Explain 4U

Prashnawali 1.2 class 10th One Shot | Ncert class 10th exercise 1.2 full solution | Explain 4U Maths https://youtu.be/W-ayI4u1_sM

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How to Convert Fraction Into Percentage | भिन्न को प्रतिशत में बदलना | #percentage #maths #pratishat https://youtube.com/shorts/QESwVMCFJks?feature=share

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⭐ Sphere Volume = 4/3πr³ ⭐ Pythagoras = a² + b² = c² ⭐ sin θ = P/H ⭐ cos θ = B/H ⭐ tan θ = P/B ━━━━━━━━━━━━━━━━━━ 🎯 CLASS 1 → CLASS 10 MATHS FORMULA REVISION ━━━━━━━━━━━━━━━━━━ अगर आप Maths में अच्छे marks लाना चाहते हैं, तो formulas को सिर्फ याद न करें — उनके पीछे का concept भी समझें। 📖 ✅ रोज़ 10–15 formulas revise करें। ✅ हर formula पर कम से कम 2–3 questions solve करें। ✅ Geometry के formulas को diagrams के साथ याद करें। ✅ Algebraic identities को रोज़ practice करें। ✅ Trigonometry के values को बार-बार revise करें। 📌 इस पोस्ट को SAVE कर लें, क्योंकि exam के समय यह पूरी formula sheet बहुत काम आएगी। ❤️ ━━━━━━━━━━━━━━━━━━ ❤️ अगर यह Maths Formula Post आपको Useful लगी हो तो: 👍 LIKE करें ❤️ HEART दें 📤 अपने दोस्तों के साथ SHARE करें 🔔 WhatsApp Channel को FOLLOW करें 📚 और ऐसे ही Maths के Important Questions, Tricks & Formulas के लिए जुड़े रहें। ❤️ *एक Heart तो बनता है Maths Lovers! ❤️*

━━━━━━━━━━━━━━━━━━ 📌 33. COORDINATE GEOMETRY ━━━━━━━━━━━━━━━━━━ दो points: A(x₁, y₁) B(x₂, y₂) 🔹 Distance Formula: AB = √[(x₂ − x₁)² + (y₂ − y₁)²] 🔹 Midpoint Formula: ((x₁ + x₂)/2, (y₁ + y₂)/2) 🔹 Section Formula: अगर point m:n के ratio में divide करता है: ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n)) ━━━━━━━━━━━━━━━━━━ 📌 34. TRIGONOMETRY ━━━━━━━━━━━━━━━━━━ Right-angled triangle में: 🔹 sin θ = Perpendicular/Hypotenuse 🔹 cos θ = Base/Hypotenuse 🔹 tan θ = Perpendicular/Base 🔹 cosec θ = Hypotenuse/Perpendicular 🔹 sec θ = Hypotenuse/Base 🔹 cot θ = Base/Perpendicular ━━━━━━━━━━━━━━━━━━ 📌 35. TRIGONOMETRIC IDENTITIES ━━━━━━━━━━━━━━━━━━ ⭐ बहुत महत्वपूर्ण: sin²θ + cos²θ = 1 1 + tan²θ = sec²θ 1 + cot²θ = cosec²θ ━━━━━━━━━━━━━━━━━━ 📌 36. TRIGONOMETRIC VALUES ━━━━━━━━━━━━━━━━━━ θ = 0° sin 0° = 0 cos 0° = 1 tan 0° = 0 θ = 30° sin 30° = 1/2 cos 30° = √3/2 tan 30° = 1/√3 θ = 45° sin 45° = 1/√2 cos 45° = 1/√2 tan 45° = 1 θ = 60° sin 60° = √3/2 cos 60° = 1/2 tan 60° = √3 θ = 90° sin 90° = 1 cos 90° = 0 tan 90° = Not Defined ━━━━━━━━━━━━━━━━━━ 📌 37. STATISTICS ━━━━━━━━━━━━━━━━━━ 🔹 Mean: Mean = Sum of observations / Number of observations 🔹 Grouped Data Mean: Mean = Σfx / Σf जहाँ, f = Frequency x = Observation 🔹 Median: Data को ascending/descending order में लगाने के बाद बीच का value. 