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

41. Chapter 2: Polynomials · mcq

For $p(x)=x^3-4x+1$ , find $p(2)$ .

-1

Show answer and explanation

$p(2)=2^3-4(2)+1=8-8+1=1$ .

42. Chapter 2: Polynomials · mcq

Which is a factor of $x^2-4$ ?

$x+1$

$x+2$

$x+4$

$x-4$

Show answer and explanation

$x+2$

The difference of squares gives $x^2-4=(x-2)(x+2)$ . Therefore $x+2$ is a factor.

43. Chapter 2: Polynomials · mcq

What are the zeroes of $x(3x-12)$ ?

$3,4$

$-3,-4$

$0,4$

$0,-4$

Show answer and explanation

$0,4$

The product is zero when $x=0$ or $3x-12=0$ . The second equation gives $x=4$ .

44. Chapter 2: Polynomials · mcq

If -2 is a zero of a polynomial $p(x)$ , which expression must be a factor of it?

$x-2$

$x+4$

$2x-1$

$x+2$

Show answer and explanation

$x+2$

A zero $r$ corresponds to a factor $x-r$ . For $r=-2$ , the factor is $x-(-2)=x+2$ .

45. Chapter 2: Polynomials · mcq

How many distinct real zeroes does $8x^2$ have?

Show answer and explanation

$8x^2=0$ implies $x=0$ . Zero is a repeated zero, but it is only one distinct real value.

46. Chapter 2: Polynomials · mcq

How many zeroes does the nonzero constant polynomial $p(x)=7$ have?

Infinitely many

Show answer and explanation

For every x, p(x) equals 7 and can never equal zero. Therefore it has no zeroes.

47. Chapter 2: Polynomials · mcq

Which linear polynomial has zero -4?

$x+2$

$4x+2$

$2x+8$

$2x-8$

Show answer and explanation

$2x+8$

Substituting $x=-4$ into $2x+8$ gives $-8+8=0$ . The other choices do not vanish at -4.

48. Chapter 2: Polynomials · mcq

Which quadratic polynomial has zeroes $-\frac12$ and 3?

$2x^2+5x-3$

$2x^2-5x+3$

$2x^2-7x-3$

$2x^2-5x-3$

Show answer and explanation

$2x^2-5x-3$

The factors can be written $(2x+1)(x-3)$ . Multiplying gives $2x^2-5x-3$ .

49. Chapter 2: Polynomials · mcq

If $p(x)=x^2+kx+6$ and $p(1)=0$ , what is k?

-7

-5

Show answer and explanation

-7

$p(1)=1+k+6=0$ , so $k=-7$ .

50. Chapter 2: Polynomials · mcq

Which monic quadratic polynomial has sum of zeroes -4 and product of zeroes -12?

$x^2-12x-4$

$x^2+4x-12$

$x^2-4x-12$

$x^2+4x+12$

Show answer and explanation

$x^2+4x-12$

Use $x^2-Sx+P$ with $S=-4$ and $P=-12$ . This gives $x^2+4x-12$ . Its zeroes 2 and -6 have the required sum and product.