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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110 ready questions · 10 per page

21. Chapter 2: Polynomials · mcq

What is the degree of $4x^3-x^2+7$ ?

Show answer and explanation

The highest power of x with a nonzero coefficient is 3. Therefore the degree is 3.

22. Chapter 2: Polynomials · mcq

What is the zero of $5x-15$ ?

-3

Show answer and explanation

A zero makes the polynomial equal to zero. Solving $5x-15=0$ gives $x=3$ .

23. Chapter 2: Polynomials · mcq

What are the zeroes of $x^2-7x+12$ ?

$2,6$

$-2,-6$

$3,4$

$-3,-4$

Show answer and explanation

$3,4$

$x^2-7x+12=(x-3)(x-4)$ . Thus the zeroes are 3 and 4.

24. Chapter 2: Polynomials · mcq

What is the sum of the zeroes of $3x^2-8x+2$ ?

$-\frac{8}{3}$

$\frac{2}{3}$

$-\frac{2}{3}$

$\frac{8}{3}$

Show answer and explanation

$\frac{8}{3}$

For $ax^2+bx+c$ , the sum of the zeroes is $-b/a$ . Here it is $-(-8)/3=8/3$ .

25. Chapter 2: Polynomials · mcq

What is the product of the zeroes of $5x^2+7x-6$ ?

$-\frac{6}{5}$

$\frac{6}{5}$

$-\frac{7}{5}$

$\frac{7}{5}$

Show answer and explanation

$-\frac{6}{5}$

The product of the zeroes of $ax^2+bx+c$ is $c/a$ . Therefore the product is $-6/5$ .

26. Chapter 2: Polynomials · mcq

Which monic quadratic polynomial has zeroes -3 and 2?

$x^2-5x+6$

$x^2+x-6$

$x^2-x-6$

$x^2+x+6$

Show answer and explanation

$x^2+x-6$

The polynomial is $(x+3)(x-2)=x^2+x-6$ . Equivalently, the sum is -1 and the product is -6.

27. Chapter 2: Polynomials · mcq

Which monic quadratic polynomial has zeroes 0 and -5?

$x^2+5$

$x^2-5$

$x^2+5x$

$x^2-5x$

Show answer and explanation

$x^2+5x$

The factors are $x$ and $x+5$ . Their product is $x(x+5)=x^2+5x$ .

28. Chapter 2: Polynomials · mcq

If 3 is a zero of $x^2+kx-18$ , what is k?

-3

-6

Show answer and explanation

Substituting $x=3$ gives $9+3k-18=0$ . Thus $3k=9$ and $k=3$ .

29. Chapter 2: Polynomials · mcq

If 2 is a zero of $2x^2-5x+k$ , what is k?

-2

Show answer and explanation

Substitution gives $2(2)^2-5(2)+k=0$ , or $8-10+k=0$ . Hence $k=2$ .

30. Chapter 2: Polynomials · mcq

Which polynomial has two zeroes that are opposites of each other?

$x^2-3x$

$x^2-9$

$x^2-5x+6$

$x^2+4x+3$

Show answer and explanation

$x^2-9$

$x^2-9=(x-3)(x+3)$ has zeroes 3 and -3. Their sum is zero, as expected when the coefficient of x is zero.