CBSE Class 12 Maths Previous Year Question Paper 2013
This CBSE Class 12 Maths previous year question paper from 2013 focuses on the topic of Transpose of a Matrix & Symmetric Matrix. It includes one-mark questions that test fundamental concepts. For instance, students are asked to identify a matrix that is both symmetric and skew-symmetric, determine the value of an element to make a matrix skew-symmetric, and perform operations involving matrix transposes like finding A^T - B^T and A + A'. Solving these previous year papers helps students understand the exam pattern, identify important concepts, and build confidence for their board examinations.
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Quick info
| Board | CBSE |
|---|---|
| Class | 12 |
| Subject | Maths |
| Session | 2013 |
| Language | English |
| Type | Previous Year Question Paper |
| Exam type | Board Exam |
Paper pattern
This paper consists of one-mark questions testing concepts related to matrix transpose, symmetric, and skew-symmetric matrices.
Topics covered
Paper topics
- Matrix Transpose
- Symmetric Matrix
- Skew-Symmetric Matrix
Important topics
- Symmetric and Skew-Symmetric Matrices
- Properties of Skew-Symmetric Matrices
- Matrix Addition and Transpose
PDF preview
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Question paper text
Transpose of a Matrix & Symmetric Matrix
1 Mark Questions
- Write <math>2 \times 2</math> matrix which is both symmetric
and skew-symmetric matrices. Delhi 2014C
A null matrix of order <math>2 \times 2</math> is both symmetric and skew-symmetric matrices.
For a symmetric matrix,
<math>a_{ii} = a_{ii}</math>
...(i)
and for a skew-symmetric matrix,
<math>a_{ii} = -a_{ii}</math>
...(ii)
From Eqs. (i) and (ii), we get <math>a_{ii} = 0</math> (1) 2. For what value of x, is the matrix
<math display="block">A = \begin{bmatrix} 0 & 1 & -2 \\ -1 & 0 & 3 \end{bmatrix}</math> a skew-symmetric matrix? x -3 0
All India 2013: HOTS
If A is a skew-symmetric matrix, then <math>A = -A^T</math>, where <math>A^T</math> is transpose of matrix A.
Given, <math>A = \begin{vmatrix} 0 & 1 & -2 \\ -1 & 0 & 3 \\ x & -3 & 0 \end{vmatrix}</math>
We know that, if A is a skew-symmetric matrix, then <math>A = -A^{T}</math> ...(i)
From Eq. (i), we get
<math display="block">\begin{bmatrix} 0 & 1 & -2 \\ -1 & 0 & 3 \\ x & -3 & 0 \end{bmatrix} = - \begin{bmatrix} 0 & -1 & x \\ 1 & 0 & -3 \\ -2 & 3 & 0 \end{bmatrix}</math> <math display="block">\Rightarrow \begin{bmatrix} 0 & 1 & -2 \\ -1 & 0 & 3 \\ x & -3 & 0 \end{bmatrix} = \begin{bmatrix} 0 & 1 & -x \\ -1 & 0 & 3 \\ 2 & -3 & 0 \end{bmatrix}</math>
(1/2)
On comparing the corresponding element,
we get
<math>x = 2</math>
(1/2)
- If <math>A^T = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix}</math> and <math>B = \begin{bmatrix} -1 & 2 & 1 \\ 1 & 2 & 3 \end{bmatrix}</math>, then find
<math>A^{T} - B^{T}</math>. All India 2012
Given, <math>B = \begin{bmatrix} -1 & 2 & 1 \\ 1 & 2 & 3 \end{bmatrix}</math>
Transpose of <math>B = B^T = \begin{bmatrix} -1 & 1 \\ 2 & 2 \\ 1 & 3 \end{bmatrix}</math>
(1/2)
Now, <math>A^{T} - B^{T} = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix} - \begin{bmatrix} -1 & 1 \\ 2 & 2 \\ 1 & 3 \end{bmatrix}</math> <math display="block">= \begin{bmatrix} 3+1 & 4-1 \\ -1-2 & 2-2 \\ 0-1 & 1-3 \end{bmatrix} = \begin{bmatrix} 4 & 3 \\ -3 & 0 \\ -1 & -2 \end{bmatrix} </math> (1/2)
4. If <math>A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}</math>, then find <math>A + A'</math>.
All India 2010C
Firstly, we find the transpose of matrix A and then add the corresponding elements of both matrices A and A'.
Given, <math>A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}</math> <math display="block">\therefore A' = \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix}</math>
Now, <math>A + A' = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} + \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix} = \begin{bmatrix} 2 & 5 \\ 5 & 8 \end{bmatrix}</math> (1)
- If <math>A = \begin{bmatrix} 3 & 4 \\ 2 & 3 \end{bmatrix}</math>, then find <math>A + A'</math>, where <math>A'</math> is
transpose of A. All India 2009C
Frequently asked questions
What is this document?
This is a CBSE Class 12 Maths previous year board question paper from 2013, focusing on Transpose of a Matrix & Symmetric Matrix.
What topics are covered?
The paper covers concepts related to matrix transpose, symmetric matrices, and skew-symmetric matrices, including their properties and operations.
How can solving this paper help?
Solving this previous year question paper helps students understand the exam pattern, practice specific topics, and improve their score in the CBSE Class 12 Maths board exam.
What is the format of the questions?
The questions in this paper are primarily one-mark questions designed to test fundamental understanding of the covered matrix concepts.
Is this a complete question paper?
This extract contains selected one-mark questions from the 2013 CBSE Class 12 Maths board paper focusing on Transpose of a Matrix & Symmetric Matrix.
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