Question 1

1. If a pair of linear equations is consistent, then the lines plotted graphically will be:

A) ParallelB) Always coincidentC) Intersecting or coincidentD) Always intersecting

Answer

✓ Correct Answer: Option C

Question 2

2. The condition for a pair of linear equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to have infinitely many solutions is:

A) $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$B) $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$C) $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$D) $\frac{a_1}{a_2} = \frac{c_1}{c_2} \neq \frac{b_1}{b_2}$

Question 3

3. The pair of equations y = 0 and y = -7 has:

A) One solutionB) Two solutionsC) Infinitely many solutionsD) No solution

Answer

✓ Correct Answer: Option D

Question 4

4. Solve the linear equations: x + y = 14 and x - y = 4.

A) x = 10, y = 4B) x = 9, y = 5C) x = 5, y = 9D) x = 8, y = 6

Answer

✓ Correct Answer: Option B

Question 5

5. For what value of k, does the pair of equations kx + 2y = 5 and 3x + y = 1 have a unique solution?

A) k = 6B) $k \neq 6$C) k = 3D) $k \neq 3$

Answer

✓ Correct Answer: Option B

Question 6

6. The value of k for which the equations 3x - y + 8 = 0 and 6x - ky = -16 represent coincident lines is:

A) 1/2B) -1/2C) 2D) -2

Answer

✓ Correct Answer: Option C

Question 7

7. Graphically, the pair of equations 6x - 3y + 10 = 0 and 2x - y + 9 = 0 represents two lines which are:

A) Intersecting at exactly one pointB) Intersecting at exactly two pointsC) CoincidentD) Parallel

Answer

✓ Correct Answer: Option D

Question 8

8. The difference between two numbers is 26 and one number is three times the other. Find the larger number.

A) 39B) 26C) 13D) 52

Answer

✓ Correct Answer: Option A

Question 9

9. A fraction becomes $\frac{1}{3}$ when 1 is subtracted from the numerator, and it becomes $\frac{1}{4}$ when 8 is added to its denominator. What is the fraction?

A) $\frac{7}{12}$B) $\frac{3}{8}$C) $\frac{5}{12}$D) $\frac{9}{20}$

Answer

✓ Correct Answer: Option C

Question 10

10. Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old is Nuri now?

A) 20 yearsB) 40 yearsC) 50 yearsD) 60 years

Answer

✓ Correct Answer: Option C

Question 11

11. The pair of equations x = a and y = b graphically represents lines which are:

A) ParallelB) Intersecting at (b, a)C) CoincidentD) Intersecting at (a, b)

Answer

✓ Correct Answer: Option D

Question 12

12. If 2x + 3y = 11 and 2x - 4y = -24, find the value of m for which y = mx + 3.

A) 1B) -1C) 2D) -2

Answer

✓ Correct Answer: Option B

Question 13

13. For what value of p, the pair of equations px + 3y = p-3 and 12x + py = p has no solution?

A) 6B) -6C) 12D) -12

Answer

✓ Correct Answer: Option B

Question 14

14. If x = a, y = b is the solution of the equations x - y = 2 and x + y = 4, then the values of a and b are, respectively:

A) 3 and 1B) 4 and 2C) 5 and 3D) -1 and -3

Answer

✓ Correct Answer: Option A

Question 15

15. The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

A) 81B) 27C) 18D) 36

Answer

✓ Correct Answer: Option C

Question 16

16. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

A) Length = 20 m, Width = 16 mB) Length = 22 m, Width = 14 mC) Length = 18 m, Width = 18 mD) Length = 24 m, Width = 12 m

Answer

✓ Correct Answer: Option A

Question 17

17. A boat covers 32 km upstream and 36 km downstream in 7 hours. Also, it covers 40 km upstream and 48 km downstream in 9 hours. What is the speed of the boat in still water?

A) 8 km/hB) 10 km/hC) 12 km/hD) 14 km/h

Answer

✓ Correct Answer: Option B

Question 18

18. Which of the following pairs of linear equations is inconsistent?

A) 2x + y = 6 and 4x - 2y = 4B) x - y = 8 and 3x - 3y = 24C) 2x - 3y = 8 and 4x - 6y = 9D) 3x + 2y = 5 and 2x - 3y = 7

Answer

✓ Correct Answer: Option C

Question 19

19. Graph of the equation x = -2 is a line:

A) Parallel to x-axisB) Parallel to y-axisC) Passing through originD) Intersecting both axes

Answer

✓ Correct Answer: Option B

Question 20

20. Determine the area of the triangle formed by the lines x = 3, y = 4, and x = y.

A) 1 sq. unitB) 2 sq. unitsC) 0.5 sq. unitsD) 1.5 sq. units

Answer

✓ Correct Answer: Option C

Accepted Answer

✓ Correct Answer: Option C

Grade 10 Maths Quiz - Linear Equations

1. If a pair of linear equations is consistent, then the lines plotted graphically will be:

2. The condition for a pair of linear equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to have infinitely many solutions is:

3. The pair of equations y = 0 and y = -7 has:

4. Solve the linear equations: x + y = 14 and x - y = 4.

5. For what value of k, does the pair of equations kx + 2y = 5 and 3x + y = 1 have a unique solution?

6. The value of k for which the equations 3x - y + 8 = 0 and 6x - ky = -16 represent coincident lines is:

7. Graphically, the pair of equations 6x - 3y + 10 = 0 and 2x - y + 9 = 0 represents two lines which are:

8. The difference between two numbers is 26 and one number is three times the other. Find the larger number.

9. A fraction becomes $\frac{1}{3}$ when 1 is subtracted from the numerator, and it becomes $\frac{1}{4}$ when 8 is added to its denominator. What is the fraction?

10. Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old is Nuri now?

11. The pair of equations x = a and y = b graphically represents lines which are:

12. If 2x + 3y = 11 and 2x - 4y = -24, find the value of m for which y = mx + 3.

13. For what value of p, the pair of equations px + 3y = p-3 and 12x + py = p has no solution?

14. If x = a, y = b is the solution of the equations x - y = 2 and x + y = 4, then the values of a and b are, respectively:

15. The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

16. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

17. A boat covers 32 km upstream and 36 km downstream in 7 hours. Also, it covers 40 km upstream and 48 km downstream in 9 hours. What is the speed of the boat in still water?

18. Which of the following pairs of linear equations is inconsistent?

19. Graph of the equation x = -2 is a line:

20. Determine the area of the triangle formed by the lines x = 3, y = 4, and x = y.