संक्षेप में: Jharkhand Academic Council (JAC) Class 10 Maths exam 80 marks theory + 20 marks internal assessment का होता है। हर साल ~4 लाख JAC students में से Maths में fail होने वालों का percentage सबसे ज़्यादा होता है — लेकिन इसका कारण paper कठिन होना नहीं बल्कि practice की कमी है। JAC Maths paper NCERT based है और Trigonometry, Statistics, Quadratic Equations तीनों chapters से combined 40+ marks आते हैं। यह guide chapter-wise marks distribution, complete formula sheet, 20 most repeated numerical types, और Hindi medium scoring strategy cover करती है।
JAC Class 10 Maths Paper Pattern 2027
| Feature | Details |
|---|---|
| Total Marks | 100 (80 Theory + 20 Internal) |
| Exam Duration | 3 घंटे |
| Medium | Hindi / English |
| Passing | 33% overall |
| Exam Month | February-March 2027 |
Section Breakdown:
| Section | Type | Marks/Q | Questions | Total |
|---|---|---|---|---|
| A | MCQ / Fill in Blanks | 1 | 10-12 | 10-12 |
| B | Very Short Answer | 2 | 5-6 | 10-12 |
| C | Short Answer | 3 | 8-10 | 24-30 |
| D | Long Answer | 5 | 4-5 | 20-25 |
JAC Maths paper में internal choice long answer section में मिलती है — typically 2 में से 1 choose करो।
Chapter-Wise Marks Distribution
| Ch | Chapter Name | Expected Marks | Scoring Difficulty |
|---|---|---|---|
| 8 | त्रिकोणमिति का परिचय | 10-12 | Medium — formula based |
| 9 | त्रिकोणमिति के अनुप्रयोग | 6-8 | Medium — application |
| 14 | सांख्यिकी (Statistics) | 10-11 | Easy — formula apply |
| 4 | द्विघात समीकरण (Quadratic) | 7-8 | Medium — formula + logic |
| 5 | समान्तर श्रेढ़ी (AP) | 6-7 | Medium — formula based |
| 3 | दो चरों वाले रैखिक समीकरण | 5-6 | Easy-Medium |
| 6 | त्रिभुज (Triangles) | 5-6 | Medium — proof based |
| 7 | निर्देशांक ज्यामिति | 4-5 | Easy — formula apply |
| 10 | वृत्त (Circles) | 4-5 | Medium |
| 13 | पृष्ठीय क्षेत्रफल और आयतन | 5-6 | Medium — formula apply |
| 12 | वृत्तों से संबंधित क्षेत्रफल | 3-4 | Easy-Medium |
| 15 | प्रायिकता (Probability) | 3-4 | Easy |
| 1 | वास्तविक संख्याएँ | 3-4 | Easy |
| 2 | बहुपद (Polynomials) | 2-3 | Easy-Medium |
| 11 | रचनाएँ (Constructions) | 3-4 | Easy — practical |
Top 3 Scoring Chapters (Combined ~30 marks):
- त्रिकोणमिति (Ch 8+9): 16-20 marks
- सांख्यिकी (Ch 14): 10-11 marks
- द्विघात समीकरण (Ch 4): 7-8 marks
Complete Formula Sheet
त्रिकोणमिति (Trigonometry)
| Ratio | Formula | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|---|
| sin θ | लम्ब/कर्ण | 0 | ½ | 1/√2 | √3/2 | 1 |
| cos θ | आधार/कर्ण | 1 | √3/2 | 1/√2 | ½ | 0 |
| tan θ | लम्ब/आधार | 0 | 1/√3 | 1 | √3 | ∞ |
Identities:
- sin²θ + cos²θ = 1
- 1 + tan²θ = sec²θ
- 1 + cot²θ = cosec²θ
- sin(90°-θ) = cosθ, cos(90°-θ) = sinθ
Heights & Distances:
- tan θ = height / distance (angle of elevation)
- Shadow problems: tan θ = object height / shadow length
सांख्यिकी (Statistics)
| Method | Formula | कब use करें |
|---|---|---|
| Direct Mean | x̄ = Σfᵢxᵢ / Σfᵢ | छोटे values |
| Assumed Mean | x̄ = a + (Σfᵢdᵢ / Σfᵢ) | बड़े values |
| Step Deviation | x̄ = a + (Σfᵢuᵢ / Σfᵢ) × h | Equal intervals |
| Median | l + [(n/2 - cf) / f] × h | Grouped data |
| Mode | l + [(f₁-f₀) / (2f₁-f₀-f₂)] × h | बहुलक |
द्विघात समीकरण (Quadratic Equations)
| Formula | Use |
|---|---|
| ax² + bx + c = 0 | Standard form |
| x = (-b ± √D) / 2a | श्रीधराचार्य सूत्र |
| D = b² - 4ac | Discriminant |
