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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51. Chapter 3: Pair of Linear Equations in Two Variables · mcq

Solve $x+y=11$ and $x-y=3$ .

$x=8,\ y=3$

$x=6,\ y=5$

$x=7,\ y=4$

$x=4,\ y=7$

Show answer and explanation

$x=7,\ y=4$

Adding the equations gives $2x=14$ , so $x=7$ . Substituting into $x+y=11$ gives $y=4$ .

52. Chapter 3: Pair of Linear Equations in Two Variables · mcq

Solve $2x+y=13$ and $x-y=2$ .

$x=3,\ y=5$

$x=4,\ y=5$

$x=6,\ y=1$

$x=5,\ y=3$

Show answer and explanation

$x=5,\ y=3$

From the second equation, $y=x-2$ . Substitution gives $2x+x-2=13$ , so $x=5$ and $y=3$ .

53. Chapter 3: Pair of Linear Equations in Two Variables · mcq

Solve $3x+2y=16$ and $x+y=6$ .

$x=4,\ y=2$

$x=2,\ y=4$

$x=3,\ y=3$

$x=5,\ y=1$

Show answer and explanation

$x=4,\ y=2$

Twice the second equation is $2x+2y=12$ . Subtracting this from the first gives $x=4$ ; hence $y=2$ .

54. Chapter 3: Pair of Linear Equations in Two Variables · mcq

Solve $\frac{x}{2}+\frac{y}{3}=4$ and $x+y=10$ .

$x=8,\ y=2$

$x=4,\ y=6$

$x=6,\ y=4$

$x=2,\ y=8$

Show answer and explanation

$x=4,\ y=6$

Multiply the first equation by 6 to get $3x+2y=24$ . Twice the second is $2x+2y=20$ . Subtract to obtain $x=4$ , then $y=6$ .

55. Chapter 3: Pair of Linear Equations in Two Variables · mcq

Solve $0.2x+0.3y=1.3$ and $x+y=5$ .

$x=1,\ y=4$

$x=4,\ y=1$

$x=2,\ y=3$

$x=3,\ y=2$

Show answer and explanation

$x=2,\ y=3$

Multiplying the first equation by 10 gives $2x+3y=13$ . Subtract $2x+2y=10$ to get $y=3$ , so $x=2$ .

56. Chapter 3: Pair of Linear Equations in Two Variables · mcq

How many solutions do $2x+3y=7$ and $4x+6y=15$ have?

Exactly one

Exactly two

Infinitely many

No solution

Show answer and explanation

No solution

Doubling the first equation gives $4x+6y=14$ , which contradicts $4x+6y=15$ . The lines are parallel and distinct.

57. Chapter 3: Pair of Linear Equations in Two Variables · mcq

How many solutions do $2x-3y=5$ and $6x-9y=15$ have?

Infinitely many

No solution

Exactly one

Exactly three

Show answer and explanation

Infinitely many

The second equation is exactly three times the first. Both represent the same line, so every point on that line solves both equations.

58. Chapter 3: Pair of Linear Equations in Two Variables · mcq

Which pair of equations has a unique solution?

$2x-y=4,\ 4x-2y=8$

$x+y=5,\ x-y=1$

$x+y=5,\ 2x+2y=10$

$x+y=5,\ 2x+2y=12$

Show answer and explanation

$x+y=5,\ x-y=1$

For $x+y=5$ and $x-y=1$ , the coefficient determinant is $1(-1)-1(1)=-2\ne0$ , so the lines intersect once. The other pairs are coincident or parallel.

59. Chapter 3: Pair of Linear Equations in Two Variables · mcq

For what value of k do $kx+2y=5$ and $3x+6y=15$ have infinitely many solutions?

-1

Show answer and explanation

For coincident lines, the first equation multiplied by 3 must equal the second. Thus $3k=3$ , giving $k=1$ ; the y coefficients and constants also match.

60. Chapter 3: Pair of Linear Equations in Two Variables · mcq

For what value of k do $2x+3y=7$ and $4x+ky=14$ have infinitely many solutions?

Show answer and explanation

Doubling the first equation gives 4x + 6y = 14. Therefore k must equal 6 for the equations to represent the same line.