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πŸ“ 22 Questions πŸŽ‰ 100% FREE β€’ No Login
πŸ“ Question 1
Math Real Numbers ⭐ 4 Marks
πŸ“– Case Study
Real-life Application: Cost optimization using quadratic equations.
Q. A shopkeeper buys a certain number of books for β‚Ή960. If he had bought 4 more books for the same amount, each book would have cost β‚Ή8 less. Find the number of books bought.
βœ… 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 = 8xΒ² + 32x xΒ² + 4x - 480 = 0 (x+24)(x-20) = 0 x = 20 books βœ“
πŸŽ“ Learning Outcomes
  • Form quadratic equations
  • Apply algebra to real-life
  • Solve word problems
πŸ“ 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.
βœ… 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 βœ“
πŸŽ“ Learning Outcomes
  • Form simultaneous equations
  • Solve linear equations
  • Verify solutions
πŸ“ 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.
βœ… Detailed Solution
Let speed = x km/h 360/x - 360/(x+5) = 1 360(x+5) - 360x = x(x+5) 1800 = xΒ² + 5x xΒ² + 5x - 1800 = 0 (x+45)(x-40) = 0 Speed = 40 km/h βœ“
πŸŽ“ Learning Outcomes
  • Time-speed-distance
  • Form quadratic equations
  • Solve real problems
πŸ“ Question 4
Math Arithmetic Progressions ⭐ 3 Marks
Q. Find sum of first 15 multiples of 8.
βœ… Detailed Solution
AP: 8, 16, 24... (a=8, d=8, n=15) Sβ‚™ = n/2 Γ— [2a + (n-1)d] S₁₅ = 15/2 Γ— [16 + 112] S₁₅ = 15/2 Γ— 128 = 960 βœ“
πŸŽ“ Learning Outcomes
  • Identify AP
  • Apply sum formula
  • Calculate efficiently
πŸ“ Question 5
Math Triangles ⭐ 4 Marks
πŸ“– 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.
βœ… Detailed Solution
By BPT: AD/DB = AE/EC 4/6 = 5/EC EC = 30/4 = 7.5 cm βœ“
πŸŽ“ Learning Outcomes
  • Apply BPT theorem
  • Solve proportions
  • Similar triangles
πŸ“ Question 6
Math Coordinate Geometry ⭐ 3 Marks
Q. Find distance between A(3,4) and B(-1,2).
βœ… Detailed Solution
d = √[(xβ‚‚-x₁)Β² + (yβ‚‚-y₁)Β²] d = √[(-4)Β² + (-2)Β²] d = √[16 + 4] = √20 d = 2√5 units βœ“
πŸŽ“ Learning Outcomes
  • Distance formula
  • Simplify surds
  • Coordinate geometry
πŸ“ Question 7
Math Trigonometry ⭐ 4 Marks
Q. Angle of elevation of tower top is 30Β°. Moving 20m towards tower, it becomes 60Β°. Find tower height.
βœ… Detailed Solution
Let height = h, initial distance = x tan30Β° = h/x β†’ x = h√3 tan60Β° = h/(x-20) β†’ x-20 = h/√3 h√3 - 20 = h/√3 2h/√3 = 20 h = 10√3 m β‰ˆ 17.32 m βœ“
πŸŽ“ Learning Outcomes
  • Trig ratios
  • Height & distance
  • Simultaneous equations
πŸ“ Question 8
Math Circles ⭐ 3 Marks
Q. PA, PB are tangents to circle with centre O. If ∠APB=70°, find ∠AOB.
βœ… Detailed Solution
In quadrilateral OAPB: ∠OAP = 90Β° (tangent βŠ₯ radius) ∠OBP = 90Β° ∠AOB + 90Β° + 70Β° + 90Β° = 360Β° ∠AOB = 110Β° βœ“
πŸŽ“ Learning Outcomes
  • Tangent properties
  • Angle sum
  • Circle theorems
πŸ“ Question 9
Math Statistics ⭐ 4 Marks
Q. Find mean: Classes 10-20, 20-30, 30-40, 40-50 with frequencies 5, 8, 12, 5.
βœ… Detailed Solution
Mid-points: 15, 25, 35, 45 Ξ£fx = 75+200+420+225 = 920 Ξ£f = 30 Mean = 920/30 = 30.67 βœ“
πŸŽ“ Learning Outcomes
  • Class mid-points
  • Mean formula
  • Data organization
πŸ“ Question 10
Math Probability ⭐ 3 Marks
Q. Bag has 5 red, 4 green, 3 blue balls. Find P(red) and P(not green).
βœ… Detailed Solution
Total = 12 balls (i) P(red) = 5/12 (ii) P(not green) = 1 - 4/12 = 8/12 = 2/3 βœ“
πŸŽ“ Learning Outcomes
  • Calculate probability
  • Complement rule
  • Multi-part problems
πŸ“ Question 11
Physics Light - Reflection ⭐ 3 Marks
Q. Concave mirror produces 3Γ— magnified real image at object distance 10cm. Find image position and focal length.
βœ… Detailed Solution
u = -10cm, m = -3 (real image) m = -v/u β†’ v = -30cm Mirror formula: 1/f = 1/v + 1/u 1/f = -1/30 - 1/10 = -4/30 f = -7.5 cm βœ“
πŸŽ“ Learning Outcomes
  • Mirror formula
  • Sign conventions
  • Magnification
πŸ“ Question 12
Physics Motion ⭐ 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/sΒ²)
βœ… Detailed Solution
(a) vΒ² = uΒ² - 2gh 0 = 400 - 20h β†’ h = 20 m (b) v = u - gt 0 = 20 - 10t β†’ t = 2 s (c) Total = 2 Γ— 2 = 4 s βœ“
