Quadratic Equations helps students understand equations involving variables raised to the power of two and learn different methods to find their solutions. The chapter covers factorisation, the quadratic formula, and the nature of roots, helping students develop algebraic thinking and problem-solving skills. Regular practice of Quadratic Equations MCQs improves calculation accuracy and prepares students for objective questions in Class 10 Maths.
Understanding these concepts helps students solve algebraic problems with greater confidence and apply formulas correctly. Students can explore MCQs and Class 10 MCQs for chapter-wise practice and revision. Additional CBSE Board resources can also help students prepare for objective questions based on the latest syllabus and exam pattern.
Topics Covered
Before solving Quadratic Equations MCQs with Answers, students should revise all important concepts carefully because most board-level questions are concept-oriented. Important topics covered in this chapter :
- Standard form of quadratic equation
- Meaning of roots of equations
- Factorization method
- Completing square method
- Quadratic formula
- Discriminant
- Nature of roots
- Real roots
- Equal roots
- Distinct roots
- Algebraic simplification
- Transformation of equations
- Solution verification
Download MCQs for Class 10 Maths Chapter 4 PDF
Prepare for your Maths exam with a downloadable set of Class 10 Quadratic Equations questions for regular practice.
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Class 10 Maths Chapter 4 MCQs with Answers and Explanations
Take some time to practise these Quadratic Equations questions before your next Maths test. These objective questions help students improve equation-solving accuracy, discriminant understanding, algebraic reasoning, and board exam preparation skills effectively.
Q1. The graphical representation of the equations six x minus three y plus ten equals zero and two x minus y plus nine equals zero will form:
A) Intersecting lines
B) Coincident lines
C) Parallel lines
D) Perpendicular lines
Answer: C
Explanation: Comparing the coefficients gives six divided by two equals minus three divided by minus one, but ten divided by nine is different. Hence, both lines are parallel and never meet.
Q2. The pair of equations x plus two y plus five equals zero and minus three x minus six y plus one equals zero is:
A) Consistent with one solution
B) Inconsistent
C) Dependent
D) Coincident
Answer: B
Explanation: Ratios of x and y coefficients are equal, but constant terms are not proportional. Therefore, the system has no common solution.
Q3. A pair of linear equations is called consistent when the lines are:
A) Always parallel
B) Either intersecting or coincident
C) Only coincident
D) Only intersecting
Answer: B
Explanation: A consistent pair has at least one solution. Intersecting lines have one solution, while coincident lines have infinitely many solutions.
Q4. The equations y equals zero and y equals minus seven represent:
A) Intersecting horizontal lines
B) Coincident lines
C) Two parallel horizontal lines
D) Perpendicular lines
Answer: C
Explanation: Both equations are horizontal lines with different y-values, so they remain parallel and never intersect.
Q5. The equations x equals a and y equals b intersect at the point:
A) (b, a)
B) (a, a)
C) (b, b)
D) (a, b)
Answer: D
Explanation: x equals a fixes the x-coordinate, while y equals b fixes the y-coordinate. Hence, they meet at (a, b).
Q6. The graph represented by x equals minus two is:
A) Parallel to x-axis
B) Passing through origin
C) Parallel to y-axis
D) Inclined line
Answer: C
Explanation: Any equation of the form x equals constant produces a vertical line parallel to the y-axis.
Q7. In the equation x plus two y equals ten, if y equals six, then x becomes:
A) Minus two
B) Two
C) Four
D) Six
Answer: A
Explanation: Replacing y by six gives x plus twelve equals ten, so x equals minus two.
Q8. A linear equation in two variables always represents a:
A) Straight line
B) Circle
C) Curve
D) Point
Answer: A
Explanation: Every linear equation in two variables forms a straight line on the Cartesian plane.
Q9. The equations x plus two y minus five equals zero and minus three x minus six y plus fifteen equals zero have:
A) Unique solution
B) No solution
C) Infinite solutions
D) Two solutions
Answer: C
Explanation: All corresponding ratios are equal, showing that both equations represent the same line.
Q10. If the lines three x plus two k y equals two and two x plus five y plus one equals zero are parallel, then k equals:
A) Five by four
B) Two by five
C) Fifteen by four
D) Three by two
Answer: C
Explanation: For parallel lines, coefficient ratios must match. Solving three divided by two equals two k divided by five gives k equals fifteen by four.
Q11. Two numbers are in the ratio five is to six. If eight is subtracted from each number, the ratio becomes four is to five. The numbers are:
A) Forty and forty-two
B) Forty-two and forty-eight
C) Forty and forty-eight
D) Forty-four and fifty
Answer: C
Explanation: Taking numbers as five x and six x and applying the ratio condition gives x equals eight. Thus, numbers are forty and forty-eight.
Q12. Which pair of equations has solution x equals two and y equals minus three?
A) x plus y equals minus one and two x minus three y equals minus five
B) Two x plus five y equals minus eleven and four x plus ten y equals minus twenty-two
C) Two x minus y equals one and three x plus two y equals zero
D) x minus four y minus fourteen equals zero and five x minus y minus thirteen equals zero
Answer: D
Explanation: Substituting x equals two and y equals minus three satisfies both equations in option D.
Q13. If x minus y equals two and x plus y equals four, then the values of x and y are:
A) Three and five
B) Five and three
C) Three and one
D) Minus one and minus three
Answer: C
Explanation: Adding both equations gives two x equals six, so x equals three. Substituting gives y equals one.
Q14. A father is six times as old as his son. After four years, he will become four times his son’s age. Their present ages are:
Options:
A) Four and twenty-four
B) Five and thirty
C) Six and thirty-six
D) Three and twenty-four
Answer: C
Explanation: Let son’s age be six years. Then father’s age becomes thirty-six years, satisfying both conditions.
