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

81. Chapter 4: Quadratic Equations · mcq

Which equation is quadratic in x?

$x^2+3x+2=0$

$3x+2=0$

$x^3+2x=0$

$(x+1)^2=x^2+3$

Show answer and explanation

$x^2+3x+2=0$

$x^2+3x+2=0$ has degree 2 with a nonzero quadratic coefficient. The last choice simplifies to $2x-2=0$ , which is linear.

82. Chapter 4: Quadratic Equations · mcq

For $kx^2+3x+1=0$ to be a quadratic equation, what condition is necessary?

$k>0\text{ only}$

$k\ne0$

$k=0$

$k=1\text{ only}$

Show answer and explanation

$k\ne0$

A quadratic equation must have a nonzero coefficient of $x^2$ . Thus $k\ne0$ ; k may be positive or negative.

83. Chapter 4: Quadratic Equations · mcq

Write $(x-2)(x+3)=4$ in standard quadratic form.

$x^2-x-10=0$

$x^2+5x-10=0$

$x^2+x-10=0$

$x^2+x-2=0$

Show answer and explanation

$x^2+x-10=0$

Expanding gives $x^2+x-6=4$ . Moving 4 to the left gives $x^2+x-10=0$ .

84. Chapter 4: Quadratic Equations · mcq

What are the roots of $x^2-9x+20=0$ ?

$-4,-5$

$2,10$

$1,20$

$4,5$

Show answer and explanation

$4,5$

$x^2-9x+20=(x-4)(x-5)$ , so the roots are 4 and 5.

85. Chapter 4: Quadratic Equations · mcq

Solve $2x^2-7x+3=0$ .

$x=\frac12,\ 3$

$x=-\frac12,\ -3$

$x=1,\ 3$

$x=\frac32,\ 2$

Show answer and explanation

$x=\frac12,\ 3$

$2x^2-7x+3=(2x-1)(x-3)$ . Therefore $x=1/2$ or $x=3$ .

86. Chapter 4: Quadratic Equations · mcq

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

$x=1,\ 6$

$x=-2,\ -3$

$x=2,\ 3$

$x=-1,\ -6$

Show answer and explanation

$x=-2,\ -3$

$x^2+5x+6=(x+2)(x+3)$ . Setting each factor to zero gives -2 and -3.

87. Chapter 4: Quadratic Equations · mcq

What are the real roots of $x^2-25=0$ ?

$-5,-5$

$25,-25$

$5,-5$

$5,5$

Show answer and explanation

$5,-5$

$x^2=25$ , so $x=5$ or $x=-5$ . Both values satisfy the original equation.

88. Chapter 4: Quadratic Equations · mcq

Solve $x^2-8x=0$ .

$x=0,\ -8$

$x=4,\ -4$

$x=8\text{ only}$

$x=0,\ 8$

Show answer and explanation

$x=0,\ 8$

Factor out x: $x(x-8)=0$ . Thus $x=0$ or $x=8$ . Dividing by x would incorrectly discard the root 0.

89. Chapter 4: Quadratic Equations · mcq

Solve $3x^2+12x=0$ .

$x=0,\ -4$

$x=0,\ 4$

$x=-3,\ -4$

$x=0,\ -12$

Show answer and explanation

$x=0,\ -4$

$3x^2+12x=3x(x+4)=0$ . Therefore the roots are 0 and -4.

90. Chapter 4: Quadratic Equations · mcq

What is the repeated root of $(x-3)^2=0$ ?

-3

Show answer and explanation

A square is zero only when its base is zero. Thus $x-3=0$ , giving the repeated root $x=3$ .