πŸŽ“ Learning Outcomes
  • Equations of motion
  • Projectile motion
  • Multi-part problems
πŸ“ Question 13
Physics Electricity ⭐ 4 Marks
Q. 4Ξ© and 6Ξ© in parallel, then in series with 5Ξ©. Find total resistance and current from 12V.
βœ… Detailed Solution
Parallel: 1/Rp = 1/4 + 1/6 = 5/12 Rp = 2.4 Ξ© Total: R = 2.4 + 5 = 7.4 Ξ© Current: I = V/R = 12/7.4 = 1.62 A βœ“
πŸŽ“ Learning Outcomes
  • Parallel resistance
  • Series combination
  • Ohm's law
πŸ“ Question 14
Physics Magnetism ⭐ 3 Marks
Q. State Fleming's Left Hand Rule. Current flows N-S, field E-W. Find force direction.
βœ… Detailed Solution
Fleming's LHR: β€’ Forefinger β†’ Field (B) β€’ Middle finger β†’ Current (I) β€’ Thumb β†’ Force (F) Given: Current Nβ†’S, Field Eβ†’W Force = Vertically UPWARD βœ“
πŸŽ“ Learning Outcomes
  • Fleming's rule
  • Force direction
  • 3D visualization
πŸ“ Question 15
Physics Light - Refraction ⭐ 4 Marks
Q. Convex lens f=15cm, object at 20cm. Find image position and nature.
βœ… Detailed 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, 3Γ— βœ“
πŸŽ“ Learning Outcomes
  • Lens formula
  • Sign interpretation
  • Image characteristics
πŸ“ Question 16
Physics Electricity ⭐ 3 Marks
Q. Heater 44Ξ© connected to 220V. Find current, power, energy in 2 hours.
βœ… Detailed Solution
(a) I = V/R = 220/44 = 5 A (b) P = VI = 220Γ—5 = 1100 W (c) E = Pt = 1100Γ—2 = 2200 Wh = 2.2 kWh (units) βœ“
πŸŽ“ Learning Outcomes
  • Ohm's law
  • Power formula
  • Energy units
πŸ“ Question 17
Chemistry Chemical Reactions ⭐ 3 Marks
Q. What happens when ethanol reacts with sodium? Write balanced equation.
βœ… Detailed Solution
2Cβ‚‚Hβ‚…OH + 2Na β†’ 2Cβ‚‚Hβ‚…ONa + H₂↑ Observations: β€’ Brisk effervescence (Hβ‚‚) β€’ Sodium dissolves β€’ Solution becomes basic Type: Substitution reaction βœ“
πŸŽ“ Learning Outcomes
  • Balanced equations
  • Reaction types
  • Mechanisms
πŸ“ Question 18
Chemistry Acids, Bases & Salts ⭐ 4 Marks
πŸ“– 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.
βœ… Detailed Solution
Gas: HYDROGEN (Hβ‚‚) Zn + 2HCl β†’ ZnClβ‚‚ + H₂↑ Pop sound confirms Hβ‚‚ (Burns: 2Hβ‚‚ + Oβ‚‚ β†’ 2Hβ‚‚O) Type: Displacement reaction βœ“
πŸŽ“ Learning Outcomes
  • Gas identification
  • Lab tests
  • Reactivity series
πŸ“ Question 19
Chemistry Metals & Non-metals ⭐ 3 Marks
Q. Why is aluminum used for cooking utensils and electrical cables?
βœ… Detailed Solution
Cooking Utensils: β€’ Good heat conductor β€’ Light weight β€’ Corrosion resistant (Alβ‚‚O₃ layer) Electrical Cables: β€’ Good electrical conductor β€’ Light weight (less load on poles) β€’ Cheaper than copper β€’ Ductile βœ“
πŸŽ“ Learning Outcomes
  • Properties & uses
  • Compare metals
  • Conductivity
πŸ“ Question 20
Chemistry Carbon Compounds ⭐ 4 Marks
Q. What is homologous series? Give characteristics and first 3 alkanes.
βœ… Detailed Solution
Homologous Series: Compounds with same functional group, differing by -CHβ‚‚. Characteristics: β€’ Same general formula β€’ Differ by -CHβ‚‚ (14 u) β€’ Similar chemical properties Alkanes (Cβ‚™Hβ‚‚β‚™β‚Šβ‚‚): β€’ Methane: CHβ‚„ β€’ Ethane: Cβ‚‚H₆ β€’ Propane: C₃Hβ‚ˆ βœ“
πŸŽ“ Learning Outcomes
  • Define series
  • List characteristics
  • Molecular formulas
πŸ“ Question 21
Chemistry Periodic Classification ⭐ 3 Marks
Q. Why does atomic size decrease across a period? Compare Na and Cl.
βœ… Detailed Solution
Reason: Same shells, more protons β†’ Increased nuclear charge β†’ 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 βœ“
πŸŽ“ Learning Outcomes
  • Periodic trends
  • Compare properties
  • Electronic configuration
πŸ“ Question 22
Chemistry Life Processes ⭐ 4 Marks
Q. Write photosynthesis equation. Why is it important for Earth?
βœ… Detailed Solution
6COβ‚‚ + 6Hβ‚‚O β†’ C₆H₁₂O₆ + 6Oβ‚‚ (Sunlight + Chlorophyll) Importance: 1. Food Production - Converts light to chemical energy - Base of food chains 2. Oxygen Release - Maintains 21% Oβ‚‚ 3. COβ‚‚ Removal - Controls global warming βœ“
πŸŽ“ Learning Outcomes
  • Balanced equations
  • Biological importance
  • Ecology

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