Q15. The equations a x plus two y equals seven and three x plus b y equals sixteen represent parallel lines if:
A) a equals b
B) Three a equals two b
C) Two a equals three b
D) a b equals six
Answer: D
Explanation: For parallel lines, coefficient ratios must be equal. Cross multiplication gives a multiplied by b equals six.
Q16. The value of k for which the equations x plus (k plus one)y equals five and (k plus one)x plus nine y equals eight k minus one have infinitely many solutions is:
A) Two
B) Three
C) Four
D) Five
Answer: A
Explanation: Infinite solutions occur when all coefficient ratios are equal. Solving gives k equals two.
Q17. One equation is two x plus five y equals three. Which equation will make the pair dependent?
A) Two x plus five y equals six
B) Three x plus five y equals three
C) Minus ten x minus twenty-five y plus fifteen equals zero
D) Ten x plus twenty-five y equals fifteen
Answer: C
Explanation: Dividing option C by minus five produces the same equation, so both represent identical lines.
Q18. For what value of k will x plus y minus four equals zero and two x plus k y equals three have no solution?
A) Minus two
B) Not equal to two
C) Three
D) Two
Answer: D
Explanation: No solution occurs for parallel lines. Matching coefficient ratios gives k equals two.
Q19. The point where two lines meet can be determined by:
A) Solving both equations together
B) Solving only first equation
C) Solving only second equation
D) Ignoring both equations
Answer: A
Explanation: The common values satisfying both equations give the intersection point.
Q20. If speed of a boat in still water is u and speed of stream is v, then upstream speed is:
A) u plus v
B) u minus v
C) v minus u
D) u multiplied by v
Answer: B
Explanation: While moving upstream, stream speed opposes boat speed, so subtraction is used.
Q21. The equations kx plus two y equals five and three x plus four y equals one will have no solution when k equals:
A) Five
B) Two by three
C) Six
D) Three by two
Answer: D
Explanation: For parallel lines, k divided by three must equal two divided by four. Hence, k equals three by two.
Q22. If the point (minus two, p) lies on the line two x minus three y plus seven equals zero, then p equals:
A) Minus one
B) One
C) Two
D) Three
Answer: B
Explanation: Substituting x equals minus two gives minus four minus three p plus seven equals zero, resulting in p equals one.
Q23. Reversing the digits of the number thirty-six gives:
A) Sixty-three
B) Ninety
C) Twenty-seven
D) Forty-five
Answer: A
Explanation: Interchanging the digits three and six forms sixty-three.
Q24. The equations six x minus two y equals three and kx minus y equals two will have a unique solution if:
A) k equals three
B) k not equal to four
C) k not equal to three
D) k equals four
Answer: C
Explanation: Unique solution exists when coefficient ratios are not equal, giving k not equal to three.
Q25. Half of the perimeter of a rectangular garden is thirty-six metres. If the length is four metres more than the width, then the width is:
A) Sixteen metres
B) Twenty metres
C) Eighteen metres
D) Fourteen metres
Answer: A
Explanation: Let width be x metres. Then x plus x plus four equals thirty-six, giving x equals sixteen.
Q26. Taxi fare consists of a fixed charge x and a charge y per kilometre. The fare for ten kilometres is:
A) Ten x plus y
B) x plus ten y
C) Ten multiplied by (x plus y)
D) x divided by ten plus y
Answer: B
Explanation: Total fare equals fixed charge plus distance charge for ten kilometres.
Q27. For which value of k do the equations three x minus y plus eight equals zero and six x minus k y equals minus sixteen represent coincident lines?
A) One by two
B) Two
C) Minus two
D) Four
Answer: B
Explanation: Coincident lines require all corresponding ratios to be equal, which gives k equals two.
Q28. The substitution method becomes easiest when one variable has coefficient:
A) Zero
B) One or minus one
C) Two
D) A prime number
Answer: B
Explanation: Variables with coefficient one or minus one can be isolated quickly without fractions.
Q29. The lines x equals zero and x equals minus four are:
A) Intersecting
B) Coincident
C) Parallel
D) Passing through origin
Answer: C
Explanation: Both are vertical lines with different x-values, so they never intersect.
Q30. One equation of a dependent pair is minus three x plus five y minus two equals zero. Which can be the second equation?
A) Minus six x plus ten y minus four equals zero
B) Six x minus ten y minus four equals zero
C) Six x plus ten y minus four equals zero
D) Minus six x plus ten y plus four equals zero
Answer: A
Explanation: Option A is exactly twice the original equation, so both equations represent the same straight line.
Different Methods Used to Solve Quadratic Equations
Factorization Method
In this method, the quadratic equation is broken into two linear factors.
Example: x² + 5x + 6 = 0
This can be written as: (x + 2)(x + 3) = 0
Therefore:
x = -2
x = -3
This method is useful when the equation can be factorized easily.
Completing the Square Method
This method converts the equation into a perfect square form.
Students mainly use this method when:
factorization becomes difficult,
equations are not easily splittable,
or conceptual understanding is required.
Although the process looks longer initially, it helps students understand quadratic structure more deeply.
Quadratic Formula Method
The quadratic formula is one of the most important concepts in this chapter.
Formula:
x = (-b ± √(b² − 4ac)) / 2a
This method works for all quadratic equations and is especially useful when factorization is difficult.
Common Errors Students Make in Quadratic Equation Questions
Many students lose marks in quadratic equation MCQs because of avoidable mistakes rather than lack of preparation. Common errors :
- Incorrect factorization
- Sign mistakes during simplification
- Wrong discriminant calculation
- Formula substitution errors
- Arithmetic mistakes
- Missing square terms
- Confusion between roots and factors
- Incomplete simplification steps
