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CBSE Class 10 — free MCQ practice

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CBSE Class 10 subjects

Social Science (2,250)Science (1,188)Mathematics (710)English (261)

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Resources, Agriculture & MineralsPower Sharing and FederalismEconomic Development & BankingNationalism in India & EuropeRefraction of Light and LensesGlobal World & IndustrialisationEffects of Electric CurrentChemical Reactions and EquationsIntroduction to TrigonometryLife Processes in Living Organisms Part 2Print Culture and Modern WorldEnglish GrammarMensuration: Surface Areas & VolumesLife Processes in Living Organisms Part 1Real Numbers and PolynomialsArithmetic ProgressionMetals and Non-metalsVocabulary & Language StudyEnvironmental & Disaster ManagementStatistics and ProbabilityReading ComprehensionAcids, Bases and SaltsCarbon CompoundsCell Biology and Animal ClassificationCoordinate GeometryHeredity and EvolutionLinear Equations in Two VariablesPeriodic Classification of ElementsQuadratic EquationsTriangles and Circles

Try a CBSE Class 10 question

If the discriminant of a quadratic equation is negative, what can be concluded about its roots?Read the answer and worked solution →For the quadratic equation $ax^2+bx+c=0$, what is the discriminant?Read the answer and worked solution →Find the roots of $2x^2-5x+3=0$ by factorisation.Read the answer and worked solution →What is the maximum number of real roots a quadratic equation can have?Read the answer and worked solution →

Worked practice questions

If the discriminant of a quadratic equation is negative, what can be concluded about its roots?

  1. The equation has two distinct real roots
  2. The equation has two equal real roots
  3. The equation has no real roots
  4. The equation has exactly one real root
Show answer and solution

Correct answer: C. The equation has no real roots

If $b^2-4ac<0$, then the square root term in the quadratic formula is not a real number. **Therefore, the quadratic equation has no real roots.**

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For the quadratic equation $ax^2+bx+c=0$, what is the discriminant?

  1. $b^2+4ac$
  2. $4ac-b^2$
  3. $b^2-4ac$
  4. $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Show answer and solution

Correct answer: C. $b^2-4ac$

The discriminant of the quadratic equation $ax^2+bx+c=0$ is the expression under the square root in the quadratic formula, namely $b^2-4ac$. It determines the nature of the roots.

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Find the roots of $2x^2-5x+3=0$ by factorisation.

  1. $x=\frac{3}{2},\ 1$
  2. $x=\frac{5}{2},\ 3$
  3. $x=-\frac{3}{2},\ -1$
  4. $x=\frac{2}{3},\ 1$
Show answer and solution

Correct answer: A. $x=\frac{3}{2},\ 1$

Factorise $2x^2-5x+3$ by splitting the middle term: $2x^2-2x-3x+3=2x(x-1)-3(x-1)=(2x-3)(x-1)$. So $(2x-3)(x-1)=0$, giving $2x-3=0$ or $x-1=0$. **Hence the roots are $x=\frac{3}{2}$ and $x=1$.**

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How to practise

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