📚 Latest CBQ Questions

📝 22 Questions 🎉 Free Access

📖 Chapter: Real Numbers

Question 1

Math ⭐ 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.

✅ 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 ✓

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

📖 Chapter: Polynomials

Question 2

Math ⭐ 3 Marks

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

✅ 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 ✓

✓ Form simultaneous equations ✓ Solve linear equations ✓ Verify solutions

📖 Chapter: Quadratic Equations

Question 3

Math ⭐ 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.

✅ 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 ✓

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

📖 Chapter: Arithmetic Progressions

Question 4

Math ⭐ 3 Marks

Q. Find sum of first 15 multiples of 8.

✅ 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 ✓

✓ Identify AP ✓ Apply sum formula ✓ Calculate efficiently

📖 Chapter: Triangles

Question 5

Math ⭐ 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.

✅ SOLUTION:

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

✓ Apply BPT theorem ✓ Solve proportions ✓ Similar triangles

📖 Chapter: Coordinate Geometry

Question 6

Math ⭐ 3 Marks

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

✅ SOLUTION:

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

✓ Distance formula ✓ Simplify surds ✓ Coordinate geometry

📖 Chapter: Trigonometry

Question 7

Math ⭐ 4 Marks

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

✅ 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 ✓

✓ Trig ratios ✓ Height & distance ✓ Simultaneous equations

📖 Chapter: Circles

Question 8

Math ⭐ 3 Marks

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

✅ SOLUTION:

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

✓ Tangent properties ✓ Angle sum ✓ Circle theorems

📖 Chapter: Statistics

Question 9

Math ⭐ 4 Marks

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

✅ SOLUTION:

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

✓ Class mid-points ✓ Mean formula ✓ Data organization

📖 Chapter: Probability

Question 10

Math ⭐ 3 Marks

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

✅ SOLUTION:

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

✓ Calculate probability ✓ Complement rule ✓ Multi-part problems

📖 Chapter: Light - Reflection

Question 11

Physics ⭐ 3 Marks

Q. Concave mirror produces 3× magnified real image at object distance 10cm. Find image position and focal length.

✅ SOLUTION:

u = -10cm, m = -3 (real image) m = -v/u → v = -30cm Mirror formula: 1/f = 1/v + 1/u 1/f = -1/30 - 1/10 = -4/30 f = -7.5 cm ✓

✓ Mirror formula ✓ Sign conventions ✓ Magnification

📖 Chapter: Motion

Question 12

Physics ⭐ 4 Marks

Q. Ball thrown up at 20 m/s. Find: (a) max height (b) time to max height (c) total flight time. (g=10 m/s²)

✅ SOLUTION:

(a) v² = u² - 2gh 0 = 400 - 20h → h = 20 m (b) v = u - gt 0 = 20 - 10t → t = 2 s (c) Total = 2 × 2 = 4 s ✓

✓ Equations of motion ✓ Projectile motion ✓ Multi-part problems

📖 Chapter: Electricity

Question 13

Physics ⭐ 4 Marks

Q. 4Ω and 6Ω in parallel, then in series with 5Ω. Find total resistance and current from 12V.

✅ SOLUTION:

Parallel: 1/Rp = 1/4 + 1/6 = 5/12 Rp = 2.4 Ω Total: R = 2.4 + 5 = 7.4 Ω Current: I = V/R = 12/7.4 = 1.62 A ✓

✓ Parallel resistance ✓ Series combination ✓ Ohm's law

📖 Chapter: Magnetism

Question 14

Physics ⭐ 3 Marks

Q. State Fleming's Left Hand Rule. Current flows N-S, field E-W. Find force direction.

✅ SOLUTION:

Fleming's LHR: • Forefinger → Field (B) • Middle finger → Current (I) • Thumb → Force (F) Given: Current N→S, Field E→W Force = Vertically UPWARD ✓

