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Prabhat Kumar Rai
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2672354Released 10mo ago100% Free# Mathematics Question Paper for Class 9 **Time: 3 Hours** **Maximum Marks: 80** --- ### Section A: Multiple Choice Questions (MCQs) **1.** The area of a square is 64 square units. What is the length of its side? - (a) 6 units - (b) 8 units - (c) 10 units - (d) 12 units **2.** Which of the following is a linear equation in one variable? - (a) \( x^2 + 3x + 2 = 0 \) - (b) \( 2x + 3y = 5 \) - (c) \( 4x + 7 = 0 \) - (d) \( x + y + z = 10 \) **3.** The sum of the interior angles of a triangle is: - (a) 90° - (b) 180° - (c) 270° - (d) 360° **4.** If \( x = 2 \) and \( y = 3 \), then \( x^2 + y^2 \) is: - (a) 5 - (b) 10 - (c) 13 - (d) 16 **5.** The HCF of 12 and 18 is: - (a) 2 - (b) 3 - (c) 6 - (d) 9 --- ### Section B: Short Answer Questions **6.** Solve the equation: \( 3x - 5 = 16 \). **7.** Find the value of \( x \) if \( 2x + 3 = 7 \). **8.** Simplify: \( \frac{3}{4} + \frac{1}{2} \). **9.** Find the area of a rectangle with length 12 cm and breadth 5 cm. **10.** If a number is increased by 20%, it becomes 60. Find the number. --- ### Section C: Long Answer Questions **11.** Prove that the sum of the angles of a triangle is 180°. **12.** Solve the simultaneous equations: \[ \begin{cases} 2x + 3y = 12 \\ 4x - y = 5 \end{cases} \] **13.** Find the value of \( x \) if \( \sqrt{x} + 5 = 10 \). **14.** A shopkeeper sells a book for ₹240, making a profit of 20%. Find the cost price of the book. **15.** In a triangle ABC, if \( \angle A = 90° \), \( AB = 3 \) cm, and \( AC = 4 \) cm, find the length of \( BC \). --- ### Section D: Higher Order Thinking Questions (HOTS) **16.** If \( x = 2 \) and \( y = 3 \), find the value of \( (x + y)^2 - (x^2 + y^2) \). **17.** A man walks 5 km due North and then 12 km due East. Find the straight-line distance from his starting point. **18.** If \( a + b = 5 \) and \( ab = 6 \), find the value of \( a^2 + b^2 \). **19.** A square and a rectangle have the same perimeter. If the length of the rectangle is 10 cm and its breadth is 6 cm, find the side length of the square. **20.** Prove that the product of two odd numbers is always odd. --- **End of Question Paper**
