10 Question MCQ (including Assertion)

Question 1 of 10

NCERT Exemplar

Which of the following equations has no real roots?

A \(x^2-4 x+3 \sqrt{2}=0\) B \(x^2+4 x-3 \sqrt{2}=0\) C \(x^2-4 x-3 \sqrt{2}=0\) D \(3 x^2+4 \sqrt{3} x+4=0\)

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Question 2 of 10

NCERT Exemplar

The quadratic equation \(2 x^2-\sqrt{5} x+1=0\) has

A two distinct real roots B two equal real roots C no real roots D more than 2 real roots

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Question 3 of 10

NCERT Exemplar

Which of the following equations has 2 as a root?

A \(x^2-4 x+5=0\) B \(x^2+3 x-12=0\) C \(2 x^2-7 x+6=0\) D \(3 x^2-6 x-2=0\)

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Question 4 of 10

CBSE Board Exam 2026

The equation \(x+\frac{1}{x}=3(x \neq 0)\) is expressed as a quadratic equation in the form of \(\mathrm{ax}^2+\mathrm{bx}+\mathrm{c}=0\). The value of \(\mathrm{a}-\mathrm{b}+\mathrm{c}\) is :

A 5 B 2 C 1 D -1

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Question 5 of 10

CBSE Board Exam 2026

The roots of the quadratic equation \(4 x^2-(a-1)^2=0\) are :

A \(\mathrm{a}-1, \mathrm{a}+1\) B \(\frac{\mathrm{a}-1}{2}, \frac{-\mathrm{a}+1}{2}\) C \(\frac{\mathrm{a}-1}{2}, \frac{-\mathrm{a}-1}{2}\) D \(\quad \pm(\mathrm{a}-1)\)

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Question 6 of 10

NCERT Exemplar

If \(\frac{1}{2}\) is a root of the equation \(x^2+k x-\frac{5}{4}=0\), then the value of \(k\) is

A 2 B -2 C \(\frac{1}{4}\) D \(\frac{1}{2}\)

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Question 7 of 10

NCERT Exemplar

Which of the following equations has the sum of its roots as 3 ?

A \(2 x^2-3 x+6=0\) B \(-x^2+3 x-3=0\) C \(\sqrt{2} x^2-\frac{3}{\sqrt{2}} x+1=0\) D \(3 x^2-3 x+3=0\)

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Question 8 of 10

NCERT Exemplar

\(\left(x^2+1\right)^2-x^2=0\) has

A four real roots B two real roots C no real roots D one real root.

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Question 9 of 10

NCERT Exemplar

Which one of the following is not a quadratic equation?

A \(\quad(x+2)^2=2(x+3)\) B \(\quad x^2+3 x=(-1)(1-3 x)^2\) C \(\quad(x+2)(x-1)=x^2-2 x-3\) D \(\quad x^3-x^2+2 x+1=(x+1)^3\)

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Question 10 of 10

CBSE Board Exam 2026

If the roots of the quadratic equation \(\sqrt{3} \mathrm{x}^2-\mathrm{kx}+2 \sqrt{3}=0\) are real and equal, then the value(s) of k is/are :

A \(\quad \pm \sqrt{24}\) B 0 C 4 D -5

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10 Question MCQ (including Assertion)