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Maharashtra SSC Algebra HOTS Questions with Answers – Quadratic Equations | Class 10 Board Exam 2027

Practice set · 1 hr · 70 marks · for SSC 10th and similar exams

2027 60 minutes 70 marks Save WhatsApp

Sections

Most repeated board questions (2024–2026) 12 Q
HOTS: likely questions for 2027 15 Q

About this HOTS set

Students call the most important, most-likely-to-come questions of a chapter its HOTS or IMP questions. This page collects them for Quadratic Equations (Maharashtra SSC Class 10 Algebra) for the 2027 board exam. Part 1 has the questions the board has actually repeated in its recent papers; Part 2 has new questions in the same board style, covering the patterns that keep coming back and the parts of the chapter not yet asked, with a few harder thinking-type questions.

The board questions are taken from the official MSBSHSE SSC Algebra question papers of March 2024, July 2024, March 2025, July 2025, March 2026 and June 2026. All step-by-step answers and all the new questions are written by Doubtly.

Marks from this chapter in recent board papers

Board paperMarks (including internal options)
March 202412
July 202412
March 202512
July 202512
March 202611
June 202612

Question types that repeat most

  • A 3- or 4-mark word problem, discriminant or sum-and-product-of-roots question in every paper (taps, bananas, ages, consecutive numbers, “real and equal roots”, sum of cubes of roots).
  • Solving by factorisation (2 marks) and by formula method (3 marks) in almost every paper; \(x^2 + x - 20 = 0\) came twice.
  • “One root is given, find \(k\)” (March 2024, July 2024, March 2026, June 2026).
  • Forming the equation from given roots using sum and product of roots, and writing an equation in standard form.
  • Nature of roots using \(b^2 - 4ac\), and the completing-the-square activity.

Exam tips

  • Always write \(a\), \(b\), \(c\) with their signs before using the formula or the discriminant.
  • In word problems, reject the negative or impossible root and say why in one line.
  • For “real and equal roots” questions, check that your value of \(k\) does not make the \(x^2\) coefficient zero.
  • Remember \(x^2 - (\alpha + \beta)x + \alpha\beta = 0\) and \(\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha\beta(\alpha + \beta)\).

Chapters covered

Instructions

Solve on paper with a timer, then check against the solutions.

Most repeated board questions (2024–2026)

  1. Asked in: July 2025 and March 2026 board papers

    Write the following quadratic equation in standard form : \(2y = 10 - y^2\)

    1 mark See answer →

  2. Asked in: July 2024 board paper; the same “a root is given, find the constant” type came in March 2024 (3 is a root of \(kx^2 - 7x + 12 = 0\)), March 2026 (\(-\dfrac{7}{5}\) is a root of \(5m^2 + 2m + k = 0\)) and June 2026 (2 is a root of \(x^2 + mx - 5 = 0\))

    Find ‘\(k\)’ if \(x = 3\) is a root of quadratic equation \(kx^2 - 10x + 3 = 0\).

    2 marks See answer →

  3. Asked in: March 2025 board paper; forming the equation from given roots also came in March 2024 (roots 2 and 5) and June 2026 (roots 3 and −10)

    Complete the following activity to form a quadratic equation.

    Activity :
    I am a quadratic equation.
    → My standard form is ____ .
    → My roots are 5 and 12.
    → Sum of my roots ____ .
    → Product of my roots ____ .
    → My quadratic equation is ____ .

    2 marks See answer →

  4. Asked in: March 2024 and March 2026 board papers (exactly the same equation); factorisation sums also came in March 2025, July 2025 and June 2026

    Solve the following quadratic equation by factorisation method : \(x^2 + x - 20 = 0\)

    2 marks See answer →

  5. Asked in: July 2024 board paper

    Determine the nature of roots of the following quadratic equation.

    Activity : \(m^2 + 2m + 9 = 0\)

    \(a = \) ____ , \(b = 2\), \(c = 9\)
    \(b^2 - 4ac = 2^2 - 4 \times 1 \times \) ____
    \(= \) ____ \(- 36\)
    \(\therefore b^2 - 4ac = \) ____
    \(\therefore b^2 - 4ac \lt 0\)
    \(\therefore\) Roots of quadratic equation are not real.

