IIT JEE 2008 PAPER 1 OFFLINE20081View paper
IIT JEE 2008 PAPER 2 OFFLINE20081View paper
IIT JEE 2007 PAPER 2 OFFLINE20071View paper
IIT JEE 200620062View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 200420042View paper
IIT JEE 2004 SCREENING20041View paper
IIT JEE 2003 SCREENING20031View paper
IIT JEE 199619961View paper
IIT JEE 199419942View paper
IIT JEE 198319832View paper
IIT JEE 197819781View paper

All 3D Geometry previous year questions

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

1
1978 · Mathematics · Algebra · 3D Geometry
IIT JEE 1978
From a point \(O\) inside a triangle \(ABC,\) perpendiculars \(OD\), \(OE, OF\) are drawn to the sides \(BC, CA, AB\) respectively. Prove that the perpendiculars from \(A, B, C\) to the sides \(EF, FD, DE\) are concurrent.
Write your response
Open complete paper
2
1983 · Mathematics · Algebra · 3D Geometry
IIT JEE 1983
The volume of the parallelopiped whose sides are given by
\(\overrightarrow {OA} = 2i - 2j,\,\overrightarrow {OB} = i + j - k,\,\overrightarrow {OC} = 3i - k,\) is
A
\({4 \over {13}}\)
B
\(4\)
C
\({2 \over 7}\)
D
none of these
Open complete paper
3
1983 · Mathematics · Algebra · 3D Geometry
IIT JEE 1983
The points with position vectors \(60i+3j,\) \(40i-8j,\) \(ai-52j\) are collinear if
A
\(a=-40\)
B
\(a=40\)
C
\(a=20\)
D
none of these
Open complete paper
4
1994 · Mathematics · Algebra · 3D Geometry
IIT JEE 1994
Let \(\alpha ,\beta ,\gamma\) be distinct real numbers. The points with position
vectors \(\alpha \widehat i + \beta \widehat j + \gamma \widehat k,\,\,\beta \widehat i + \gamma \widehat j + \alpha \widehat k,\,\,\gamma \widehat i + \alpha \widehat j + \beta \widehat k\)
A
are collinear
B
form an equilateral triangle
C
form a scalene triangle
D
form a right-angled triangle
Open complete paper
5
1994 · Mathematics · Algebra · 3D Geometry
IIT JEE 1994
Let \(\overrightarrow p\) and \(\overrightarrow q\) be the position vectors of \(P\) and \(Q\) respectively, with respect to \(O\) and \(\left| {\overrightarrow p } \right| = p,\left| {\overrightarrow q } \right| = q.\) The points \(R\) and \(S\) divide \(PQ\) internally and externally in the ratio \(2:3\) respectively. If \(OR\) and \(OS\) are perpendicular then
A
\(9{q^2} = 4{q^2}\)
B
\(4{p^2} = 9{q^2}\)
C
\(9p = 4q\)
D
\(4p = 9q\)
Open complete paper
6
1996 · Mathematics · Algebra · 3D Geometry
IIT JEE 1996
The position vectors of the vertices \(A, B\) and \(C\) of a tetrahedron \(ABCD\) are \(\widehat i + \widehat j + \widehat k,\,\widehat i\) and \(3\widehat i\,,\) respectively. The altitude from vertex \(D\) to the opposite face \(ABC\) meets the median line through \(A\) of the triangle \(ABC\) at a point \(E.\) If the length of the side \(AD\) is \(4\) and the volume of the tetrahedron is \({{2\sqrt 2 } \over 3},\) find the position vector of the point \(E\) for all its possible positions.
Write your response
Open complete paper
7
2003 · Mathematics · Algebra · 3D Geometry
IIT JEE 2003 SCREENING
The value of \(k\) such that \({{x - 4} \over 1} = {{y - 2} \over 1} = {{z - k} \over 2}\) lies in the plane \(2x -4y +z = 7,\) is
A
\(7\)
B
\(-7\)
C
no real value
D
\(4\)
Open complete paper
8
2004 · Mathematics · Algebra · 3D Geometry
IIT JEE 2004
A parallelopiped \('S'\) has base points \(A, B, C\) and \(D\) and upper face points \(A',\) \(B',\) \(C'\) and \(D'.\) This parallelopiped is compressed by upper face \(A'B'C'D'\) to form a new parallelopiped \('T'\) having upper face points \(A'',B'',C''\) and \(D''.\) Volume of parallelopiped \(T\) is \(90\) percent of the volume of parallelopiped \(S.\) Prove that the locus of \('A''',\) is a plane.
Write your response
Open complete paper
9
2004 · Mathematics · Algebra · 3D Geometry
IIT JEE 2004
\({P_1}\) and \({P_2}\) are planes passing through origin. \({L_1}\) and \({L_2}\) are two line on \({P_1}\) and \({P_2}\) respectively such that their intersection is origin. Show that there exists points \(A, B, C,\) whose permutation \(A',B',C'\) can be chosen such that (i) \(A\) is on \({L_1},\) \(B\) on \({P_1}\) but not on \({L_1}\) and \(C\) not on \({P_1}\) (ii) \(A'\) is on \({L_2},\) \(B'\) on \({P_2}\) but not on \({L_2}\) and \(C'\) not on \({P_2}\)
Write your response
Open complete paper
10
2004 · Mathematics · Algebra · 3D Geometry
IIT JEE 2004 SCREENING
If the lines \({{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 1} \over 4}\) and \(\,{{x - 3} \over 1} = {{y - k} \over 2} = {z \over 1}\) intersect, then the value of \(k\) is
A
\(3/2\)
B
\(9/2\)
C
\(-2/9\)
D
\(-3/2\)
Open complete paper
11
2005 · Mathematics · Algebra · 3D Geometry
IIT JEE 2005 SCREENING
A variable plane at a distance of the one unit from the origin cuts the coordinates axes at \(A,\) \(B\) and \(C.\) If the centroid \(D\) \((x, y, z)\) of triangle \(ABC\) satisfies the relation \({1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = k,\) then the value \(k\) is
A
\(3\)
B
\(1\)
C
\({1 \over 3}\)
D
\(9\)
Open complete paper
12
2006 · Mathematics · Algebra · 3D Geometry
IIT JEE 2006

