🔢 Mathematics CBQ

📝 Question 1

Math Real Numbers ⭐ 4 Marks

📖 Case Study

Real-life Application: Cost optimization using quadratic equations.

Q. A shopkeeper buys a certain number of books for ₹960. If he had bought 4 more books for the same amount, each book would have cost ₹8 less. Find the number of books bought.

👁️ View Answer & Solution

✅ Detailed Solution

Let x = number of books Cost per book = 960/x Given: 960/x - 960/(x+4) = 8 960(x+4) - 960x = 8x(x+4) 3840 = 8x² + 32x x² + 4x - 480 = 0 (x+24)(x-20) = 0 x = 20 books ✓

🎓 Learning Outcomes

• Form quadratic equations
• Apply algebra to real-life
• Solve word problems

📝 Question 2

Math Polynomials ⭐ 3 Marks

Q. Sum of digits of a two-digit number is 9. If 27 is added, digits get reversed. Find the number.

👁️ View Answer & Solution

✅ Detailed Solution

Let tens = x, units = y x + y = 9 ... (1) 10x + y + 27 = 10y + x x - y = -3 ... (2) Solving: x = 3, y = 6 Number = 36 ✓

🎓 Learning Outcomes

• Form simultaneous equations
• Solve linear equations
• Verify solutions

📝 Question 3

Math Quadratic Equations ⭐ 4 Marks

Q. A train travels 360 km at uniform speed. If speed was 5 km/h more, it would take 1 hour less. Find the speed.

👁️ View Answer & Solution

✅ Detailed Solution

Let speed = x km/h 360/x - 360/(x+5) = 1 360(x+5) - 360x = x(x+5) 1800 = x² + 5x x² + 5x - 1800 = 0 (x+45)(x-40) = 0 Speed = 40 km/h ✓

🎓 Learning Outcomes

• Time-speed-distance
• Form quadratic equations
• Solve real problems

📝 Question 4

Math Arithmetic Progressions ⭐ 3 Marks

Q. Find sum of first 15 multiples of 8.

👁️ View Answer & Solution

✅ Detailed Solution

AP: 8, 16, 24... (a=8, d=8, n=15) Sₙ = n/2 × [2a + (n-1)d] S₁₅ = 15/2 × [16 + 112] S₁₅ = 15/2 × 128 = 960 ✓

🎓 Learning Outcomes

• Identify AP
• Apply sum formula
• Calculate efficiently

📝 Question 5

Math Triangles ⭐ 4 Marks

📖 Case Study

BPT: If line parallel to one side, it divides other sides proportionally.

Q. In triangle ABC, DE || BC. If AD=4cm, DB=6cm, AE=5cm, find EC.

👁️ View Answer & Solution

✅ Detailed Solution

By BPT: AD/DB = AE/EC 4/6 = 5/EC EC = 30/4 = 7.5 cm ✓

🎓 Learning Outcomes

• Apply BPT theorem
• Solve proportions
• Similar triangles

📝 Question 6

Math Coordinate Geometry ⭐ 3 Marks

Q. Find distance between A(3,4) and B(-1,2).

👁️ View Answer & Solution

✅ Detailed Solution

d = √[(x₂-x₁)² + (y₂-y₁)²] d = √[(-4)² + (-2)²] d = √[16 + 4] = √20 d = 2√5 units ✓

🎓 Learning Outcomes

• Distance formula
• Simplify surds
• Coordinate geometry

📝 Question 7

Math Trigonometry ⭐ 4 Marks

Q. Angle of elevation of tower top is 30°. Moving 20m towards tower, it becomes 60°. Find tower height.

👁️ View Answer & Solution

✅ Detailed Solution

Let height = h, initial distance = x tan30° = h/x → x = h√3 tan60° = h/(x-20) → x-20 = h/√3 h√3 - 20 = h/√3 2h/√3 = 20 h = 10√3 m ≈ 17.32 m ✓

🎓 Learning Outcomes

• Trig ratios
• Height & distance
• Simultaneous equations

📝 Question 8

Math Circles ⭐ 3 Marks

Q. PA, PB are tangents to circle with centre O. If ∠APB=70°, find ∠AOB.

👁️ View Answer & Solution

✅ Detailed Solution

In quadrilateral OAPB: ∠OAP = 90° (tangent ⊥ radius) ∠OBP = 90° ∠AOB + 90° + 70° + 90° = 360° ∠AOB = 110° ✓

🎓 Learning Outcomes

• Tangent properties
• Angle sum
• Circle theorems

📝 Question 9

Math Statistics ⭐ 4 Marks

Q. Find mean: Classes 10-20, 20-30, 30-40, 40-50 with frequencies 5, 8, 12, 5.

👁️ View Answer & Solution

✅ Detailed Solution

Mid-points: 15, 25, 35, 45 Σfx = 75+200+420+225 = 920 Σf = 30 Mean = 920/30 = 30.67 ✓

🎓 Learning Outcomes

• Class mid-points
• Mean formula
• Data organization

📝 Question 10

Math Probability ⭐ 3 Marks

Q. Bag has 5 red, 4 green, 3 blue balls. Find P(red) and P(not green).

👁️ View Answer & Solution

✅ Detailed Solution

Total = 12 balls (i) P(red) = 5/12 (ii) P(not green) = 1 - 4/12 = 8/12 = 2/3 ✓

🎓 Learning Outcomes

• Calculate probability
• Complement rule
• Multi-part problems