https://file.aiquickdraw.com/mathbot/file/1726655919397j1hapgap.pdf

The uploaded file contains a **Class 10 Mathematics Sample Question Paper** with various types of questions, including:

1. **Part A**: Contains multiple-choice questions, case-study-based questions, and very short-answer questions (1 mark each).
2. **Part B**: Includes short-answer and long-answer questions (2, 3, and 5 marks respectively).

Here’s a breakdown of a few questions from the paper:

### Part A - Section I (1 mark each):
1. **LCM Calculation**:
   - If \( xy = 180 \) and \( HCF(x, y) = 3 \), find the LCM.
2. **Value of \( k \)**:
   - In the quadratic polynomial \( 3x^2 - kx + 6 \), if the sum of the zeroes is 3, find \( k \).
3. **Linear Equation System**:
   - For what value of \( k \), the system \( 3x + y = 3 \) and \( 6x + ky = 8 \) has no solution?

### Part A - Section II (Case Study based questions):
1. **Sunroom Construction**: 
   - Various geometry-related questions about a sunroom, such as calculating midpoints, distances, and line segment ratios.

### Part B - Short and Long Answer Questions:
1. **LCM of 3 Bells**: 
   - Three bells ring at intervals of 4, 7, and 14 minutes. When will they next ring together after 6 a.m.?
2. **Polynomial Roots**:
   - Find a quadratic polynomial whose zeroes are \( 5 - 3\sqrt{2} \) and \( 5 + 3\sqrt{2} \).
3. **Speed of a Motorboat**:
   - A motorboat covers 16 km upstream and 24 km downstream in 6 hours. Determine the speed of the boat in still water and the speed of the stream.

If you want detailed solutions for any specific questions, feel free to ask!

### Relative Questions:
1. How do you find the LCM when HCF and product of two numbers are known?
2. What method is used to solve quadratic equations when given the sum of the zeroes?
3. How do you determine if a system of linear equations has no solution?
4. What is the significance of the case study approach in mathematics?
5. How can trigonometry be applied in real-world geometry problems like the sunroom example?

### Tip:
Always check for internal choices in exam questions to maximize your chances by attempting the easiest ones for you.

The uploaded file contains various types of math questions, including multiple-choice questions, case studies, and short and long-answer questions. Examples include LCM calculation, determining the value of k in a quadratic equation, and case-study-based questions on geometry.

This Class 10 Mathematics sample paper includes questions on LCM, quadratic equations, and geometry-based case studies. Key topics covered include algebraic concepts like HCF and LCM, trigonometry, and the application of geometric principles in real-world scenarios.

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