CBSE Class 12 Maths Previous Year Question Paper 2014
This is the CBSE Class 12 Maths Previous Year Question Paper from 2014, focusing on topics like Inverse of a Matrix and Application of Determinants & Matrices. The paper includes questions designed to test students' understanding of matrix operations and their application in solving systems of linear equations. One of the questions, worth 6 marks, involves a real-world scenario where two schools award students based on values like discipline, politeness, and punctuality, requiring the use of matrices to find the award money for each value. The paper also includes a value-based question, suggesting the importance of holistic development. Solving this previous year's paper helps students familiarize themselves with the exam pattern, question types, and marking scheme, ultimately aiding in better preparation and improved performance in the board examinations.
Quick info
| Board | CBSE |
|---|---|
| Class | 12 |
| Subject | Maths |
| Session | 2014 |
| Language | English |
| Type | Previous Year Question Paper |
| Exam type | Board Exam |
Paper pattern
The paper includes 6 marks questions and value-based questions.
Topics covered
Paper topics
- Inverse of a Matrix
- Application of Determinants
- Matrices
- Systems of Linear Equations
Important topics
- Inverse of a Matrix
- Application of Determinants & Matrices
PDF preview
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Question paper text
Inverse of a Matrix and Application of Determinants & Matrix
6 Marks Questions
- Two schools P and Q want to award their selected students on the values of discipline, politeness and punctuality. The school P wants to award ₹ x each, ₹ y each and ₹ z each for the three respective values to 3, 2 and 1 students respectively with a total award money of ₹ 1000. School Q wants to spend ₹ 1500 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is ₹600, using matrices, find the award money for each value. Apart from the above three values, suggest one more value for awards.
Value Based Question; Delhi 2014
<math display="block">\therefore \text{ adj}(A) = \begin{vmatrix} -2 & -1 & 3 \\ -1 & 2 & -1 \\ 5 & -5 & -5 \end{vmatrix} = \begin{vmatrix} -2 & -1 & 5 \\ -1 & 2 & -5 \\ 3 & -1 & -5 \end{vmatrix}</math>
Then, <math>A^{-1} = \frac{1}{|A|} (adj A)</math> <math display="block">= \frac{1}{-5} \begin{vmatrix} -2 & -1 & 5 \\ -1 & 2 & -5 \\ 3 & -1 & -5 \end{vmatrix} = \frac{1}{5} \begin{vmatrix} 2 & 1 & -5 \\ 1 & -2 & 5 \\ -3 & 1 & 5 \end{vmatrix}</math> (1) Now, the solution of given system is given by
<math>X = A^{-1}B</math> <math display="block">\Rightarrow \begin{vmatrix} x \\ y \\ z \end{vmatrix} = \frac{1}{5} \begin{vmatrix} 2 & 1 & -5 \\ 1 & -2 & 5 \\ -3 & 1 & 5 \end{vmatrix} \begin{bmatrix} 1000 \\ 1500 \\ 600 \end{bmatrix}</math> <math display="block">= \frac{1}{5} \begin{bmatrix} 2000 + 1500 - 3000 \\ 1000 - 3000 + 3000 \\ -3000 + 1500 + 3000 \end{bmatrix} = \frac{1}{5} \begin{bmatrix} 500 \\ 1000 \\ 1500 \end{bmatrix}</math> <math display="block">\begin{vmatrix} x \\ y \\ z \end{vmatrix} = \begin{bmatrix} 100 \\ 200 \\ 300 \end{bmatrix}</math> (1)
On comparing corresponding elements, we get <math>x = 100</math>, <math>y = 200</math> and <math>z = 300</math>
Honesty is one more value which is also considered for the award. (1)
- Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award <math>\xi x</math> each, <math>\xi y</math> each and <math>\xi z</math> each for the three respective values of 3, 2 and 1 students, respectively with a total award money of ₹ 1600. School B wants to
Frequently asked questions
What is this document?
This is a CBSE Class 12 Maths Previous Year Question Paper from 2014 for board exam practice.
What topics are covered?
The paper covers topics such as Inverse of a Matrix and Application of Determinants & Matrices.
How can solving this paper help?
Solving this previous year question paper helps students understand the board pattern, question types, and improve their marks.
What is the marking scheme for the questions?
One of the questions is a 6 marks question, and there are also value-based questions.
What is the suggested additional value for awards?
Honesty is suggested as an additional value for awards, besides discipline, politeness, and punctuality.
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