✓ Fleming's rule ✓ Force direction ✓ 3D visualization

📖 Chapter: Light - Refraction

Question 15

Physics ⭐ 4 Marks

Q. Convex lens f=15cm, object at 20cm. Find image position and nature.

✅ SOLUTION:

f = +15cm, u = -20cm 1/v - 1/u = 1/f 1/v = 1/15 + 1/20 = 7/60 v = +60 cm m = v/u = -3 (inverted, magnified) Image: Real, Inverted, 3× ✓

✓ Lens formula ✓ Sign interpretation ✓ Image characteristics

📖 Chapter: Electricity

Question 16

Physics ⭐ 3 Marks

Q. Heater 44Ω connected to 220V. Find current, power, energy in 2 hours.

✅ SOLUTION:

(a) I = V/R = 220/44 = 5 A (b) P = VI = 220×5 = 1100 W (c) E = Pt = 1100×2 = 2200 Wh = 2.2 kWh (units) ✓

✓ Ohm's law ✓ Power formula ✓ Energy units

📖 Chapter: Chemical Reactions

Question 17

Chemistry ⭐ 3 Marks

Q. What happens when ethanol reacts with sodium? Write balanced equation.

✅ SOLUTION:

2C₂H₅OH + 2Na → 2C₂H₅ONa + H₂↑ Observations: • Brisk effervescence (H₂) • Sodium dissolves • Solution becomes basic Type: Substitution reaction ✓

✓ Balanced equations ✓ Reaction types ✓ Mechanisms

📖 Chapter: Acids, Bases & Salts

Question 18

Chemistry ⭐ 4 Marks

📖 Case Study

Lab Test: Pop sound is characteristic test for hydrogen gas.

Q. HCl added to zinc. Colorless gas with pop sound. Identify gas, write equation.

✅ SOLUTION:

Gas: HYDROGEN (H₂) Zn + 2HCl → ZnCl₂ + H₂↑ Pop sound confirms H₂ (Burns: 2H₂ + O₂ → 2H₂O) Type: Displacement reaction ✓

✓ Gas identification ✓ Lab tests ✓ Reactivity series

📖 Chapter: Metals & Non-metals

Question 19

Chemistry ⭐ 3 Marks

Q. Why is aluminum used for cooking utensils and electrical cables?

✅ SOLUTION:

Cooking Utensils: • Good heat conductor • Light weight • Corrosion resistant (Al₂O₃ layer) Electrical Cables: • Good electrical conductor • Light weight (less load on poles) • Cheaper than copper • Ductile ✓

✓ Properties & uses ✓ Compare metals ✓ Conductivity

📖 Chapter: Carbon Compounds

Question 20

Chemistry ⭐ 4 Marks

Q. What is homologous series? Give characteristics and first 3 alkanes.

✅ SOLUTION:

Homologous Series: Compounds with same functional group, differing by -CH₂. Characteristics: • Same general formula • Differ by -CH₂ (14 u) • Similar chemical properties Alkanes (CₙH₂ₙ₊₂): • Methane: CH₄ • Ethane: C₂H₆ • Propane: C₃H₈ ✓

✓ Define series ✓ List characteristics ✓ Molecular formulas

📖 Chapter: Periodic Classification

Question 21

Chemistry ⭐ 3 Marks

Q. Why does atomic size decrease across a period? Compare Na and Cl.

✅ SOLUTION:

Reason: Same shells, more protons → Increased nuclear charge → Electrons pulled closer Na (Period 3): 11 protons Atomic radius = 186 pm Cl (Period 3): 17 protons Atomic radius = 99 pm Na > Cl in size ✓

✓ Periodic trends ✓ Compare properties ✓ Electronic configuration

📖 Chapter: Life Processes

Question 22

Chemistry ⭐ 4 Marks

Q. Write photosynthesis equation. Why is it important for Earth?

✅ SOLUTION:

6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ (Sunlight + Chlorophyll) Importance: 1. Food Production - Converts light to chemical energy - Base of food chains 2. Oxygen Release - Maintains 21% O₂ 3. CO₂ Removal - Controls global warming ✓

✓ Balanced equations ✓ Biological importance ✓ Ecology

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