Class 10 Mathematics Chapter 3: Variations – MCQs -(FBISE)

Short Description:
These MCQs are based on the latest Curriculum of Mathematics for SSC-II (Class 10) provided by the Federal Board of Intermediate and Secondary Education (FBISE). This set of 45 multiple-choice questions covers direct variation, inverse variation, joint variation, combined variation, and application problems. These MCQs are ideal for exam revision and self-assessment before the Class 10 exams.

MCQs – Variations

1. If y varies directly as x and y = 10 when x = 2, then y = ? when x = 5
   A. 25
   B. 20
   C. 15
   D. 10
2. If y varies inversely as x and y = 6 when x = 2, then y when x = 3 is:
   A. 4
   B. 6
   C. 3
   D. 2
3. If y varies directly as x and inversely as z, y = 12 when x = 2, z = 3. Find y when x = 3, z = 2:
   A. 12
   B. 18
   C. 24
   D. 9
4. y varies jointly as x and z. If y = 24 when x = 2, z = 3, find y when x = 3, z = 4:
   A. 48
   B. 54
   C. 72
   D. 36
5. If y varies directly as x² and y = 16 when x = 2, find y when x = 4:
   A. 32
   B. 64
   C. 48
   D. 16
6. If y varies inversely as the square of x and y = 8 when x = 2, find y when x = 4:
   A. 4
   B. 2
   C. 1
   D. 8
7. If y varies directly as x and inversely as z², y = 18 when x = 3, z = 2. Find y when x = 6, z = 3:
   A. 6
   B. 4
   C. 8
   D. 12
8. If y varies jointly as x² and z, and y = 24 when x = 2, z = 3, find y when x = 4, z = 2:
   A. 64
   B. 32
   C. 48
   D. 16
9. If y varies directly as x³, y = 27 when x = 3. Find y when x = 6:
   A. 54
   B. 108
   C. 216
   D. 162
10. If y varies inversely as x and directly as z, y = 12 when x = 2, z = 3. Find y when x = 4, z = 6:
    A. 18
    B. 9
    C. 12
    D. 6
11. If y varies directly as x and y = 5 when x = 10, then y = ? when x = 15
    A. 7.5
    B. 10
    C. 15
    D. 5
12. y varies inversely as x. If y = 9 when x = 3, then x = ? when y = 6:
    A. 4.5
    B. 6
    C. 3
    D. 2
13. y varies directly as x and inversely as z. If y = 10 when x = 2, z = 5, find y when x = 4, z = 10:
    A. 4
    B. 5
    C. 2
    D. 8
14. If y varies jointly as x and z², y = 18 when x = 2, z = 3, find y when x = 3, z = 4:
    A. 32
    B. 64
    C. 48
    D. 72
15. If y varies inversely as x², y = 12 when x = 2, find y when x = 4:
    A. 6
    B. 3
    C. 12
    D. 8
16. If y varies directly as x and inversely as z, y = 20 when x = 4, z = 2, find y when x = 5, z = 5:
    A. 10
    B. 8
    C. 5
    D. 4
17. y varies directly as x² and inversely as z. If y = 18 when x = 3, z = 2, find y when x = 6, z = 3:
    A. 36
    B. 54
    C. 72
    D. 48
18. If y varies directly as x³ and inversely as z, y = 24 when x = 2, z = 3. Find y when x = 4, z = 6:
    A. 32
    B. 64
    C. 48
    D. 16
19. If y varies jointly as x, z, and w, y = 36 when x = 2, z = 3, w = 2. Find y when x = 3, z = 2, w = 4:
    A. 36
    B. 48
    C. 72
    D. 54
20. If y varies inversely as x and y = 10 when x = 5, find x when y = 2:
    A. 25
    B. 20
    C. 15
    D. 10
21. y varies directly as x and inversely as z². If y = 8 when x = 2, z = 1, find y when x = 4, z = 2:
    A. 2
    B. 4
    C. 8
    D. 16
22. If y varies jointly as x² and z³, y = 16 when x = 2, z = 2. Find y when x = 4, z = 4:
    A. 128
    B. 256
    C. 512
    D. 64
