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Quadratic Equations Questions

Practice 61 Quadratic Equations questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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61
Total Questions
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2
Easy
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57
Medium
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2
Hard
Practice by Exam:Quantitative Aptitude(27)Mathematics(22)Mathematics and Science(6)Algebra(4)Quantitative Aptitude@NUM: 58(1)Quantitative Aptitude@NUM: 60(1)

About Quadratic Equations — practice questions, PYQs & concepts

Quadratic Equations is a frequently-tested topic on Quantitative Aptitude, Mathematics, Mathematics and Science. ExamTest.live currently lists 61 Quadratic Equations questions spanning previous-year papers from 2004 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Quadratic Equations weight in competitive exams

Across our Quadratic Equations question bank, the largest sources are Quantitative Aptitude (27), Mathematics (22), Mathematics and Science (6), Algebra (4) and Quantitative Aptitude@NUM: 58 (1). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 2 easy Quadratic Equations questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
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  • Read every explanation: Even on questions you got right — the explanation often surfaces a faster approach you can reuse.

All Quadratic Equations Questions(1–61 of 61)

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Q1mediummcqQuantitative AptitudeCompetitive Exams2026
0% accuracy
Which of the following quadratic equations has equal roots?
Q2mediummcqQuantitative AptitudeCompetitive Exam Practice2026
33% accuracy
The sum of two numbers is . If the sum of their reciprocals is , then find the two numbers?
Q3mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
A brother is elder to his sister by 7 years. Five years ago, the product of their ages was 30. What is the current age of the brother?
Q4mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If the sum of the roots of a quadratic equation is −7 and the product of the roots is 12, find the quadratic equation.
Q5mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
What is the probability that the roots of the equation are real, where and ?
Q6mediummcqAlgebraSSC CGL2026
0% accuracy
What are the roots of the quadratic equation: x
2
+3x−154=0
Q7mediummcqAlgebraSSC CGL2026
0% accuracy
Divide 32 into two parts such that the sum of the square of the parts is 674. What is the value of the parts?
Q8mediummcqQuantitative Aptitude@NUM: 58SSC CGL2026
0% accuracy
What will be the roots of the quadratic equation ?
Q9mediummcqQuantitative Aptitude@NUM: 60SSC CGL2026
0% accuracy
Which of the following is not a quadratic equation?
Q10mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
A number is greater than twice its reciprocal by . Find the number.
Q11mediummcqMathematicsStaff Selection Commission2026
0% accuracy
Which of the following quadratic equations has real roots?
Q12mediummcqQuantitative AptitudePrepp2026
0% accuracy
What will be the possible value of that satisfies the given equation?
Q13mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
If are the roots of the equation , then the value of the determinant is:
Q14mediummcqQuantitative AptitudeIndian Competitive Exam Prep2026
0% accuracy
A group of children seated in rows for a group photo session. Each row contains three less children than the row in front of it. Which one of the following number of rows is not possible?
Q15mediummcqMathematicsAIEEE 20072026
0% accuracy
If the difference between the roots of the equation is less than , then the set of possible values of is:
Q16mediummcqMathematicsAIEEE 20062026
0% accuracy
If the roots of the quadratic equation are and , respectively, then the value of is:
Q17mediummcqMathematicsAIEEE 20062026
0% accuracy
All the values of for which both roots of the equation are greater than but less than , lie in the interval:
Q18mediummcqQuantitative AptitudeWBCS Prelims2026
The difference of a proper fraction and its reciprocal is . Find the fraction.
Q19mediummcqAlgebraCompetitive Exam2026
The number of coconuts plucked from each tree is more than the total number of coconut trees in Anil's garden. If the total number of coconuts plucked is , find the total number of coconut trees in the garden.
Q20mediummcqQuantitative AptitudeCompetitive Exam2026
Solve the following equation for :
Q21mediummcqQuantitative AptitudeWBCS Prelims 20212026
The roots of the equation are:
Q22mediummcqQuantitative AptitudeCompetitive Exam2026
If the current ratio of the father's age to the son's age is and the product of their ages is , what will be the ratio of their ages after years?
Q23mediummcqQuantitative AptitudeCompetitive Exam2026
Ram and Shyam solve a quadratic equation. Ram makes a mistake in the constant term and finds the roots as . Shyam makes a mistake in the co-efficient of and gets the roots as . The correct roots are:
Q24mediummcqQuantitative AptitudeCompetitive Exam2026
The addition of a rational number and its reciprocal is . Calculate the number.
Q25mediummcqQuantitative AptitudeCompetitive Exam2026
If is a factor of , then find the possible values of .
Q26mediummcqQuantitative AptitudeSSC CGL2026
The sum of a non-zero number and ten times its reciprocal is 7. Find the number.
Q27mediummcqQuantitative AptitudeSSC CGL2026
A number is greater than five times its reciprocal by . Find the number.
Q28mediummcqQuantitative AptitudeSSC CGL2026
The sum of a non-zero number and thrice its reciprocal is
7
52
​
. Find the number.
Q29mediummcqQuantitative AptitudeCompetitive Exam2026
If and are the roots of the quadratic equation and , are the roots of , then which one of the following is correct?
Q30mediummcqQuantitative AptitudeSSC CGL2026
The sum of a non-zero number and twice its reciprocal is
4
33
​
. Find the number.
Q31mediummcqAlgebraCompetitive Exams2026
What value of ensures that the two roots of the quadratic equation are reciprocal to each other?
Q32mediummcqQuantitative AptitudeCompetitive Examination2026
If the product of two successive positive integers is , which is the greatest integer?
Q33mediummcqQuantitative AptitudeSSC CGL2026
The sum of a non-zero number and thrice its reciprocal is
2
13
​
. Find the number.
Q34mediummcqQuantitative AptitudeCompetitive Exam2026
The square of a number is more than times of itself. Find the number.
Q35mediummcqMathematicsAIEEE2026
If roots of the equation are two consecutive integers, then equals:
Q36mediummcqMathematicsJEE Main2026
If the equations and , , have a common root, then is:
Q37mediummcqMathematicsAIEEE2026
In a triangle , . If and are the roots of , then:
Q38mediummcqMathematicsAIEEE2026
The value of for which the sum of the squares of the roots of the equation assumes the least value is:
Q39mediummcqMathematicsAIEEE2026
If both the roots of the quadratic equation are less than , then lies in the interval:
Q40mediummcqMathematicsAIEEE-CBSE-ENG-032026
The value of ' ' for which one root of the quadratic equation is twice as large as the other, is:
Q41mediummcqMathematicsAIEEE-CBSE-ENG-032026
The number of real solutions of the equation is:
Q42mediummcqMathematicsAIEEE-CBSE-ENG-032026
If the sum of the roots of the quadratic equation is equal to the sum of the squares of their reciprocals, then , and are in:
Q43mediummcqMathematicsAIEEE2026
The quadratic equations and have one root in common. The other roots of the first and second equations are integers in the ratio . Then the common root is:
Q44mediummcqMathematicsAIEEE 20092026
If the roots of the equation be imaginary, then for all real values of , the expression is:
Q45easymcqMathematicsAIEEE2026
If and are the roots of the equation , then
Q46mediummcqQuantitative AptitudeCompetitive Exam2026
If 4sin
2
θ−4
3