A plane passes through $(1,-2,1)$ and is perpendicular to two planes $2 x-2 y+z=0$ and $x-y+2 z=4$. The distance of the plane from the point $(1,2,2)$ is:

A

0

B

1

C

$\sqrt{2}$

D

$2 \sqrt{2}$

Open complete paper
13
2006 · Mathematics · Algebra · 3D Geometry
IIT JEE 2006
Let \({\overrightarrow A }\) be vector parallel to line of intersection of planes \({P_1}\) and \({P_2}.\) Planes \({P_1}\) is parallel to the vectors \(2\widehat j + 3\widehat k\) and \(4\widehat j - 3\widehat k\) and that \({P_2}\) is parallel to \(\widehat j - \widehat k\) and \(3\widehat i + 3\widehat j,\) then the angle between vector \({\overrightarrow A }\) and a given vector \(2\widehat i + \widehat j - 2\widehat k\) is
A
\({\pi \over 2}\)
B
\({\pi \over 4}\)
C
\({\pi \over 6}\)
D
\({3\pi \over 4}\)
Open complete paper
14
2007 · Mathematics · Algebra · 3D Geometry
IIT JEE 2007 PAPER 2 OFFLINE

Consider the planes \(3 x-6 y-2 z=15\) and \(2 x+y-2 z=5\).

STATEMENT - 1 : The parametric equations of the line of intersection of the given planes are \(x=3+14 t, y=1+2 t, z=15 t\)

STATEMENT - 2 : The vectors \(14 \hat{i}+2 \hat{j}+15 \hat{k}\) is parallel to the line of intersection of the given planes.

