Class 10 Maths Important MCQ — Chapter Wise (2026-27)

Updated

Chapter-wise objective practice for CBSE Class 10 Maths, checked question by question against the 2026-27 syllabus. Nothing here tests a topic that has been dropped. 89 objective questions across 8 chapters.

All Class 10 Maths practice

MCQ practice

Board papers & answer keys

Guides

Chapter-wise practice for the Maths syllabus is below.

1

Real Numbers

Unit I — Number Systems

17 objective · 7 written

Removed: Decimal expansion of rational numbers — terminating and non-terminating; Euclid's division lemma and division algorithm
2

Polynomials

Unit II — Algebra

13 objective · 2 written

Removed: Cubic polynomials — zeros, graphs and coefficient relationships; Division algorithm for polynomials
3

Pair of Linear Equations in Two Variables

Unit II — Algebra

5 objective · 20 written

Removed: Cross-multiplication method; Equations reducible to linear equations
4

Quadratic Equations

Unit II — Algebra

13 objective · 5 written

Removed: Completing the square as a method of solution; Situational problems on equations reducible to quadratic equations
5

Arithmetic Progressions

Unit II — Algebra

16 objective · 11 written

Removed: Applications based on the sum to n terms of an AP for raising money
6

Triangles

Unit IV — Geometry

12 objective · 8 written

Removed: Pythagoras Theorem and its converse; Ratio of the areas of two similar triangles
7

Coordinate Geometry

Unit III — Coordinate Geometry

8 objective · 3 written

Removed: Area of a triangle from the coordinates of its vertices
8

Introduction to Trigonometry

Unit V — Trigonometry

5 objective · 8 written

Removed: Trigonometric ratios of complementary angles
9

Some Applications of Trigonometry

Unit V — Trigonometry

8 objective · 8 written

Removed: Problems involving more than two right triangles

Coming soon
10

Circles

Unit IV — Geometry

9 objective · 2 written

Removed: Number of tangents from a point on or inside a circle; Cyclic quadrilaterals, alternate segment and angle-at-centre results

Coming soon
11

Areas Related to Circles

Unit VI — Mensuration

9 objective · 2 written

Removed: Plane figures involving triangles, simple quadrilaterals and circles in combination

Coming soon
12

Surface Areas and Volumes

Unit VI — Mensuration

15 objective · 7 written

Removed: Frustum of a cone; Conversion of one solid shape into another; Problems involving combinations of more than two solids

Coming soon
13

Statistics

Unit VII — Statistics and Probability

11 objective · 2 written

Removed: Cumulative frequency graphs and the ogive method of finding the median; Step-deviation problems on ungrouped data

Coming soon
14

Probability

Unit VII — Statistics and Probability

17 objective · 5 written

Removed: Geometric or area-based probability; Empirical probability from experimental trials

Coming soon
—

Constructions

Removed from the syllabus

Removed: The entire chapter is absent from the 2026-27 syllabus — division of a line segment, tangents to a circle from an external point, and all related constructions

Removed from syllabus

What has been removed from the 2026-27 Maths syllabus

Most question banks online still serve this content. It carries no marks in 2026-27, and nothing on this site tests it.

ChapterNo longer assessed
Real NumbersDecimal expansion of rational numbers — terminating and non-terminating
Real NumbersEuclid's division lemma and division algorithm
PolynomialsCubic polynomials — zeros, graphs and coefficient relationships
PolynomialsDivision algorithm for polynomials
Pair of Linear Equations in Two VariablesCross-multiplication method
Pair of Linear Equations in Two VariablesEquations reducible to linear equations
Quadratic EquationsCompleting the square as a method of solution
Quadratic EquationsSituational problems on equations reducible to quadratic equations
Arithmetic ProgressionsApplications based on the sum to n terms of an AP for raising money
TrianglesPythagoras Theorem and its converse
TrianglesRatio of the areas of two similar triangles
Coordinate GeometryArea of a triangle from the coordinates of its vertices
Introduction to TrigonometryTrigonometric ratios of complementary angles
Some Applications of TrigonometryProblems involving more than two right triangles
CirclesNumber of tangents from a point on or inside a circle
CirclesCyclic quadrilaterals, alternate segment and angle-at-centre results
Areas Related to CirclesPlane figures involving triangles, simple quadrilaterals and circles in combination
Surface Areas and VolumesFrustum of a cone
Surface Areas and VolumesConversion of one solid shape into another
Surface Areas and VolumesProblems involving combinations of more than two solids
StatisticsCumulative frequency graphs and the ogive method of finding the median
StatisticsStep-deviation problems on ungrouped data
ProbabilityGeometric or area-based probability
ProbabilityEmpirical probability from experimental trials
ConstructionsThe entire chapter is absent from the 2026-27 syllabus — division of a line segment, tangents to a circle from an external point, and all related constructions

Practise by chapter

Pair of Linear Equations in Two Variables — 5 MCQs

What the 2026-27 syllabus covers in Pair of Linear Equations in Two Variables

  • Graphical method of solution; consistency and inconsistency
  • Algebraic conditions for the number of solutions
  • Solution by substitution and by elimination
  • Simple situational problems
  1. In city A, for a journey of 10 km the charge paid is Rs 75 and for a journey of 15‌ km‌ the charge paid is Rs 110. If the fixed charge of an auto rickshaw is Rs x and the running charge is Rs y per km, the pair of linear equations representing the situation is
    1. x + 10y = 110, x + 15y = 75
    2. x + 10y = 75, x + 15y = 110
    3. 10x + y = 110, 15x + y = 75
    4. 10x + y = 75, 15x + y = 110

    Answer: b) x + 10y = 75, x + 15y = 110

    Total fare = fixed charge + running charge × distance. So x + 10y = 75 for the 10 km trip and x + 15y = 110 for the 15 km trip.

