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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.

43Papers
26Years
61Questions
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 32 50.8%
Hard 16 25.4%
Easy 11 17.5%
Not classified 4 6.3%

Question type distribution

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

MCQ 27 42.9%
MSQ 21 33.3%
Subjective 8 12.7%
Numerical Answer Type (NAT) 4 6.3%
Fill in the blanks 3 4.8%

Subject weightage

Top subjects by unique question coverage.

Mathematics
61 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
61 Qs

Subtopic coverage

Top subtopics inside this exact selection.

3D Geometry
61 Qs

Paper coverage

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

JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 2 Online
1 Qs
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 2 OFFLINE
2 Qs
JEE ADVANCED 2018 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2017 PAPER 2 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
2 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
3 Qs
IIT JEE 2005
1 Qs
IIT JEE 2005 MAINS
1 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2004
3 Qs
IIT JEE 2004 SCREENING
1 Qs
IIT JEE 2003
1 Qs
IIT JEE 2003 SCREENING
1 Qs
IIT JEE 1996
1 Qs
IIT JEE 1994
3 Qs
IIT JEE 1983
5 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 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 2 Online20261View paper
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 2018 PAPER 2 OFFLINE20182View paper
JEE ADVANCED 2017 PAPER 2 OFFLINE20171View 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 OFFLINE20102View 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 200620063View paper
IIT JEE 200520051View paper
IIT JEE 2005 MAINS20051View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 200420043View paper
IIT JEE 2004 SCREENING20041View paper
IIT JEE 200320031View paper
IIT JEE 2003 SCREENING20031View paper
IIT JEE 199619961View paper
IIT JEE 199419943View paper
IIT JEE 198319835View 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.
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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
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3
1983 · Mathematics · Algebra · 3D Geometry
IIT JEE 1983
The points with position vectors \(60i+3j,\) \(40i-8j,\) \(ai-52j\) are collinear if
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4
1983 · Mathematics · Algebra · 3D Geometry
IIT JEE 1983
A vector \(\overrightarrow A\) has components \({A_1},{A_2},{A_3}\) in a right -handed rectangular Cartesian coordinate system \(oxyz.\) The coordinate system is rotated about the \(x\)-axis through an angle \({\pi \over 2}.\) Find the components of \(A\) in the new coordinate system in terms of \({A_1},{A_2},{A_3}.\)
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5
1983 · Mathematics · Algebra · 3D Geometry
IIT JEE 1983
The unit vector perpendicular to the plane determined by \(P\left( {1, - 1,2} \right),\,Q\left( {2,0, - 1} \right)\) and \(R\left( {0,2,1} \right)\) is ...........
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6
1983 · Mathematics · Algebra · 3D Geometry
IIT JEE 1983
The area of the triangle whose vertices are \(A(1, -1, 2), B(2, 1, -1), C(3, -1, 2)\) is ..........
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7
1994 · Mathematics · Algebra · 3D Geometry
IIT JEE 1994
Let \(\alpha ,\beta ,\gamma\) be distinct real numbers. The points with position
vectors \(\alpha \widehat i + \beta \widehat j + \gamma \widehat k,\,\,\beta \widehat i + \gamma \widehat j + \alpha \widehat k,\,\,\gamma \widehat i + \alpha \widehat j + \beta \widehat k\)
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8
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
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9
1994 · Mathematics · Algebra · 3D Geometry
IIT JEE 1994
A unit vector perpendicular to the plane determined by the points \(P\left( {1, - 1,2} \right)Q\left( {2,0, - 1} \right)\) and \(R\left( {0,2,1} \right)\) is ............
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10
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.
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11
2003 · Mathematics · Algebra · 3D Geometry
IIT JEE 2003
(i) Find the equation of the plane passing through the points \((2, 1, 0), (5, 0, 1)\) and \((4, 1, 1).\)
(ii) If \(P\) is the point \((2, 1, 6)\) then find the point \(Q\) such that \(PQ\) is perpendicular to the plane in (i) and the mid point of \(PQ\) lies on it.
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12
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
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13
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.
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14
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 \({P_2}\)
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15
2004 · Mathematics · Algebra · 3D Geometry
IIT JEE 2004
Find the equation of plane passing through \((1, 1, 1)\) & parallel to the lines \({L_1},{L_2}\) having direction ratios \((1,0,-1),(1,-1,0).\) Find the volume of tetrahedron formed by origin and the points where these planes intersect the coordinate axes.
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16
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
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17
2005 · Mathematics · Algebra · 3D Geometry
IIT JEE 2005
Find the equation of the plane containing the line \(2x-y+z-3=0,3x+y+z=5\) and at a distance of \({1 \over {\sqrt 6 }}\) from the point \((2, 1, -1).\)
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18
2005 · Mathematics · Algebra · 3D Geometry
IIT JEE 2005 MAINS

Find the equation of the plane containing the line \(2 x-y+z-3=0,3 x+y+z=5\) and at a distance of \(\frac{1}{\sqrt{6}}\) from the point \((2,1,-1)\).

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19
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
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20
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:

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Showing 20 of 61 questions