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

21. Chapter 4: Quadratic Equations · mcq

If -2 is a root of $x^2+kx-6=0$ , find k.

-1

-2

Show answer and explanation

-1

Substituting $x=-2$ gives $4-2k-6=0$ , or $-2k=2$ . Hence $k=-1$ .

22. Chapter 4: Quadratic Equations · mcq

The product of two consecutive positive integers is 156. What are the integers?

14 and 15

12 and 13

11 and 12

13 and 14

Show answer and explanation

12 and 13

Let the smaller integer be $n$ . Then $n(n+1)=156$ , so $n^2+n-156=(n-12)(n+13)=0$ . The positive solution is $n=12$ , giving 12 and 13.

23. Chapter 4: Quadratic Equations · mcq

A rectangle has area 54 cm². Its length is 3 cm more than its width. What is its width?

9 cm

12 cm

6 cm

3 cm

Show answer and explanation

6 cm

Let the width be $w>0$ . Then $w(w+3)=54$ , so $(w+9)(w-6)=0$ . Rejecting the negative value gives $w=6$ cm.

24. Chapter 4: Quadratic Equations · mcq

The sum of a positive number and its square is 72. What is the number?

Show answer and explanation

Let the number be $x>0$ . Then $x^2+x-72=(x+9)(x-8)=0$ . The positive solution is $x=8$ .

25. Chapter 4: Quadratic Equations · mcq

The product of two consecutive positive even integers is 168. What is the smaller integer?

Show answer and explanation

Let the smaller integer be $x$ . Then $x(x+2)=168$ , giving $x^2+2x-168=(x+14)(x-12)=0$ . The positive value is 12.

26. Chapter 4: Quadratic Equations · mcq

A right triangle has perpendicular sides x cm and (x + 7) cm, and hypotenuse 13 cm. What is x?

Show answer and explanation

By Pythagoras, $x^2+(x+7)^2=169$ . This reduces to $x^2+7x-60=(x+12)(x-5)=0$ . Since a length is positive, $x=5$ .

27. Chapter 4: Quadratic Equations · mcq

A car travels 120 km at a constant speed. If its speed were 10 km/h greater, the trip would take 1 hour less. What is its original speed?

40 km/h

60 km/h

30 km/h

20 km/h

Show answer and explanation

30 km/h

Let the original speed be $v>0$ . Then $120/v-120/(v+10)=1$ . Multiplying gives $v^2+10v-1200=(v+40)(v-30)=0$ . Rejecting the negative speed yields $v=30$ km/h.

28. Chapter 4: Quadratic Equations · mcq

A rectangular garden is 8 m by 6 m. A path of uniform width x m runs inside it along all four edges, leaving a central rectangle of area 24 m². What is x?

2 m

3 m

6 m

1 m

Show answer and explanation

1 m

The central rectangle has sides $8-2x$ and $6-2x$ . Thus $(8-2x)(6-2x)=24$ , giving $x^2-7x+6=(x-1)(x-6)=0$ . A valid path needs $0<x<3$ , so $x=1$ m; $x=6$ is physically impossible.

29. Chapter 4: Quadratic Equations · mcq

For what value of k does $x^2+(k-2)x+9=0$ have equal negative roots?

-4

-8

Show answer and explanation

Equal roots require $(k-2)^2-36=0$ , so $k=8$ or $k=-4$ . For $k=8$ , the equation is $(x+3)^2=0$ and the roots are -3. For $k=-4$ , they are +3, so only 8 works.

30. Chapter 4: Quadratic Equations · mcq

Which equation has roots $\frac23$ and $-\frac32$ ?

$6x^2-13x+6=0$

$6x^2+5x-6=0$

$6x^2-5x-6=0$

$6x^2+5x+6=0$

Show answer and explanation

$6x^2+5x-6=0$

The factors are $(3x-2)(2x+3)$ . Multiplying gives $6x^2+5x-6=0$ , whose roots are $2/3$ and $-3/2$ .