SBI PO - Number Series, Quadratic Equations Online Test (MCQ Quiz)

1. Which of the following is NOT a common type of number series found in competitive exams?

A) Arithmetic Progression B) Geometric Progression C) Fibonacci Series D) Harmonic Progression

2. In a quadratic equation ax^2 + bx + c = 0, if the discriminant (b^2 - 4ac) is positive, what can be said about the roots?

A) The roots are real and equal. B) The roots are real and distinct. C) The roots are imaginary. D) There are no real roots.

3. Identify the pattern in the series: 2, 5, 10, 17, 26, ...

A) Add 3, then add 5, then add 7, ... B) Multiply by 2, then add 1, ... C) n^2 + 1, where n starts from 1 D) n^2 - 1, where n starts from 2

4. Consider the quadratic equation x^2 - 5x + 6 = 0. What are the roots of this equation?

A) 2 and 3 B) -2 and -3 C) 1 and 6 D) -1 and -6

5. What is the next number in the series: 3, 7, 15, 31, 63, ...?

A) 94 B) 127 C) 128 D) 150

6. For the quadratic equation 2x^2 + 4x + 2 = 0, what is the nature of the roots?

A) Real and distinct B) Real and equal C) Imaginary D) One real and one imaginary root

7. Find the missing term in the series: 1, 4, 9, 16, __, 36

A) 20 B) 25 C) 30 D) 32

8. If the discriminant (b^2 - 4ac) of a quadratic equation is zero, the roots are:

A) Real and distinct B) Real and equal C) Imaginary D) One positive and one negative

9. What is the next number in the series: 1, 1, 2, 3, 5, 8, ...?

A) 11 B) 13 C) 16 D) 21

10. Consider the quadratic equation x^2 + x + 1 = 0. What is the nature of its roots?

A) Real and distinct B) Real and equal C) Imaginary D) One root is zero

11. Identify the pattern and find the next term: 5, 10, 20, 40, ...

A) 50 B) 60 C) 80 D) 100

12. Solve for x: 3x^2 - 12x + 9 = 0

A) 1 and 3 B) -1 and -3 C) 1 and -3 D) -1 and 3

13. What is the next number in the series: 10, 20, 30, 40, ...?

A) 45 B) 50 C) 60 D) 70

14. In the quadratic equation ax^2 + bx + c = 0, if b^2 - 4ac < 0, the roots are:

A) Real and distinct B) Real and equal C) Imaginary D) One positive, one negative

15. Find the missing term: 2, 6, 12, 20, __, 42

A) 28 B) 30 C) 32 D) 36

16. Consider the quadratic equation y^2 - 9 = 0. What are the values of y?

A) 3 B) -3 C) 3 and -3 D) 9

17. What is the next term in the series: 100, 90, 80, 70, ...?

A) 60 B) 65 C) 50 D) 75

18. If one root of the quadratic equation x^2 - 7x + k = 0 is 3, what is the value of k?

A) 10 B) 12 C) 15 D) 18

19. Find the next number in the series: 1, 3, 6, 10, 15, ...

A) 18 B) 20 C) 21 D) 24

20. For the quadratic equation 4x^2 - 12x + 9 = 0, the roots are:

A) Real and distinct B) Real and equal C) Imaginary D) Zero

21. What is the missing term in the series: 7, 14, 21, 28, __, 42?

A) 30 B) 32 C) 35 D) 36

22. Consider the quadratic equation 2x^2 + 5x - 3 = 0. What are the roots?

A) 1/2 and -3 B) -1/2 and 3 C) 1/2 and 3 D) -1/2 and -3

23. Find the next number in the series: 1, 5, 14, 30, 55, ...

A) 80 B) 85 C) 91 D) 100

24. If the sum of the roots of the quadratic equation ax^2 + bx + c = 0 is 5 and the product of the roots is 6, what is the equation?

