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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31. Chapter 2: Polynomials · mcq

Which polynomial has two real zeroes that are reciprocals of each other?

$2x^2-7x+4$

$2x^2-7x+1$

$2x^2-7x+2$

$2x^2-7x-2$

Show answer and explanation

$2x^2-7x+2$

Reciprocal zeroes have product 1. For $2x^2-7x+2$ , the product is $c/a=2/2=1$ , and its discriminant is $49-16=33>0$ , so both zeroes are real.

32. Chapter 2: Polynomials · mcq

For what value of k does $x^2-6x+k$ have both zeroes equal to 3?

-9

Show answer and explanation

A monic polynomial with zeroes 3 and 3 is $(x-3)^2=x^2-6x+9$ . Thus $k=9$ .

33. Chapter 2: Polynomials · mcq

The graph of a polynomial meets the x-axis at exactly three distinct points. How many distinct real zeroes does it have?

Show answer and explanation

A real zero is an x-coordinate at which the graph meets the x-axis. Three distinct meeting points therefore give three distinct real zeroes.

34. Chapter 2: Polynomials · mcq

The graph of a polynomial does not meet the x-axis. How many real zeroes does the polynomial have?

Infinitely many

Show answer and explanation

A real zero requires the graph to meet the x-axis. Since there are no such points, the polynomial has no real zeroes.

35. Chapter 2: Polynomials · mcq

What is the maximum possible number of distinct real zeroes of a quadratic polynomial?

Show answer and explanation

A nonzero polynomial of degree 2 has at most two distinct zeroes. For example, x² - 1 has the two zeroes -1 and 1.

36. Chapter 2: Polynomials · mcq

Which monic quadratic polynomial has sum of zeroes 4 and product of zeroes -5?

$x^2+4x-5$

$x^2-5x+4$

$x^2-4x+5$

$x^2-4x-5$

Show answer and explanation

$x^2-4x-5$

For sum $S$ and product $P$ , the monic polynomial is $x^2-Sx+P$ . Substituting $S=4$ , $P=-5$ gives $x^2-4x-5$ .

37. Chapter 2: Polynomials · mcq

One zero of $x^2-9x+20$ is 4. What is the other zero?

-5

Show answer and explanation

The sum of the zeroes is 9. If one is 4, the other is $9-4=5$ . The product check is $4\times5=20$ .

38. Chapter 2: Polynomials · mcq

The zeroes of $x^2-6x+8$ are $\alpha,\beta$ . Find $\alpha^2+\beta^2$ .

Show answer and explanation

Here $\alpha+\beta=6$ and $\alpha\beta=8$ . Thus $\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha\beta=36-16=20$ .

39. Chapter 2: Polynomials · mcq

The zeroes of $x^2-5x+6$ are $\alpha,\beta$ . Find $(\alpha-\beta)^2$ .

Show answer and explanation

$\alpha+\beta=5$ and $\alpha\beta=6$ . Therefore $(\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\beta=25-24=1$ .

40. Chapter 2: Polynomials · mcq

The zeroes of $x^2-3x-4$ are $\alpha,\beta$ . Find $\frac1\alpha+\frac1\beta$ .

$\frac34$

$-\frac43$

$\frac43$

$-\frac34$

Show answer and explanation

$-\frac34$

The zeroes are nonzero because their product is -4. Hence $1/\alpha+1/\beta=(\alpha+\beta)/(\alpha\beta)=3/(-4)=-3/4$ .