🔹 Mode: सबसे अधिक बार आने वाला value. ━━━━━━━━━━━━━━━━━━ 📌 38. PROBABILITY ━━━━━━━━━━━━━━━━━━ 🔹 Probability: P(E) = Favourable Outcomes / Total Outcomes 🔹 Probability की range: 0 ≤ P(E) ≤ 1 🔹 Impossible Event: P(E) = 0 🔹 Certain Event: P(E) = 1 🔹 Complementary Event: P(E) + P(not E) = 1 ━━━━━━━━━━━━━━━━━━ 📌 39. REAL NUMBERS ━━━━━━━━━━━━━━━━━━ 🔹 Euclid Division Lemma: a = bq + r जहाँ, 0 ≤ r < b 🔹 HCF × LCM: दो positive integers a और b के लिए: HCF × LCM = a × b ━━━━━━━━━━━━━━━━━━ 📌 40. QUADRATIC EQUATION ━━━━━━━━━━━━━━━━━━ Standard form: ax² + bx + c = 0 जहाँ a ≠ 0 🔹 Quadratic Formula: x = [-b ± √(b² − 4ac)] / 2a 🔹 Discriminant: D = b² − 4ac अगर, D > 0 → दो अलग real roots D = 0 → दो equal real roots D < 0 → real roots नहीं 🔹 Sum of roots: α + β = −b/a 🔹 Product of roots: αβ = c/a ━━━━━━━━━━━━━━━━━━ 📌 41. ARITHMETIC PROGRESSION (AP) ━━━━━━━━━━━━━━━━━━ First term = a Common Difference = d Number of terms = n 🔹 nth term: aₙ = a + (n − 1)d 🔹 Sum of n terms: Sₙ = n/2 [2a + (n − 1)d] या, Sₙ = n/2(a + l) जहाँ l = last term ━━━━━━━━━━━━━━━━━━ 📌 42. USEFUL NUMBER FORMULAS ━━━━━━━━━━━━━━━━━━ 🔹 Sum of first n natural numbers: n(n + 1)/2 🔹 Sum of first n odd numbers: n² 🔹 Sum of first n even numbers: n(n + 1) 🔹 Sum of squares: n(n + 1)(2n + 1)/6 🔹 Sum of cubes: [n(n + 1)/2]² ━━━━━━━━━━━━━━━━━━ 📌 43. BASIC UNIT CONVERSIONS ━━━━━━━━━━━━━━━━━━ 1 km = 1000 m 1 m = 100 cm 1 cm = 10 mm 1 kg = 1000 g 1 litre = 1000 mL 1 hour = 60 minutes 1 minute = 60 seconds 1 day = 24 hours 1 week = 7 days ━━━━━━━━━━━━━━━━━━ 📌 44. IMPORTANT GEOMETRY FACTS ━━━━━━━━━━━━━━━━━━ 🔹 Vertically opposite angles are equal. 🔹 Linear pair का sum = 180° 🔹 Parallel lines में corresponding angles equal होते हैं। 🔹 Alternate interior angles equal होते हैं। 🔹 Co-interior angles का sum = 180° 🔹 Triangle के तीनों angles का sum = 180° 🔹 Quadrilateral के चारों angles का sum = 360° ━━━━━━━━━━━━━━━━━━ 📌 45. VERY IMPORTANT FORMULA SHORTCUTS ━━━━━━━━━━━━━━━━━━ ⭐ Distance = Speed × Time ⭐ Speed = Distance ÷ Time ⭐ Time = Distance ÷ Speed ⭐ Profit = SP − CP ⭐ Loss = CP − SP ⭐ SI = PRT/100 ⭐ Amount = Principal + Interest ⭐ Percentage = Part/Whole × 100 ⭐ Average = Sum/Number ⭐ Rectangle Area = Length × Breadth ⭐ Square Area = Side² ⭐ Triangle Area = 1/2 × Base × Height ⭐ Circle Area = πr² ⭐ Circle Circumference = 2πr ⭐ Cuboid Volume = lbh ⭐ Cube Volume = a³ ⭐ Cylinder Volume = πr²h ⭐ Cone Volume = 1/3πr²h

