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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Chapter 3: Pair of Linear Equations in Two VariablesAll chapters

30 ready questions · 10 per page

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

A farm has only chickens and goats. There are 18 heads and 50 legs in total. How many goats are there?

Show answer and explanation

Let chickens be $c$ and goats be $g$ . Then $c+g=18$ and $2c+4g=50$ . Subtracting $2c+2g=36$ gives $2g=14$ , so $g=7$ .

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

Two angles are complementary. The larger is twice the smaller. What is the larger angle?

$30^\circ$

$45^\circ$

$120^\circ$

$60^\circ$

Show answer and explanation

$60^\circ$

Complementary angles sum to $90^\circ$ . If the smaller angle is $s$ , then $s+2s=90^\circ$ , giving $s=30^\circ$ and the larger angle $60^\circ$ .

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

A rectangle has perimeter 50 cm. Its length is 5 cm more than its width. What is its area?

$150\text{ cm}^2$

$100\text{ cm}^2$

$125\text{ cm}^2$

$200\text{ cm}^2$

Show answer and explanation

$150\text{ cm}^2$

$l+w=25$ and $l-w=5$ . Adding gives $l=15$ cm, so $w=10$ cm. The area is $15\times10=150\text{ cm}^2$ .

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

Two kilograms of apples and three kilograms of oranges cost ₹310. Three kilograms of apples and two kilograms of oranges cost ₹340. What is the price per kilogram of apples?

₹90

₹80

₹50

₹60

Show answer and explanation

₹80

Let prices per kilogram be $a,o$ . The equations are $2a+3o=310$ and $3a+2o=340$ . Multiply by 2 and 3 respectively to get $4a+6o=620$ and $9a+6o=1020$ . Hence $5a=400$ , so $a=80$ .

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

A boat travels at 15 km/h downstream and 9 km/h upstream. Assuming constant boat and current speeds, what is the speed of the current?

9 km/h

12 km/h

3 km/h

6 km/h

Show answer and explanation

3 km/h

Let the speed in still water be $b$ and current speed be $c$ . Then $b+c=15$ and $b-c=9$ . Subtraction gives $2c=6$ , hence $c=3$ km/h.

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

A positive fraction has numerator 3 less than its denominator. Their sum is 11. What is the fraction?

$\frac74$

$\frac38$

$\frac56$

$\frac47$

Show answer and explanation

$\frac47$

Let numerator be $n$ and denominator be $d$ . Then $d-n=3$ and $n+d=11$ . These give $d=7,n=4$ , so the fraction is $4/7$ .

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

Solve $5x+2y=12$ and $3x-2y=4$ .

$x=2,\ y=1$

$x=1,\ y=2$

$x=2,\ y=-1$

$x=3,\ y=-2$

Show answer and explanation

$x=2,\ y=1$

Adding the equations eliminates $y$ : $8x=16$ , so $x=2$ . Then $10+2y=12$ , giving $y=1$ .

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

For which value of m is the pair $mx+y=4$ and $x-y=2$ inconsistent?

-1

Show answer and explanation

-1

For $m=-1$ , the first equation becomes $-x+y=4$ , or $x-y=-4$ , which contradicts $x-y=2$ . For other m the coefficient determinant $-m-1$ is nonzero.

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

If $(x,y)=(2,3)$ satisfies $x+ky=11$ , what is k?

Show answer and explanation

Substitute $x=2,y=3$ : $2+3k=11$ . Thus $3k=9$ and $k=3$ .

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

For $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ , with nonzero $a_2,b_2,c_2$ , which condition guarantees a unique solution?

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$

The two equations are identical

$\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$

Show answer and explanation

$\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$

A unique solution occurs when $a_1b_2-a_2b_1\ne0$ , equivalent to unequal ratios $a_1/a_2$ and $b_1/b_2$ . The lines then intersect at exactly one point.