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Previous year question hub

Linear Algebra - Engineering Mathematics - Instrumentation Engineering Previous Year Questions

Practice Linear Algebra - Engineering Mathematics - Instrumentation Engineering previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

21Papers
18Years
44Questions
1Topics

Linear Algebra question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Linear Algebra. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Easy 37 84.1%
Medium 7 15.9%

Question type distribution

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

MCQ 32 72.7%
Numerical Answer Type (NAT) 7 15.9%
MSQ 3 6.8%
Fill in the blanks 2 4.5%

Subject weightage

Top subjects by unique question coverage.

Instrumentation Engineering
44 Qs

Most asked topics

Top topics across the included previous year papers.

Engineering Mathematics
44 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Linear Algebra
44 Qs

Paper coverage

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

Instrumentation Engineering (IN) 2026
2 Qs
Instrumentation Engineering (IN) 2025
2 Qs
Instrumentation Engineering (IN) 2024
2 Qs
Instrumentation Engineering (IN) 2023
2 Qs
Instrumentation Engineering (IN) 2022
2 Qs
Instrumentation Engineering (IN) 2021
3 Qs
Instrumentation Engineering (IN) 2020
3 Qs
Instrumentation Engineering (IN) 2019
2 Qs
Instrumentation Engineering (IN) 2018
2 Qs
Instrumentation Engineering (IN) 2017
4 Qs
Instrumentation Engineering (IN) 2016
2 Qs
Instrumentation Engineering (IN) 2015
1 Qs
Instrumentation Engineering (IN) 2014
1 Qs
Instrumentation Engineering (IN) 2013 [Session 1]
2 Qs
Instrumentation Engineering (IN) 2013 [Session 2]
2 Qs
Instrumentation Engineering (IN) 2013 [Session 3]
2 Qs
Instrumentation Engineering (IN) 2013 [Session 4]
2 Qs
Instrumentation Engineering (IN) 2011
1 Qs
Instrumentation Engineering (IN) 2010
2 Qs
Instrumentation Engineering (IN) 2009
3 Qs
Instrumentation Engineering (IN) 2007
2 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
Instrumentation Engineering (IN) 202620262View paper
Instrumentation Engineering (IN) 202520252View paper
Instrumentation Engineering (IN) 202420242View paper
Instrumentation Engineering (IN) 202320232View paper
Instrumentation Engineering (IN) 202220222View paper
Instrumentation Engineering (IN) 202120213View paper
Instrumentation Engineering (IN) 202020203View paper
Instrumentation Engineering (IN) 201920192View paper
Instrumentation Engineering (IN) 201820182View paper
Instrumentation Engineering (IN) 201720174View paper
Instrumentation Engineering (IN) 201620162View paper
Instrumentation Engineering (IN) 201520151View paper
Instrumentation Engineering (IN) 201420141View paper
Instrumentation Engineering (IN) 2013 [Session 1]20132View paper
Instrumentation Engineering (IN) 2013 [Session 2]20132View paper
Instrumentation Engineering (IN) 2013 [Session 3]20132View paper
Instrumentation Engineering (IN) 2013 [Session 4]20132View paper
Instrumentation Engineering (IN) 201120111View paper
Instrumentation Engineering (IN) 201020102View paper
Instrumentation Engineering (IN) 200920093View paper
Instrumentation Engineering (IN) 200720072View paper