A
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
B
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
C
Statement-1 is True, Statement-2 is False
D
Statement-1 is False, Statement-2 is True
Open complete paper
15
2008 · Mathematics · Algebra · 3D Geometry
IIT JEE 2008 PAPER 1 OFFLINE
Consider three planes \({P_1}:x - y + z = 1\) \({P_2}:x + y - z = 1\) \({P_3}:x - 3y + 3z = 2\)

Let \({L_1},\) \({L_2},\) \({L_3}\) be the lines of intersection of the planes \({P_2}\) and \({P_3},\) \({P_3}\) and \({P_1},\) \({P_1}\) and \({P_2},\) respectively.

STATEMENT - 1Z: At least two of the lines \({L_1},\) \({L_2}\) and \({L_3}\) are non-parallel and

STATEMENT - 2: The three planes doe not have a common point.

A
STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is a correct explanation for STATEMENT - 1
B
STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is NOT a correct explanation for STATEMENT - 1
C
STATEMENT - 1 is True, STATEMENT - 2 is False
D
STATEMENT - 1 is False, STATEMENT - 2 is True
Open complete paper
16
2008 · Mathematics · Algebra · 3D Geometry
IIT JEE 2008 PAPER 2 OFFLINE
The distance of the point \((1, 1, 1)\) from the plane passing through the point \((-1, -2, -1)\) and whose normal is perpendicular to both the lines \({L_1}\) and \({L_2}\) is :
A
\({2 \over {\sqrt {75} }}\)
B
\({7 \over {\sqrt {75} }}\)
C
\({13 \over {\sqrt {75} }}\)
D
\({23 \over {\sqrt {75} }}\)
Open complete paper
17
2009 · Mathematics · Algebra · 3D Geometry
IIT JEE 2009 PAPER 1 OFFLINE
Let \(P(3,2,6)\) be a point in space and \(Q\) be a point on the line \(\widehat r = \left( {\widehat i - \widehat j + 2\widehat k} \right) + \mu \left( { - 3\widehat i + \widehat j + 5\widehat k} \right)\)

Then the value of \(\mu\) for which the vector \({\overrightarrow {PQ} }\) is parallel to the plane \(x - 4y + 3z = 1\) is :

A
\({1 \over 4}\)
B
\(-{1 \over 4}\)
C
\({1 \over 8}\)
D
\(-{1 \over 8}\)
Open complete paper
18
2009 · Mathematics · Algebra · 3D Geometry
IIT JEE 2009 PAPER 2 OFFLINE

A line with positive direction cosines passes through the point P(2, \(-\)1, 2) and makes equal angles with the coordinate axes. The line meets the plane \(2x + y + z = 9\) at point Q. The length of the line segment PQ equals

A
\(1\)
B
\({\sqrt 2 }\)
C
\({\sqrt 3 }\)
D
\(2\)
Open complete paper
19
2010 · Mathematics · Algebra · 3D Geometry
IIT JEE 2010 PAPER 1 OFFLINE
If the distance between the plane \(Ax-2y+z=d\) 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 \(\left| d \right|\) is ___________.
Enter a numerical response
Open complete paper
20
2010 · Mathematics · Algebra · 3D Geometry
IIT JEE 2010 PAPER 1 OFFLINE
Equation of the plane containing the straight line \({x \over 2} = {y \over 3} = {z \over 4}\) and perpendicular to the plane containing the straight lines \({x \over 3} = {y \over 4} = {z \over 2}\) and \({x \over 4} = {y \over 2} = {z \over 3}\) is
A
\(x+2y-2z=0\)
B
\(3x+2y-2z=0\)
C
\(x-2y+z=0\)
D
\(5x+2y-4z=0\)
Open complete paper

Showing 20 of 46 questions