  2. A person travels a distance of‌ 50​ km. The amount he has to pay is
    1. Rs 155
    2. Rs 255
    3. Rs 355
    4. Rs 455

    Answer: c) Rs 355

    Subtracting the two equations gives 5y = 35, so y = 7 and x = 5. For 50 km: 5 + 50×7 = Rs 355.

  3. In city B, for a journey of 8 km the charge paid is Rs 91 and for 14​ km‌ it is Rs 145. What will a person have to pay for travelling a distance of 30 km?
    1. Rs 185
    2. Rs 289
    3. Rs 275
    4. Rs 305

    Answer: b) Rs 289

    From x + 8y = 91 and x + 14y = 145, subtracting gives 6y = 54, so y = 9 and x = 19. For 30 km: 19 + 270 = Rs 289.

  4. If the lines 3x + 2ky – 2 =​ 0​ and 2x + 5y + 1 = 0 are parallel, then the value of k is
    1. 4/15
    2. 15/4
    3. 4/5
    4. 5/4

    Answer: b) 15/4

    Parallel lines need a₁/a₂ = b₁/b₂. So 3/2 = 2k/5, giving 4k = 15 and k = 15/4.

  5. In the theatre​ canteen,‌ two packets of popcorn and a mango drink cost Rs 330. One packet of popcorn and two mango drinks cost Rs 300. What is the cost of the packet of popcorn?
    1. 100
    2. 120
    3. 150
    4. 200

    Answer: b) 120

    With 2p + m = 330 and p + 2m = 300, adding gives p + m = 210 and subtracting gives p − m = 30. Hence p = Rs 120.

Pair of Linear Equations in Two Variables — chapter notes

Two linear equations in two variables can meet once, never, or everywhere, and the coefficients tell you which before you solve anything. If a₁/a₂ ≠ b₁/b₂ the lines cross at one point and the pair is consistent with a unique solution. If a₁/a₂ = b₁/b₂ ≠ c₁/c₂ the lines are parallel and there is no solution. If all three ratios are equal the lines coincide and there are infinitely many.

Questions asking you to find k for parallel or coincident lines are testing exactly this. For solving, you have the graphical method and two algebraic ones, substitution and elimination — pick elimination when a variable already has matching coefficients. Most of the marks in this chapter sit in word problems: fares with a fixed and a per-kilometre charge, ages, tickets, boats. Define your two variables in writing before forming the equations; that step alone prevents most errors.

Introduction to Trigonometry — 5 MCQs

What the 2026-27 syllabus covers in Introduction to Trigonometry

  • Trigonometric ratios of an acute angle of a right-angled triangle
  • Values of the ratios at 30°, 45° and 60°; ratios defined at 0° and 90°
  • Relationships between the ratios
  • Proof and applications of the identity sin²A + cos²A = 1 — simple identities only
  1. In right-angled ΔABC, AB = 13 cm, BC = 5 cm and AC = 12 cm. What is the value‌ of​ cos B?
    1. 5/12
    2. 5/13
    3. 12/13
    4. 13/12

    Answer: b) 5/13

    AB = 13 is the longest side, so the right angle is at C. Then cos B = (side adjacent to B)/hypotenuse = BC/AB = 5/13.

  2. The value of θ for which sin​ 2θ​ = ½, 0° < θ < 90°, is
    1. 15°
    2. 30°
    3. 45°
    4. 60°

    Answer: a) 15°

    sin 30° = ½, so 2θ = 30° and θ = 15°. Check it lies in the given range: it does.

  3. If tan A =‌ 3/4,‌ then cos A equals
    1. 4/5
    2. 3/5
    3. 4/3
    4. 3/4

    Answer: a) 4/5

    Using 1 + tan²A = sec²A: sec²A = 1 + 9/16 = 25/16, so sec A = 5/4 and cos A = 4/5.

  4. ABC is an isosceles right triangle, right-angled​ at​ B. What is the value of 2 sin A × cos A?
    1. ½
    2. 1
    3. 3/2
    4. 2

    Answer: b) 1

    Right-angled and isosceles means the other two angles are 45° each. So 2 sin 45° cos 45° = 2 × (1/√2) × (1/√2) = 1.

  5. Which one of the following statements is true about trigonometric ratios in​ a‌ right triangle?
    1. The values of cot and tan vary from 0 to 1.
    2. The values of sin and cos vary from 0 to 1.
    3. The values of cos and sec vary from 0 to 1.
    4. The values of sin and cosec vary from 0 to 1.

    Answer: b) The values of sin and cos vary from 0 to 1.

    In a right triangle both sine and cosine are a leg divided by the hypotenuse, and the hypotenuse is always the longest side, so both stay between 0 and 1. sec and cosec are always at least 1, and tan and cot are unbounded.

Introduction to Trigonometry — chapter notes

In a right triangle the three ratios are defined against a chosen acute angle: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, tangent is opposite over adjacent. Everything else follows. You need the exact values at 30°, 45° and 60° from memory, plus what happens at 0° and 90°, and it is worth knowing why sine and cosine can never exceed 1 — both are a side divided by the hypotenuse, which is always the longest side.

The identity to prove and apply is sin²A + cos²A = 1, and from it come 1 + tan²A = sec²A and 1 + cot²A = cosec²A, which turn most simplification questions into one substitution. When a question gives one ratio and asks for another, the identities get you there without needing the third side. Keep the labelling straight: opposite and adjacent swap when you switch which acute angle you are working from.