🔹 a² − b² = (a + b)(a − b) 🔹 (a + b)³ = a³ + b³ + 3ab(a + b) 🔹 (a − b)³ = a³ − b³ − 3ab(a − b) 🔹 a³ + b³ = (a + b)(a² − ab + b²) 🔹 a³ − b³ = (a − b)(a² + ab + b²) 🔹 (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca 🔹 a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca) अगर, a + b + c = 0 तो, a³ + b³ + c³ = 3abc ━━━━━━━━━━━━━━━━━━ 📌 15. LAWS OF EXPONENTS ━━━━━━━━━━━━━━━━━━ 🔹 aᵐ × aⁿ = aᵐ⁺ⁿ 🔹 aᵐ ÷ aⁿ = aᵐ⁻ⁿ 🔹 (aᵐ)ⁿ = aᵐⁿ 🔹 (ab)ⁿ = aⁿbⁿ 🔹 (a/b)ⁿ = aⁿ/bⁿ 🔹 a⁰ = 1 🔹 a⁻ⁿ = 1/aⁿ ━━━━━━━━━━━━━━━━━━ 📌 16. SQUARE & SQUARE ROOT ━━━━━━━━━━━━━━━━━━ 🔹 Square: n² = n × n 🔹 Square Root: √n × √n = n 🔹 Important: √a × √b = √ab √a/√b = √(a/b) ━━━━━━━━━━━━━━━━━━ 📌 17. CUBE & CUBE ROOT ━━━━━━━━━━━━━━━━━━ 🔹 Cube: n³ = n × n × n 🔹 Cube Root: ∛n 🔹 Important: ∛a × ∛b = ∛ab ━━━━━━━━━━━━━━━━━━ 📌 18. LINEAR EQUATION ━━━━━━━━━━━━━━━━━━ 🔹 ax + b = c तो, x = (c − b)/a 🔹 अगर: ax + b = cx + d तो, x = (d − b)/(a − c) ━━━━━━━━━━━━━━━━━━ 📌 19. GEOMETRY – ANGLES ━━━━━━━━━━━━━━━━━━ 🔹 Right Angle = 90° 🔹 Straight Angle = 180° 🔹 Complete Angle = 360° 🔹 Acute Angle: Less than 90° 🔹 Obtuse Angle: Greater than 90° and less than 180° 🔹 Complementary Angles: Sum = 90° 🔹 Supplementary Angles: Sum = 180° 🔹 Angles around a point: 360° ━━━━━━━━━━━━━━━━━━ 📌 20. TRIANGLE ━━━━━━━━━━━━━━━━━━ 🔹 Sum of angles: A + B + C = 180° 🔹 Exterior angle: Exterior Angle = Sum of two opposite interior angles 🔹 Area: Area = 1/2 × Base × Height 🔹 Equilateral Triangle: Perimeter = 3a Area = √3/4 × a² ━━━━━━━━━━━━━━━━━━ 📌 21. HERON'S FORMULA ━━━━━━━━━━━━━━━━━━ अगर triangle की sides a, b, c हैं: 🔹 Semi-perimeter: s = (a + b + c)/2 🔹 Area: Area = √[s(s − a)(s − b)(s − c)] ━━━━━━━━━━━━━━━━━━ 📌 22. PYTHAGORAS THEOREM ━━━━━━━━━━━━━━━━━━ Right-angled triangle में: Hypotenuse² = Base² + Perpendicular² या, c² = a² + b² ━━━━━━━━━━━━━━━━━━ 📌 23. QUADRILATERAL ━━━━━━━━━━━━━━━━━━ 🔹 Sum of interior angles: 360° 🔹 Rectangle: Perimeter = 2(l + b) Area = l × b 🔹 Square: Perimeter = 4a Area = a² Diagonal = a√2 🔹 Parallelogram: Area = Base × Height 🔹 Rhombus: Area = 1/2 × d₁ × d₂ ━━━━━━━━━━━━━━━━━━ 📌 24. POLYGON ━━━━━━━━━━━━━━━━━━ अगर polygon की sides = n 🔹 Sum of interior angles: (n − 2) × 180° 🔹 प्रत्येक interior angle of regular polygon: [(n − 2) × 180°]/n 🔹 Number of diagonals: n(n − 3)/2 ━━━━━━━━━━━━━━━━━━ 📌 25. CIRCLE ━━━━━━━━━━━━━━━━━━ 🔹 Diameter: d = 2r 🔹 Radius: r = d/2 🔹 Circumference: C = 2πr या, C = πd 🔹 Area: A = πr² जहाँ, π ≈ 22/7 या 3.14159... ━━━━━━━━━━━━━━━━━━ 📌 26. SEMICIRCLE ━━━━━━━━━━━━━━━━━━ 🔹 Area: 1/2 πr² 🔹 Curved Length: πr 🔹 Perimeter: πr + 2r ━━━━━━━━━━━━━━━━━━ 📌 27. CUBOID ━━━━━━━━━━━━━━━━━━ Length = l Breadth = b Height = h 🔹 Volume: V = lbh 🔹 Total Surface Area: TSA = 2(lb + bh + hl) 🔹 Lateral Surface Area: LSA = 2h(l + b) 🔹 Diagonal: d = √(l² + b² + h²) ━━━━━━━━━━━━━━━━━━ 📌 28. CUBE ━━━━━━━━━━━━━━━━━━ Side = a 🔹 Volume: V = a³ 🔹 Total Surface Area: TSA = 6a² 🔹 Lateral Surface Area: LSA = 4a² 🔹 Diagonal: d = a√3 ━━━━━━━━━━━━━━━━━━ 📌 29. CYLINDER ━━━━━━━━━━━━━━━━━━ 🔹 Curved Surface Area: CSA = 2πrh 🔹 Total Surface Area: TSA = 2πr(r + h) 🔹 Volume: V = πr²h ━━━━━━━━━━━━━━━━━━ 📌 30. CONE ━━━━━━━━━━━━━━━━━━ 🔹 Slant Height: l = √(r² + h²) 🔹 Curved Surface Area: CSA = πrl 🔹 Total Surface Area: TSA = πr(l + r) 🔹 Volume: V = 1/3 πr²h ━━━━━━━━━━━━━━━━━━ 📌 31. SPHERE ━━━━━━━━━━━━━━━━━━ 🔹 Surface Area: A = 4πr² 🔹 Volume: V = 4/3 πr³ ━━━━━━━━━━━━━━━━━━ 📌 32. HEMISPHERE ━━━━━━━━━━━━━━━━━━ 🔹 Curved Surface Area: CSA = 2πr² 🔹 Total Surface Area: TSA = 3πr² 🔹 Volume: V = 2/3 πr³

*ALL IMPORTANT MATHS FORMULAS* 📚 🔥 एक ही पोस्ट में Maths के लगभग सभी जरूरी Formulas 🔥 📌 1. ARITHMETIC FORMULAS ━━━━━━━━━━━━━━━━━━ 🔹 Natural Numbers: 1, 2, 3, 4, 5, ... 🔹 Whole Numbers: 0, 1, 2, 3, 4, ... 🔹 Even Number: 2, 4, 6, 8, 10, ... 🔹 Odd Number: 1, 3, 5, 7, 9, ... 🔹 Successor: Number + 1 🔹 Predecessor: Number − 1 🔹 Sum: a + b 🔹 Difference: a − b 🔹 Product: a × b 🔹 Quotient: Dividend ÷ Divisor 🔹 Dividend: Divisor × Quotient + Remainder 🔹 Remainder: Dividend − (Divisor × Quotient) ━━━━━━━━━━━━━━━━━━ 📌 2. BODMAS RULE ━━━━━━━━━━━━━━━━━━ B → Brackets O → Orders / Of D → Division M → Multiplication A → Addition S → Subtraction 👉 हमेशा operations को इसी क्रम में solve किया जाता है। ━━━━━━━━━━━━━━━━━━ 📌 3. FRACTIONS ━━━━━━━━━━━━━━━━━━ 🔹 Like Fractions: Denominator same 🔹 Unlike Fractions: Denominator different 🔹 Fraction of a number: Fraction × Number 🔹 Addition: a/b + c/b = (a + c)/b 🔹 Subtraction: a/b − c/b = (a − c)/b 🔹 Multiplication: a/b × c/d = ac/bd 🔹 Division: a/b ÷ c/d = a/b × d/c ━━━━━━━━━━━━━━━━━━ 📌 4. RATIO & PROPORTION ━━━━━━━━━━━━━━━━━━ 🔹 Ratio: a : b = a/b 🔹 Equivalent Ratio: a : b = ka : kb 🔹 Proportion: a : b = c : d तो, ad = bc ━━━━━━━━━━━━━━━━━━ 📌 5. PERCENTAGE ━━━━━━━━━━━━━━━━━━ 🔹 Percentage: Percentage = (Part/Whole) × 100 🔹 Part: Part = (Percentage × Whole)/100 🔹 Percentage Increase: Increase % = (Increase/Original Value) × 100 🔹 Percentage