All Linear Algebra previous year questions

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

1
2009 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2009
Let \( \mathbf{P} \neq 0 \) be a \( 3 \times 3 \) real matrix. There exist linearly independent vectors \( \mathbf{x} \) and \( \mathbf{y} \) such that \( \mathbf{Px} = 0 \) and \( \mathbf{Py} = 0 \). The dimension of the range space of \( \mathbf{P} \) is
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2
2009 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2009
The eigenvalues of a (2 × 2) matrix X are −2 and −3. The eigenvalues of the matrix (X + I)⁻¹(X + 5I) are
Open complete paper
3
2009 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2009
The matrix P = \begin{bmatrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix} rotates a vector about the axis \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} by an angle of
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4
2010 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2010
A real \( n \times n \) matrix \( A = [a_{ij}] \) is defined as follows: \( a_{ij} = i \), if \( i = j \) ; \( = 0 \), otherwise. The summation of all \( n \) eigenvalues of \( A \) is
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5
2010 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2010
X and Y are non-zero square matrices of size \(n \times n\). If \(XY = 0_{n \times n}\), then
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6
2011 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2011
The matrix \(\mathbf{M} = \begin{bmatrix} -2 & 2 & -3 \\ 2 & 1 & -6 \\ -1 & -2 & 0 \end{bmatrix}\) has eigenvalues \(-3, -3, 5\). An eigenvector corresponding to the eigenvalue 5 is \(\begin{bmatrix} 1 & 2 & -1 \end{bmatrix}^T\). One of the eigenvectors of the matrix \(\mathbf{M}^3\) is
Open complete paper
7
2013 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2013 [Session 1]
The dimension of the null space of the matrix $\begin{bmatrix} 0 & 1 & 1 \\ 1 & -1 & 0 \\ -1 & 0 & -1 \end{bmatrix}$ is
Open complete paper
8
2013 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2013 [Session 1]
One pair of eigenvectors corresponding to the two eigenvalues of the matrix \(\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}\) is
Open complete paper
9
2013 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2013 [Session 2]
The dimension of the null space of the matrix \( \begin{bmatrix} 0 & 1 & 1 \\ 1 & -1 & 0 \\ -1 & 0 & -1 \end{bmatrix} \) is
Open complete paper
10
2013 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2013 [Session 2]
One pair of eigenvectors corresponding to the two eigenvalues of the matrix $\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$ is
Open complete paper
11
2013 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2013 [Session 3]
The dimension of the null space of the matrix [0 1 1
1 -1 0
-1 0 -1] is
Open complete paper
12
2013 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2013 [Session 3]
One pair of eigenvectors corresponding to the two eigenvalues of the matrix \( \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix} \) is
Open complete paper
13
2014 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2014
For the matrix \( \mathbf{A} \) satisfying the equation given below, the eigenvalues are \[ [\mathbf{A}] \begin{bmatrix} 1 & 2 & 3 \\ 7 & 8 & 9 \\ 4 & 5 & 6 \end{bmatrix} = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \]
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14
2015 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2015
Question Number : 11 Question Type : MCQ
Let A be an n × n matrix with rank r (0 < r < n). Then Ax = 0 has p independent solutions, where p is
Open complete paper
15
2016 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2016
Consider the matrix A = \begin{pmatrix} 2 & 1 & 1 \\ 2 & 3 & 4 \\ -1 & -1 & -2 \end{pmatrix} whose eigenvalues are 1, -1 and 3. Then Trace of (A³ - 3A²) is ______.
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16
2016 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2016
The vector that is NOT perpendicular to the vectors $(i + j + k)$ and $(i + 2j + 3k)$ is ______.
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17
2024 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2024
A matrix M is constructed by stacking three column vectors v₁, v₂, v₃ as
M = [v₁ v₂ v₃].
Choose the set of vectors from the following options such that rank(M) = 3.
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18
2024 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2024
A \(3 \times 3\) matrix \(P\) with all real elements has eigenvalues \(\frac{1}{4}\), \(1\), and \(-2\). The value of \(|P^{-1}|\) is ______ (rounded off to nearest integer).
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19
2025 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2025
A \(2n \times 2n\) matrix \(A=[a_{ij}]\) has its elements as
\[a_{ij} = \begin{cases} \beta & \text{if } (i+j) \text{ is odd}, \\ -\beta & \text{if } (i+j) \text{ is even}, \end{cases}\]
where \(n\) is any integer greater than 2 and \(\beta\) is any non-zero real number. The rank of \(A\) is
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20
2025 · Instrumentation Engineering · Engineering Mathematics · Linear Algebra
Instrumentation Engineering (IN) 2025
If one of the eigenvectors of the matrix \(A=\begin{bmatrix}-1 & -1 \\ x & -4\end{bmatrix}\) is along the direction of \(\begin{bmatrix}\alpha \\ 2\alpha\end{bmatrix}\), where \(\alpha\) is any non-zero real number, then the value of \(x\) is ______ (in integer).
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Showing 20 of 42 questions