| D > 0 → 2 distinct roots | दो अलग-अलग मूल |
| D = 0 → 2 equal roots | दो समान मूल |
| D < 0 → no real roots | कोई वास्तविक मूल नहीं |
| Sum of roots = -b/a | मूलों का योग |
| Product of roots = c/a | मूलों का गुणनफल |
समान्तर श्रेढ़ी (Arithmetic Progression)
| Formula | Meaning |
|---|---|
| aₙ = a + (n-1)d | n-वाँ पद |
| Sₙ = n/2 [2a + (n-1)d] | n पदों का योग (d known) |
| Sₙ = n/2 (a + l) | n पदों का योग (last term known) |
| d = aₙ - aₙ₋₁ | सार्व अंतर |
निर्देशांक ज्यामिति (Coordinate Geometry)
| Formula | Use |
|---|---|
| Distance = √[(x₂-x₁)² + (y₂-y₁)²] | दो बिंदुओं की दूरी |
| Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2) | मध्य बिंदु |
| Section = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)) | विभाजन सूत्र |
| Area = ½ | x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂) |
क्षेत्रमिति (Mensuration)
| Shape | Surface Area | Volume |
|---|---|---|
| शंकु (Cone) | πrl + πr² | ⅓πr²h |
| बेलन (Cylinder) | 2πrh + 2πr² | πr²h |
| गोला (Sphere) | 4πr² | ⁴⁄₃πr³ |
| अर्धगोला | 3πr² | ⅔πr³ |
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20 Most Repeated Numerical Types
Trigonometry (6 Types)
| # | Type | Marks | Example Hint |
|---|---|---|---|
| 1 | Identity prove करो (LHS = RHS) | 3-5 | (sinA+cosA)² + (sinA-cosA)² = 2 |
| 2 | Table based: sin30° + cos60° calculate | 1-2 | Direct value substitution |
| 3 | Find other ratios: sinA = 3/5 दिया है | 2-3 | Pythagoras use करो |
| 4 | Height of tower/building (angle given) | 5 | tan θ = h/d |
| 5 | Two observation angles — distance find | 5 | 30°-60° combination |
| 6 | Complementary angles based | 2 | sin(90°-θ) = cosθ |
Statistics (4 Types)
| # | Type | Marks | Tip |
|---|---|---|---|
| 7 | Mean by step deviation method | 5 | Table carefully बनाओ |
| 8 | Median of grouped frequency | 5 | Cumulative frequency column |
| 9 | Mode of grouped data | 3 | Modal class identify करो |
| 10 | Ogive (less than type) draw करो | 3-5 | Graph paper पर neat |
Quadratic + AP (5 Types)
| # | Type | Marks | Tip |
|---|---|---|---|
| 11 | Solve quadratic by formula | 3 | D calculate first |
| 12 | Nature of roots (D value) | 2 | D>0, D=0, D<0 |
| 13 | Word problem → equation → solve | 5 | x unknown मानो |
| 14 | AP: n-वाँ पद ज्ञात करो | 2-3 | a, d identify करो |
| 15 | AP: Sum of n terms | 3-5 | Correct formula choose करो |
Geometry + Coordinate + Mensuration (5 Types)
| # | Type | Marks | Tip |
|---|---|---|---|
| 16 | Distance between two points | 2-3 | Formula direct apply |
| 17 | Midpoint / Section formula | 3 | Coordinates substitute |
| 18 | Combination of solids — volume | 5 | Individual volumes add/subtract |
| 19 | Sector area / segment area | 3 | θ/360 × πr² |
| 20 | HCF & LCM by prime factorisation | 2-3 | Factor tree method |
Previous Year Pattern — JAC Maths
| Topic | 2024 | 2025 | 2026 | Average |
|---|---|---|---|---|
| Trigonometry (Ch 8+9) | 18 | 20 | 18 | 18.7 |
| Statistics + Probability | 13 | 14 | 14 | 13.7 |
| Quadratic + AP | 14 | 13 | 15 | 14.0 |
| Triangles + Circles | 10 | 9 | 10 | 9.7 |
| Coordinate Geometry | 5 | 5 | 4 | 4.7 |
| Mensuration (Area + Volume) | 8 | 9 | 8 | 8.3 |
| Real Numbers + Polynomials | 5 | 4 | 5 | 4.7 |
| Constructions | 4 | 3 | 3 | 3.3 |
Insight: Top 3 topics (Trigonometry + Statistics + Quadratic/AP) = 46+ marks out of 80 — almost 60% paper!
