Public question bank · Class 10 · Mathematics

Class 10 Mathematics - Chapters 1-4

110 original MCQs with answers and worked explanations, aligned with NCERT Class 10 Mathematics: Real Numbers (20), Polynomials (30), Pair of Linear Equations in Two Variables (30), Quadratic Equations (30).

Chapters / topics

Chapter 1: Real Numbers · 20 Chapter 2: Polynomials · 30 Chapter 3: Pair of Linear Equations in Two Variables · 30 Chapter 4: Quadratic Equations · 30

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Chapter 4: Quadratic EquationsAll chapters

30 ready questions · 10 per page

11. Chapter 4: Quadratic Equations · mcq

What is the discriminant of $2x^2-4x-3=0$ ?

-40

-8

Show answer and explanation

$D=b^2-4ac=(-4)^2-4(2)(-3)=16+24=40$ .

12. Chapter 4: Quadratic Equations · mcq

What is the nature of the roots of $x^2+2x+5=0$ ?

Two distinct real roots

Two equal real roots

Exactly one positive and one negative real root

No real roots

Show answer and explanation

No real roots

$D=2^2-4(1)(5)=4-20=-16<0$ . A negative discriminant means there are no real roots.

13. Chapter 4: Quadratic Equations · mcq

What is the nature of the roots of $9x^2-12x+4=0$ ?

Two equal real roots

Two distinct real roots

No real roots

One zero root and one nonzero root

Show answer and explanation

Two equal real roots

$D=(-12)^2-4(9)(4)=144-144=0$ . Hence the real roots are equal; indeed, the equation is $(3x-2)^2=0$ .

14. Chapter 4: Quadratic Equations · mcq

What is the nature of the roots of $x^2-7x+10=0$ ?

Exactly one real root

Two distinct real roots

Two equal real roots

No real roots

Show answer and explanation

Two distinct real roots

$D=(-7)^2-4(1)(10)=49-40=9>0$ . Thus there are two distinct real roots, namely 2 and 5.

15. Chapter 4: Quadratic Equations · mcq

For what value of k does $x^2-10x+k=0$ have equal real roots?

100

Show answer and explanation

Equal roots require $D=100-4k=0$ . Thus $4k=100$ and $k=25$ . The equation becomes $(x-5)^2=0$ .

16. Chapter 4: Quadratic Equations · mcq

For which values of k does $x^2+kx+16=0$ have equal real roots?

$k=8\text{ only}$

$k=-8\text{ only}$

$k=4\text{ or }-4$

$k=8\text{ or }-8$

Show answer and explanation

$k=8\text{ or }-8$

$D=k^2-64$ . Equal roots require $k^2=64$ , so $k=8$ or $k=-8$ . Both possibilities must be included.

17. Chapter 4: Quadratic Equations · mcq

For what value of k does the quadratic equation $kx^2-6x+9=0$ have equal real roots?

Show answer and explanation

The discriminant is $36-36k$ . Setting it to zero gives $k=1$ , which is nonzero and therefore preserves the quadratic degree.

18. Chapter 4: Quadratic Equations · mcq

For which condition on k does $x^2-4x+k=0$ have no real roots?

$k\le4$

$k>4$

$k<4$

$k=4$

Show answer and explanation

$k>4$

No real roots require $D<0$ . Here $16-4k<0$ , so $k>4$ .

19. Chapter 4: Quadratic Equations · mcq

For which condition on k does $x^2-6x+k=0$ have two distinct real roots?

$k=9$

$k\ge9$

$k<9$

$k>9$

Show answer and explanation

$k<9$

Two distinct real roots require $D>0$ . Since $D=36-4k$ , this gives $36-4k>0$ , hence $k<9$ .

20. Chapter 4: Quadratic Equations · mcq

If 3 is a root of $2x^2+kx-3=0$ , find k.

-3

-5

Show answer and explanation

-5

Substituting $x=3$ gives $18+3k-3=0$ . Thus $3k=-15$ and $k=-5$ .