Decrease: Decrease % = (Decrease/Original Value) × 100 🔹 New Value after increase: New Value = Original Value × (100 + r)/100 🔹 New Value after decrease: New Value = Original Value × (100 − r)/100 ━━━━━━━━━━━━━━━━━━ 📌 6. PROFIT & LOSS ━━━━━━━━━━━━━━━━━━ 🔹 Profit: Profit = SP − CP 🔹 Loss: Loss = CP − SP 🔹 Profit Percentage: Profit% = (Profit/CP) × 100 🔹 Loss Percentage: Loss% = (Loss/CP) × 100 🔹 Selling Price: SP = CP × (100 + Profit%)/100 🔹 Selling Price in Loss: SP = CP × (100 − Loss%)/100 🔹 Cost Price: CP = SP × 100/(100 + Profit%) 🔹 Cost Price in Loss: CP = SP × 100/(100 − Loss%) ━━━━━━━━━━━━━━━━━━ 📌 7. DISCOUNT ━━━━━━━━━━━━━━━━━━ 🔹 Discount: Discount = Marked Price − Selling Price 🔹 Discount%: Discount% = (Discount/Marked Price) × 100 🔹 Selling Price: SP = MP − Discount 🔹 After discount: SP = MP × (100 − Discount%)/100 ━━━━━━━━━━━━━━━━━━ 📌 8. SIMPLE INTEREST ━━━━━━━━━━━━━━━━━━ 🔹 Simple Interest: SI = (P × R × T)/100 जहाँ, P = Principal R = Rate T = Time 🔹 Amount: A = P + SI ━━━━━━━━━━━━━━━━━━ 📌 9. COMPOUND INTEREST ━━━━━━━━━━━━━━━━━━ 🔹 Amount: A = P(1 + R/100)ⁿ 🔹 Compound Interest: CI = A − P जहाँ, P = Principal R = Rate n = Number of years 🔹 Half-yearly compounding: Rate = R/2 Time = 2n 🔹 Quarterly compounding: Rate = R/4 Time = 4n ━━━━━━━━━━━━━━━━━━ 📌 10. AVERAGE ━━━━━━━━━━━━━━━━━━ 🔹 Average: Average = Sum of observations / Number of observations 🔹 Sum: Sum = Average × Number of observations ━━━━━━━━━━━━━━━━━━ 📌 11. UNITARY METHOD ━━━━━━━━━━━━━━━━━━ 🔹 Value of 1 unit: Total Value ÷ Total Units 🔹 Value of n units: Value of 1 unit × n ━━━━━━━━━━━━━━━━━━ 📌 12. SPEED, DISTANCE & TIME ━━━━━━━━━━━━━━━━━━ 🔹 Speed: Speed = Distance / Time 🔹 Distance: Distance = Speed × Time 🔹 Time: Time = Distance / Speed 🔹 Average Speed: Average Speed = Total Distance / Total Time 🔹 Conversion: 1 km = 1000 m 1 hour = 60 minutes 1 minute = 60 seconds 🔹 km/h → m/s: × 5/18 🔹 m/s → km/h: × 18/5 ━━━━━━━━━━━━━━━━━━ 📌 13. TIME & WORK ━━━━━━━━━━━━━━━━━━ अगर A कोई काम x दिनों में करता है: 🔹 One day's work: 1/x अगर B वही काम y दिनों में करता है: 1/y दोनों मिलकर: 1/x + 1/y अगर दोनों मिलकर काम T दिनों में करते हैं: 1/T = 1/x + 1/y ━━━━━━━━━━━━━━━━━━ 📌 14. ALGEBRAIC IDENTITIES ━━━━━━━━━━━━━━━━━━ ⭐ सबसे महत्वपूर्ण identities: 🔹 (a + b)² = a² + 2ab + b² 🔹 (a − b)² = a² − 2ab + b²

π (Pi) का लगभग मान कितना होता है? What is the approximate value of π (Pi)? https://www.facebook.com/share/p/1BAnSbnoY2/

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