JAC Exam Structure — Marks Distribution Strategy
| Target Score | Strategy | Focus Chapters |
|---|---|---|
| Pass (27+) | Basic formulas + MCQ + easy questions | Statistics, Probability, Coordinate |
| 40-50 marks | + Trigonometry identities + AP | + Ch 8, 5, 4 |
| 50-60 marks | + Numericals + word problems | + Ch 9, 3, 13 |
| 60-70 marks | + Proofs + construction + all topics | + Ch 6, 10, 11 |
| 70+ marks | Perfect practice + no silly mistakes | Complete syllabus |
Hindi Medium Tips — JAC Maths
| Tip | Details |
|---|---|
| Question Hindi में, solve English notation में | Examiner दोनों accept करते हैं |
| Formula sheet Hindi + English दोनों में बनाओ | Exam hall में confusion avoid |
| Word problems carefully translate करो | Hindi में word problems tricky लगते हैं |
| Diagram labels Hindi में acceptable | JAC Hindi medium paper |
| Step-by-step answer लिखो | JAC examiners step marking देते हैं |
Last 30 Days Plan
| Week | Focus | Daily Practice |
|---|---|---|
| Week 1 | Trigonometry (Ch 8, 9) + Formulas memorize | 10 identities + 3 heights problems |
| Week 2 | Statistics (Ch 14) + Quadratic (Ch 4) + AP (Ch 5) | Mean/Median + 5 equations daily |
| Week 3 | Geometry + Coordinate + Mensuration + Probability | Proofs + distance formula + volume |
| Week 4 | Revision + Previous Year Papers + Formula Sheet | 1 full paper daily timed |
FAQ — JAC Class 10 Maths
JAC Maths paper CBSE से आसान है?
Generally JAC Maths paper CBSE comparable difficulty का होता है — दोनों NCERT based हैं। JAC में HOTS questions कम होते हैं और internal choice ज़्यादा मिलती है। अगर NCERT exercises properly solve किए हैं तो JAC paper comfortable लगेगा।
Trigonometry समझ नहीं आती — कैसे शुरू करूँ?
Step 1: Basic ratios (sin, cos, tan) definition diagram से समझो। Step 2: Standard angle table (0° to 90°) रट लो। Step 3: तीन identities याद करो। Step 4: NCERT Example problems solve करो। Step 5: रोज़ 5 identity proofs practice। 10-15 दिन में confidence आ जाएगा।
Statistics में calculation mistakes बहुत होती हैं — क्या करूँ?
Table method use करो — columns बनाओ (fᵢ, xᵢ, fᵢxᵢ, cf)। हर column addition separately verify करो। Rough work organized रखो। Calculator type shortcuts learn करो। NCERT examples 3 बार solve करो — speed और accuracy दोनों improve होगी।
Constructions chapter कैसे prepare करें?
Constructions में compass और ruler work practice ज़रूरी है। Steps याद करो और रोज़ 2 constructions actual practice करो। Similar triangles construction, tangent drawing, और angle bisector सबसे important हैं। Neat work = full marks।
JAC Maths previous year papers किसने बनाए — NCERT based हैं?
हाँ, JAC Maths papers NCERT based हैं। JAC official website पर model papers available हैं। Market में JAC specific books मिलती हैं। Online Padhaao app पर भी JAC pattern practice available है। Last 5 years papers solve करना सबसे effective strategy है।
JAC Class 10 Maths की तैयारी formula memorization + daily practice + previous year papers से होती है। Padhaao app पर chapter-wise practice और AI doubt solving Hindi में available है।
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