JUST ADDED: NTA NEET RE-TEST 2026 (JUNE 21) Question Paper with Analysis and Solution Attempt Now →
NEP 2020 Compliant

Competency-Based Assessment Made Simple.

A comprehensive platform for Teachers to create standard question papers and Students to practice Case-Based, Assertion-Reason, and Critical Thinking questions.

1,289+
Questions
6+
Subjects
100%
NEP Aligned

Generate Papers

Create professional PDF/Word papers with logo, instructions, and mixed question types in minutes.

Start Creating

Question Bank

Explore our repository by Class and Topic. Filter by "Knowledge" or "Competency" levels.

Browse Bank

Self-Regulated Test

For Students. Take timed MCQ tests to check your understanding. Get instant feedback.

Take Test
Pedagogy Shift

Why Competency-Based?

According to NEP 2020, rote learning is out. The focus has shifted to assessing a student's ability to apply concepts in real-life situations.

Case-Based Questions

Questions derived from real-world passages to test analytical skills.

Assertion-Reasoning

Testing the logic behind concepts, not just the definition.

Critical Thinking

Open-ended scenarios that require thinking beyond the textbook.

Marking Scheme
Randomly Fetched Question
Question
A furniture workshop produces three types of furniture chairs, tables and beds each day. On a particular day the total number of furniture pieces produced is 45. It was also found that production of beds exceeds that of chairs by 8, while the total production of beds and chairs together is twice the production of tables. Determine the units produced of each type of furniture, using matrix method.
UNDERSTAND COMPETENCY 5 Marks
Concept Application
50%
Calculation / Logic
50%
Target Level
MEDIUM
Unique Feature

More Than Just an Answer Key

We provide complete AI-Powered Explanations for every question.

UNDERSTAND COMPETENCY MEDIUM

Q: A furniture workshop produces three types of furniture chairs, tables and beds each day. On a particular day the total number of furniture pieces produced is 45. It was also found that production of beds exceeds that of chairs by 8, while the total production of beds and chairs together is twice the production of tables. Determine the units produced of each type of furniture, using matrix method.

Question Analysis & Solution

Detailed Solution

Step 1: Define Variables

Let $x$ be the number of chairs produced, $y$ be the number of tables produced, and $z$ be the number of beds produced.

Step 2: Formulate Equations

We are given the following information:

  1. The total number of furniture pieces produced is 45: $x + y + z = 45$
  2. Production of beds exceeds that of chairs by 8: $z = x + 8$, which can be written as $-x + z = 8$
  3. The total production of beds and chairs together is twice the production of tables: $z + x = 2y$, which can be written as $x - 2y + z = 0$

So, we have the following system of linear equations:

$$x + y + z = 45$$$$-x + z = 8$$$$x - 2y + z = 0$$

Step 3: Express in Matrix Form

We can write the system of equations in matrix form as $AX = B$, where:

$$A = \begin{bmatrix} 1 & 1 & 1 \\ -1 & 0 & 1 \\ 1 & -2 & 1 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}, \quad B = \begin{bmatrix} 45 \\ 8 \\ 0 \end{bmatrix}$$

Step 4: Calculate the Determinant of A

$$|A| = \begin{vmatrix} 1 & 1 & 1 \\ -1 & 0 & 1 \\ 1 & -2 & 1 \end{vmatrix} = 1(0 - (-2)) - 1(-1 - 1) + 1(2 - 0) = 2 + 2 + 2 = 6$$Since $|A| \neq 0$, the system has a unique solution.

Step 5: Find the Adjoint of A

The matrix of cofactors is:

$$C = \begin{bmatrix} 2 & 2 & 2 \\ -3 & 0 & 3 \\ 1 & -2 & 1 \end{bmatrix}$$The adjoint of $A$ is the transpose of the cofactor matrix:

$$adj(A) = C^T = \begin{bmatrix} 2 & -3 & 1 \\ 2 & 0 & -2 \\ 2 & 3 & 1 \end{bmatrix}$$

Step 6: Calculate the Inverse of A

The inverse of $A$ is given by $A^{-1} = \frac{1}{|A|} adj(A)$:

$$A^{-1} = \frac{1}{6} \begin{bmatrix} 2 & -3 & 1 \\ 2 & 0 & -2 \\ 2 & 3 & 1 \end{bmatrix}$$

Step 7: Solve for X

We have $X = A^{-1}B$:

$$X = \frac{1}{6} \begin{bmatrix} 2 & -3 & 1 \\ 2 & 0 & -2 \\ 2 & 3 & 1 \end{bmatrix} \begin{bmatrix} 45 \\ 8 \\ 0 \end{bmatrix} = \frac{1}{6} \begin{bmatrix} 2(45) - 3(8) + 1(0) \\ 2(45) + 0(8) - 2(0) \\ 2(45) + 3(8) + 1(0) \end{bmatrix} = \frac{1}{6} \begin{bmatrix} 90 - 24 \\ 90 \\ 90 + 24 \end{bmatrix} = \frac{1}{6} \begin{bmatrix} 66 \\ 90 \\ 114 \end{bmatrix} = \begin{bmatrix} 11 \\ 15 \\ 19 \end{bmatrix}$$Therefore, $x = 11$, $y = 15$, and $z = 19$.

Step 8: State the Solution

The number of chairs produced is 11, the number of tables produced is 15, and the number of beds produced is 19.

Final Answer: Chairs: 11, Tables: 15, Beds: 19

View Full Question Details →