23. If y varies directly as x and inversely as z, y = 12 when x = 6, z = 3. Find y when x = 4, z = 2:
    A. 12
    B. 16
    C. 8
    D. 18
24. If y varies inversely as x², y = 9 when x = 3, find y when x = 6:
    A. 9/4
    B. 3/2
    C. 12
    D. 4.5
25. y varies directly as x² and inversely as z. If y = 8 when x = 2, z = 4, find y when x = 4, z = 2:
    A. 16
    B. 32
    C. 24
    D. 8
26. If y varies jointly as x², z, and w, y = 18 when x = 1, z = 2, w = 3. Find y when x = 2, z = 3, w = 2:
    A. 24
    B. 36
    C. 48
    D. 72
27. If y varies inversely as x and directly as z², y = 8 when x = 2, z = 2. Find y when x = 4, z = 4:
    A. 16
    B. 32
    C. 8
    D. 64
28. y varies directly as x³ and inversely as z². If y = 9 when x = 1, z = 3, find y when x = 3, z = 1:
    A. 81
    B. 27
    C. 9
    D. 36
29. y varies jointly as x, z², and w³. If y = 24 when x = 2, z = 1, w = 2, find y when x = 4, z = 2, w = 1:
    A. 48
    B. 36
    C. 24
    D. 72
30. y varies inversely as x² and directly as z. If y = 16 when x = 2, z = 4, find y when x = 4, z = 8:
    A. 16
    B. 8
    C. 4
    D. 2
31. If y varies directly as x and inversely as z, y = 10 when x = 5, z = 2. Find y when x = 10, z = 4:
    A. 10
    B. 5
    C. 2.5
    D. 20
32. y varies directly as x² and inversely as z³. If y = 27 when x = 3, z = 1, find y when x = 6, z = 2:
    A. 54
    B. 27
    C. 81
    D. 12
33. y varies jointly as x, z², w³. If y = 8 when x = 1, z = 2, w = 1, find y when x = 2, z = 1, w = 2:
    A. 8
    B. 16
    C. 4
    D. 2
34. y varies inversely as x and y = 12 when x = 3. Find y when x = 6:
    A. 6
    B. 4
    C. 8
    D. 2
35. If y varies directly as x² and y = 16 when x = 2, find y when x = 4:
    A. 32
    B. 64
    C. 48
    D. 24
36. y varies inversely as x² and y = 18 when x = 3. Find y when x = 6:
    A. 4.5
    B. 9
    C. 3
    D. 2
37. y varies directly as x³ and inversely as z. If y = 8 when x = 2, z = 1, find y when x = 4, z = 2:
    A. 16
    B. 32
    C. 64
    D. 8
38. y varies jointly as x², z, and w. If y = 12 when x = 2, z = 1, w = 3, find y when x = 4, z = 2, w = 1:
    A. 16
    B. 32
    C. 48
    D. 24
39. y varies inversely as x² and directly as z². If y = 9 when x = 3, z = 2, find y when x = 6, z = 4:
    A. 9
    B. 8
    C. 4
    D. 2
40. y varies directly as x² and inversely as z. If y = 12 when x = 3, z = 2, find y when x = 6, z = 3:
    A. 24
    B. 36
    C. 48
    D. 12
41. y varies jointly as x² and z². If y = 8 when x = 1, z = 2, find y when x = 2, z = 1:
    A. 2
    B. 4
    C. 8
    D. 16
42. If y varies directly as x and inversely as z, y = 15 when x = 5, z = 3. Find y when x = 3, z = 5:
    A. 9
    B. 5
    C. 6
    D. 3
43. y varies inversely as x³. If y = 8 when x = 2, find y when x = 4:
    A. 1
    B. 2
    C. 4
    D. 1
44. y varies directly as x² and inversely as z. If y = 18 when x = 3, z = 2, find y when x = 6, z = 3:
    A. 24
    B. 36
    C. 48
    D. 12
45. y varies jointly as x and z. If y = 12 when x = 2, z = 3, find y when x = 4, z = 6:
    A. 48
    B. 24
    C. 12
    D. 36

Answers – List Form

1. B
2. A
3. C
4. C
5. B
6. B
7. B
8. C
9. C
10. B
11. A
12. A
13. C
14. D
15. B
16. B
17. B
18. D
19. C
20. A
21. B
22. B
23. B
24. A
25. B
26. B
27. B
28. A
29. B
30. B
31. B
32. B
33. B
34. A
35. B
36. A
37. B
38. C
39. C
40. B
41. B
42. A
43. D
44. B
45. B