Question Paper

Instructions:

• Attempt all questions.
• Write your answers clearly.
• Marks are mentioned alongside each question.

Section A:

Attempt all questions. Each question carries 2 marks.

1. Que 1. If \( a = 3 \) and \( b = 4 \), then \( a^2 + b^2 \) is:
   • A. 9
   • B. 16
   • C. 25
   • D. 7
   (2 Marks)
2. Aue 2. The value of \( \sin 30^\circ \) is:
   • A. 1
   • B. 0.5
   • C. 0
   • D. None
   (2 Marks)
3. Que 3. Solve: \( x^2 - 4 = 0 \). The roots are:
   • A. 2, -2
   • B. 4, 0
   • C. -2, -4
   • D. None
   (2 Marks)
4. Que 4. What is the area of a circle with radius 7 cm?
   • A. 154 cm²
   • B. 44 cm²
   • C. 22 cm²
   • D. 77 cm²
   (2 Marks)
5. Que 5.Which of the following is a Pythagorean triplet?
   • A. (3, 4, 5)
   • B. (5, 6, 7)
   • C. (1, 2, 3)
   • D. (6, 8, 10)
   (2 Marks)

Section B:

Attempt any 3 questions. Each question carries 5 marks.

6. Que 1.Prove that \( \sqrt{3} \) is an irrational number. (5 Marks)
7. Que 2.Solve the equation \( x^2 + 5x + 6 = 0 \). (5 Marks)
8. Que 3.Find the height of a triangle whose base is 10 cm and area is 50 cm². (5 Marks)
9. Que 4.Calculate the volume of a cylinder with radius 7 cm and height 10 cm. (5 Marks)
10. Que 5.Simplify: \( (a+b)^2 - (a-b)^2 \). (5 Marks)

Section C:

Attempt any 3 questions. Each question carries 10 marks.

11. Que 1.Derive the quadratic formula from the general equation \( ax^2 + bx + c = 0 \). (10 Marks)
12. Que 2.Prove the Pythagoras theorem with a diagram and example. (10 Marks)
13. Que 3.Solve the following system of equations using the elimination method: \[ 2x + 3y = 12 \\ 3x - y = 5 \] (10 Marks)
14. Que 4.Find the equation of a line passing through the point (2, 3) with slope 4. (10 Marks)
15. Que 5.Calculate the compound interest on ₹5000 for 2 years at an annual rate of 5%. (10 Marks)