CBSE Class 10 Mathematics (Standard) Chapter 4 Quadratic Equations Important Questions 2027
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22 questions from Quadratic Equations appeared in 7 of the 7 CBSE papers we analysed (2022–2026) — here are the topics that matter, the questions that repeat, and every previous-year question from this chapter.
Key facts
- Algebra unit — 20 marks in the official syllabus
- Asked in 7 of 7 analysed papers (2022–2026)
- About 3.1 questions per paper (OR alternatives counted separately)
- 3 question patterns repeated across papers
Important topics in Quadratic Equations
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Word problems on quadratic equations | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| 2 | Nature of roots / discriminant | Board 2022Board 2023Board 2024Sample 2025Sample 2026 | ★★☆☆☆ |
| 3 | Checking whether an equation is quadratic / standard form | Board 2023Board 2024Sample 2026 | ★☆☆☆☆ |
| 4 | Solving by factorisation | Board 2022Board 2024 | ★☆☆☆☆ |
| 5 | Solving by quadratic formula | Board 2024 | ★☆☆☆☆ |
Repeated questions from Quadratic Equations
1. Fixed total with changed rate (D/x - D/(x+a) = b)
2×Board 2025Board 20265 marks
A person on a tour has Rs 4,200 for expenses. If he extends his tour for 3 days, he has to cut down his daily expenses by Rs 70. Find the original duration of the tour.
2. Form quadratic equation from area context
2×Board 2023Board 20241 marks
[case context: A rectangular floor can be tiled with 200 square tiles; if each tile's side is increased by 1 unit, only 128 tiles are needed.] Assuming the original length of each side of a tile is x units, make a quadratic equation from the above information.
3. Write quadratic in standard form from case context
2×Board 2023Board 20241 marks
[case context: A rectangular floor can be tiled with 200 square tiles; if each tile's side is increased by 1 unit, only 128 tiles are needed.] Write the corresponding quadratic equation in standard form.
Quadratic Equations questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 3 | 6 |
| Board 2023 | 5 | 7 |
| Board 2024 | 5 | 7 |
| Board 2025 | 2 | 10 |
| Sample 2025 | 2 | 4 |
| Board 2026 | 2 | 10 |
| Sample 2026 | 3 | 7 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Quadratic Equations
Board 2026 2 questions
A person on a tour has Rs 4,200 for expenses. If he extends his tour for 3 days, he has to cut down his daily expenses by Rs 70. Find the original duration of the tour.
The area of a right-angled triangle is 600 cm2. If the base of the triangle exceeds the altitude by 10 cm, find all the three dimensions of the triangle.
Sample 2026 3 questions
Which one of the following is not a quadratic equation? (A) (x+2)2 = 2(x+3) (B) x2 + 3x = (-1)(1-3x)2 (C) x3 - x2 + 2x + 1 = (x+1)3 (D) (x+2)(x+1) = x2 + 2x + 3
If zeroes of the quadratic polynomial ax2 + bx + c (a, c != 0) are equal, then (A) c and b must have opposite signs (B) c and a must have opposite signs (C) c and b must have same signs (D) c and a must have same signs
A train travels at a certain average speed for a distance of 63km and then travels a distance of 72km at an average speed of 6km/hr more than its original speed. If it takes 3 hours to complete the total journey, what is the original average speed?
Board 2025 2 questions
The perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. Find the lengths of other two sides of the triangle.
A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.
Sample 2025 2 questions
The roots of the quadratic equation x2 + x - 1 = 0 are A) Irrational and distinct B) not real C) rational and distinct D) real and equal
The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbers.
Board 2024 5 questions
If the roots of equation ax2 + bx + c = 0, a != 0 are real and equal, then which of the following relation is true? (a) a = b2/c (b) b2 = ac (c) ac = b2/4 (d) c = b2/a
[case context: A rectangular floor can be tiled with 200 square tiles; if each tile's side is increased by 1 unit, only 128 tiles are needed.] Assuming the original length of each side of a tile is x units, make a quadratic equation from the above information.
[case context: A rectangular floor can be tiled with 200 square tiles; if each tile's side is increased by 1 unit, only 128 tiles are needed.] Write the corresponding quadratic equation in standard form.
[case context: A rectangular floor can be tiled with 200 square tiles; if each tile's side is increased by 1 unit, only 128 tiles are needed.] Find the value of x, the length of side of a tile, by factorisation.
[case context: A rectangular floor can be tiled with 200 square tiles; if each tile's side is increased by 1 unit, only 128 tiles are needed.] Solve the quadratic equation for x, using quadratic formula.
Board 2023 5 questions
The least positive value of k, for which the quadratic equation 2x2 + kx - 4 = 0 has rational roots, is (A) plus-minus 2 sqrt(2) (B) 2 (C) plus-minus 2 (D) sqrt(2)
[case context: school year book photo of 18 cm x 12 cm has length and width each increased by x units to double its area] Write an algebraic equation depicting the above information.
[case context: school year book photo of 18 cm x 12 cm has length and width each increased by x units to double its area] Write the corresponding quadratic equation in standard form.
[case context: school year book photo of 18 cm x 12 cm has length and width each increased by x units to double its area] What should be the new dimensions of the enlarged photo?
[case context: school year book photo of 18 cm x 12 cm has length and width each increased by x units to double its area] Can any rational value of x make the new area equal to 220 cm2?
Board 2022 3 questions
Find the value of m for which the quadratic equation (m - 1)x2 + 2(m - 1)x + 1 = 0 has two real and equal roots.
Solve the following quadratic equation for x : sqrt(3) x2 + 10x + 7 sqrt(3) = 0
The product of Rehan's age (in years) 5 years ago and his age 7 years from now, is one more than twice his present age. Find his present age.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Standard) Chapter 4 Quadratic Equations?
By how often and how recently they were asked: Word problems on quadratic equations; Nature of roots / discriminant; Checking whether an equation is quadratic / standard form.
How many marks does Quadratic Equations carry in the CBSE Class 10 Mathematics (Standard) exam?
Quadratic Equations is part of the Algebra unit, which carries 20 marks in the official syllabus. In the analysed papers it had about 3.1 questions per paper.
Do questions from Quadratic Equations repeat in board exams?
Yes — 3 question patterns from this chapter appeared in two or more past board or official sample papers. They are listed on this page with the years they were asked.