​
sinθ+3=0, then find the value of θ (0
∘
<θ<90
∘
).
Q47mediummcqQuantitative AptitudeCompetitive Exam2026
If 3sec
4
θ+8=10sec
2
θ, then the value of tanθ can be:
Q48mediummcqQuantitative AptitudePrepp2026
The possible value of satisfying the equation is:
Q49mediummcqQuantitative AptitudeCompetitive Exam2026
Som is slower than Ram, and each travels 150 km. The sum of their speeds is 25 km/h and the sum of the time taken by them is 25 hours. Then, Som's speed is:
Q50mediummcqQuantitative AptitudeSSC CGL2026
The distance between two places is 1200 km. To cover this distance, a person X takes 5 hours lesser than another person Y, whose average speed is 40 km/h lesser than that of X. The time taken by Y to complete the travel is:
Q51mediummcqMathematicsUPTET 2021 Memory Based Paper 12026
What is the present age of Mohan if the product of the ages of Mohan 5 years before and after 9 years is 15?
Q52hardmcqMathematicsUPTET 2021 Memory Based Paper 12026
Vinay sold a watch at Rs. 75. He gets profit percentage numerical value same as the cost price of the watch, then cost price of the watch is:
Q53mediummcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2018
The minimum value of is
Q54hardmcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2018
The equation whose roots are and will be
Q55mediummcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2017
If the roots of the equation x
2
−bx+c=0 are two consecutive integers, then b
2
−4c is
Q56mediummcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2017
If the roots of the equation x
2
−px+54=0 are in the ratio 2:3, then the value of p is
Q57mediummcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2017
If the roots of the equation are two consecutive integers, then is
Q58mediummcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2017
If the roots of the equation are in the ratio , then the value of is
Q59mediummcqMathematicsAIEEE 20042004
0% accuracy
If one root of the equation is while the equation has equal roots, then the value of 'q' is
Q60mediummcqMathematicsAIEEE 20042004
0% accuracy
If is a root of quadratic equation then its roots are
Q61easymcqMathematicsAIEEE 20042004
0% accuracy
Let two numbers have arithmetic mean and geometric mean Then these numbers are the roots of the quadratic equation

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How many Quadratic Equations questions are on ExamTest.live?▼
We have 61 Quadratic Equations questions spread across 1 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
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Which exams include Quadratic Equations questions?▼
Quadratic Equations questions are commonly asked in Quantitative Aptitude, Mathematics, Mathematics and Science, Algebra, Quantitative Aptitude@NUM: 58. You can filter by exam using the links above.
How do I practice Quadratic Equations questions effectively?▼
Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.