A) x^2 + 5x + 6 = 0 B) x^2 - 5x + 6 = 0 C) x^2 + 6x + 5 = 0 D) x^2 - 6x + 5 = 0

25. What is the next term in the series: 4, 16, 36, 64, ...?

A) 81 B) 100 C) 121 D) 144

26. Consider the quadratic equation 3x^2 - 2x - 1 = 0. What are the roots?

A) 1 and -1/3 B) -1 and 1/3 C) 1 and 1/3 D) -1 and -1/3

27. Find the missing number: 10, 15, 25, 40, 65, ...

A) 90 B) 100 C) 105 D) 110

28. If the roots of the quadratic equation x^2 - 10x + k = 0 are real and equal, what is the value of k?

A) 20 B) 25 C) 30 D) 35

29. What is the next number in the series: 1, 8, 27, 64, ...?

A) 100 B) 125 C) 150 D) 216

30. Consider the quadratic equation 5x^2 + 2x + 1 = 0. What is the nature of the roots?

A) Real and distinct B) Real and equal C) Imaginary D) One positive, one negative

31. Find the missing term in the series: 3, 4, 7, 11, 18, ...

A) 25 B) 29 C) 30 D) 32

32. If one root of the quadratic equation x^2 - 5x + c = 0 is 2, what is the other root?

A) 1 B) 3 C) 4 D) 5

33. What is the next number in the series: 15, 18, 21, 24, ...?

A) 25 B) 26 C) 27 D) 28

34. For the quadratic equation 9x^2 - 6x + 1 = 0, the roots are:

A) Real and distinct B) Real and equal C) Imaginary D) Zero

35. Find the missing term in the series: 1, 2, 4, 8, __, 32

A) 12 B) 16 C) 20 D) 24

36. Consider the quadratic equation 4x^2 - 7x + 3 = 0. What are the roots?

A) 1 and 3/4 B) -1 and -3/4 C) 1 and -3/4 D) -1 and 3/4

37. What is the next number in the series: 6, 12, 20, 30, 42, ...?

A) 50 B) 54 C) 56 D) 60

38. If the sum of the roots of the quadratic equation 2x^2 + bx + 8 = 0 is 4, what is the value of b?

A) -8 B) 8 C) -4 D) 4

39. Find the missing term: 0, 1, 3, 7, 15, ...

A) 20 B) 23 C) 31 D) 35

40. Consider the quadratic equation x^2 + 6x + 9 = 0. What are the roots?

A) 3 and 3 B) -3 and -3 C) 3 and -3 D) 9

41. What is the next number in the series: 5, 25, 125, 625, ...?

A) 1125 B) 3125 C) 15625 D) 78125

42. If one root of the quadratic equation x^2 + kx - 10 = 0 is 2, what is the value of k?

A) -3 B) 3 C) -5 D) 5

43. Find the missing term in the series: 2, 3, 5, 7, 11, __

A) 13 B) 15 C) 17 D) 19

44. For the quadratic equation x^2 - 4 = 0, the roots are:

A) 2 B) -2 C) 2 and -2 D) 4

45. What is the next number in the series: 10, 12, 16, 22, 30, ...?

A) 38 B) 40 C) 42 D) 44

46. If the product of the roots of the quadratic equation 3x^2 - 15x + c = 0 is 5, what is the value of c?

A) 5 B) 10 C) 15 D) 20

47. Find the missing term in the series: 1, 1, 4, 8, 16, ...

A) 20 B) 24 C) 32 D) 64

48. Consider the quadratic equation 2x^2 - 5x + 2 = 0. What are the roots?

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

49. What is the next number in the series: 8, 12, 18, 27, ...?

A) 36 B) 38.5 C) 40.5 D) 42

50. If one root of the quadratic equation x^2 - ax + 12 = 0 is 3, what is the value of 'a'?

A) 4 B) 5 C) 6 D) 7

Number Series, Quadratic Equations - Online Test

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