Saturday, 7 Mar 2026

RBSE Class 10 Maths 2026: 30 Most Important Chapter-wise Questions

Essential RBSE Class 10 Maths Questions for 2026

Preparing for RBSE Class 10 Mathematics exams? After analyzing this comprehensive video resource, I've identified the 30 highest-yield questions across all chapters that consistently appear in exams. These questions reflect actual RBSE patterns and common student pain points. Let's break them down strategically to maximize your preparation efficiency.

Chapter 1: Real Numbers

  1. Prime Factorization: Find the sum of exponents in prime factors of 196.
    Expert approach: Factorize using division method. 196 = 2² × 7² → Sum = 2 + 2 = 4
  2. HCF/LCM Application: If HCF=27, LCM=162, and one number=54, find the other number.
    Key formula: HCF × LCM = Product of two numbers → Other number = (27 × 162)/54 = 81
  3. LCM Calculation: Find LCM of 72 and 120 using prime factorization.
    Pro tip: 72=2³×3², 120=2³×3×5 → LCM = 2³ × 3² × 5 = 360

Chapter 2: Polynomials

  1. Quadratic Construction: Form quadratic polynomial with zero sum=-3, product=2.
    Polynomial = x² - (sum)x + product → x² + 3x + 2
  2. Zero Verification: Find zeros of x² - x - 6 and verify coefficient relationships.
    Solving: Factors: (x-3)(x+2) → Zeros=3,-2. Verification: Sum=1 (matches -b/a), Product=-6 (matches c/a)

Chapter 3: Pair of Linear Equations

  1. No-Solution Condition: For equations 3x + y =1 and (2k-1)x + (k-1)y=2k+1, find k where no solution exists.
    Critical insight: No solution when a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → 3/(2k-1) = 1/(k-1) → k=2
  2. Word Problem: 7 pencils + 5 pens = ₹29. Write algebraic equations.
    Let pencil cost=x, pen cost=y → 7x + 5y = 29

Chapter 4: Quadratic Equations

  1. Equal Roots: If roots of ax²+bx+c=0 are real and equal, prove discriminant=0.
    RBSE marking focus: Discriminant D=b²-4ac. For equal roots, D=0
  2. Consecutive Integers: Find two consecutive positives with squared sum=365.
    Let numbers=n, n+1 → n²+(n+1)²=365 → n=13,14

Chapter 5: Arithmetic Progressions

  1. AP Sum Calculation: 6-term AP with first term=2, last term=10. Find sum.
    Sum = n/2 × (first + last term) = 6/2 × (2+10) = 36
  2. Term Identification: Which term of AP 21,18,15,... is zero?
    Common difference d=-3 → 0=21+(n-1)(-3) → n=8

Chapter 6: Triangles

  1. Area Ratio: Similar triangles with side ratio 4:9. Find area ratio.
    Area ratio = (side ratio)² = (4/9)² = 16:81
  2. Height Application: 6m pole casts 4m shadow. Tower casts 28m shadow. Find height.
    Similar triangles → Height = (6/4)×28 = 42m

Chapter 7: Coordinate Geometry

  1. Distance Calculation: Distance from P(3,-4) to origin.
    Distance = √(3² + (-4)²) = 5 units
  2. Section Formula: Ratio where y-axis divides line joining (-2,3) and (4,-1).
    Let ratio=k:1 → x-coordinate=0 → (4k-2)/(k+1)=0 → k=1:2

Chapter 8: Trigonometry

  1. Value Calculation: Evaluate 2tan30°/(1+tan²30°).
    tan30°=1/√3 → Expression = 2×(1/√3)/(1+1/3) = sin60°=√3/2
  2. Proof: Prove (1+sinA)/(1-sinA) = (secA + tanA)²
    Key steps: Left side = [(1+sinA)²]/[(1-sinA)(1+sinA)] = (1+sinA)²/cos²A = (secA + tanA)²

Chapter 9: Circles

  1. Tangent Properties: Angle between tangent and radius at contact point.
    Always 90° (Theorem 10.1)
  2. Parallel Tangents: Prove tangents at diameter ends are parallel.
    RBSE essential proof: Angle at each end=90° → Both perpendicular to diameter → Parallel

Chapter 10: Area Related to Circles

  1. Sector Area: Formula for arc length with radius r and angle θ.
    Arc length = (θ/360°) × 2πr
  2. Horse Grazing Area: Horse tied to square field corner (side=15m) with 5m rope. Find grazable area.
    Sector area = (90°/360°) × π × 5² = 19.63 m²

Chapter 11: Surface Areas and Volumes

  1. Hemisphere TSA: Total surface area of solid hemisphere radius r.
    TSA = Curved SA + Base = 2πr² + πr² = 3πr²
  2. Tent Surface Area: Cylindrical base (height=2.1m, diameter=4m) with conical top (slant height=2.8m). Find canvas area.
    Cylinder CSA=2πrh, Cone CSA=πrl → Total=π×2×(2.1+2.8)=30.8π m²

Chapter 12: Statistics

  1. Mean Calculation: If mean=21.5 for data with frequency table, find k.
    Standard approach: Use Σ(fx)/Σf=21.5 → Solve for k
  2. Mode Formula: Write formula for grouped data mode.
    Mode = L + [(f₁-f₀)/(2f₁-f₀-f₂)] × h

Chapter 13: Probability

  1. Probability Sum: Total probability of all elementary events.
    Always 1 (Axiomatic definition)
  2. Pen Selection: 12 defective pens mixed with 132 good. Probability of drawing good pen.
    P(good) = 132/(132+12) = 11/12

Chapter 14: Applications of Trigonometry

  1. Height Calculation: Shadow length=√3 times height. Find sun's angle.
    tanθ = height/shadow = 1/√3 → θ=30°
  2. Tower Height: Shadow=40m at 30° elevation. Find height at 60°.
    h/40 = tan30° → h=40/√3m. At 60°, height same → New shadow = h/tan60° = 40/3 m

Advanced Problem-Solving Toolkit

Must-Practice Question Types

  1. HCF/LCM word problems (Chapter 1)
  2. Quadratic polynomial formation (Chapter 2)
  3. AP sum calculations (Chapter 5)
  4. Trigonometric proofs (Chapter 8)
  5. Circle theorem applications (Chapter 10)

Resource Recommendations

  • RD Sharma Class 10: Best for foundational practice with graded difficulty
  • Oswaal RBSE Question Banks: Essential for exam-pattern familiarity
  • NCERT Exemplar: Critical for higher-order thinking questions

Final Exam Strategy

  1. Time allocation: Spend max time on Chapters 3,5,8 carrying highest weightage
  2. Verification step: Always recheck discriminant calculations
  3. Diagram marks: Label all geometry/trigonometry figures clearly
  4. Unit consistency: Convert units before volume/surface area problems
  5. Formula sheet: Memorize all circle and statistics formulas

Which chapter's questions do you find most challenging? Share your practice hurdles below for personalized tips!

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