    2 marks See answer →

  6. Asked in: March 2024 board paper; a 3-mark formula-method sum came in July 2024 (\(y^2 + \dfrac{1}{3}y = 2\)), March 2025 (\(x^2 - 2x - 3 = 0\)) and June 2026 (\(x^2 - 3x - 2 = 0\)) too

    Solve the following quadratic equation by formula method : \(3m^2 - m - 10 = 0\)

    3 marks See answer →

  7. Asked in: July 2025 board paper

    Product of Shraddha’s age 2 years ago and 3 years hence is 84. Find her present age.

    3 marks See answer →

  8. Asked in: March 2025 board paper

    Find the value of ‘m’ if the quadratic equation \((m - 12)x^2 + 2(m - 12)x + 2 = 0\) has real and equal roots.

    4 marks See answer →

  9. Asked in: July 2024 board paper

    Manisha wants to distribute 540 bananas among some students. If 30 students were more, each would get 3 bananas less. Find the number of students.

    4 marks See answer →

  10. Asked in: March 2024 board paper

    A tank can be filled up by two taps in 6 hours. The smaller tap alone takes 5 hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately.

    4 marks See answer →

  11. Asked in: March 2026 board paper

    The sum of two roots of a quadratic equation is 7 and sum of their cubes is 91, find the equation.

    4 marks See answer →

  12. Asked in: June 2026 board paper

    The sum of the squares of five consecutive natural numbers is 1455. Find the numbers.

    4 marks See answer →

HOTS: likely questions for 2027

  1. Which of the following is not a quadratic equation?

    1. (A) \(x^2 + 5x = 0\)
    2. (B) \((x + 2)^2 = x^2 + 3\)
    3. (C) \(2x^2 = 7\)
    4. (D) \(x(x - 1) = 4\)
    1 mark See answer →

  2. The discriminant of \(2x^2 - 5x + 3 = 0\) is ____.

    1. (A) 49
    2. (B) −1
    3. (C) 1
    4. (D) 0
    1 mark See answer →

  3. If \(\alpha\) and \(\beta\) are the roots of \(x^2 - 6x + 8 = 0\), then \(\dfrac{1}{\alpha} + \dfrac{1}{\beta} = \) ____.

    1. (A) \(\dfrac{3}{4}\)
    2. (B) \(\dfrac{4}{3}\)
    3. (C) \(-\dfrac{3}{4}\)
    4. (D) 6
    1 mark See answer →

  4. Find the sum and product of the roots of \(3x^2 - 12x + 5 = 0\).

    1 mark See answer →

  5. If the roots of \(x^2 + kx + 9 = 0\) are real and equal, find the positive value of \(k\).

    1 mark See answer →

  6. Solve the following quadratic equation by factorisation method : \(6x^2 - x - 2 = 0\)

    2 marks See answer →

  7. Complete the following activity to solve \(x^2 - 10x + 9 = 0\) by completing the square method.

    \(x^2 - 10x + 9 = 0\)
    \(\therefore x^2 - 10x + \) ____ \( - 25 + 9 = 0\)
    \(\therefore (x - \) ____ \()^2 = \) ____
    \(\therefore x - 5 = 4\) or \(x - 5 = \) ____
    \(\therefore x = \) ____ or \(x = 1\)

    2 marks See answer →

  8. Determine the nature of the roots of \(4x^2 - 12x + 9 = 0\) and hence find the roots.

    2 marks See answer →

  9. Solve the following quadratic equation by formula method : \(5x^2 + 13x + 8 = 0\)

    3 marks See answer →

  10. Find the value of \(k\) if one root of \(x^2 - kx + 18 = 0\) is double the other root.

    3 marks See answer →

  11. If \(\alpha\) and \(\beta\) are the roots of \(x^2 - 5x + 3 = 0\), form the quadratic equation whose roots are \(\alpha^2\) and \(\beta^2\).

    3 marks See answer →

  12. The sum of a natural number and its reciprocal is \(\dfrac{26}{5}\). Find the number.

    3 marks See answer →

  13. Rohan cycles 48 km to his grandparents’ village. If his average speed were 4 km/hr more, he would reach 1 hour earlier. Find his average speed.

    4 marks See answer →

  14. Find the values of \(k\) for which the equation \((k + 4)x^2 + (k + 1)x + 1 = 0\) has real and equal roots. Also find the roots for each value of \(k\).

    4 marks See answer →

  15. The sum of the present ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. Find their present ages.

    4 marks See answer →