# MCQs for Class 10 Maths Chapter 4 Quadratic Equations.

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# MCQs for Class 10 Maths Chapter 4 Quadratic Equations.

**Maths Chapter 4**

**Quadratic Equations**

**MCQ**

1. Which of the following is not a quadratic equation

(a) x² + 3x – 5 = 0

(b) x² + x^{3} + 2 = 0

(c) 3 + x + x² = 0

(d) x² – 9 = 0

Answer: (b) x² + x^{3} + 2 = 0

2. The roots of 100x^{2} – 20x + 1 = 0 is:

(a)1/20 and 1/20

(b)1/10 and 1/20

(c)1/10 and 1/10

(d)None of the above

Answer: (c)1/10 and 1/10

3. Which constant should be added and subtracted to solve the quadratic equation 4×2 − √3x + 5 = 0 by the method of completing the square?

(a) 9/16

(b) 3/16

(c) 3/4

(d) √3/4

Answer: (b) 3/16

4.Values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is

(a) 0 only

(b) 4

(c) 8 only

(d) 0, 8

Answer: (d) 0, 8

5. Positive value of p for which equation x^{2} + px + 64 = 0 and x^{2} – 8x + p = 0 will both have real roots will be

(a) p ≥ 16

(b) p ≤ 16

(c) p = 16

(d) none of these

Answer: (c) p = 16

6. The quadratic equation 2x^{2} – 3x + 5 = 0 has

(a) Real and distinct roots

(b) Real and equal roots

(c) Imaginary roots

(d) All of the above

Answer: (c) Imaginary roots

7. The quadratic equation 2x² – √5x + 1 = 0 has

(a) two distinct real roots

(b) two equal real roots

(c) no real roots

(d) more than 2 real roots

Answer: (c) no real roots

8. The cubic equation has degree

(a) 1

(b) 2

(c) 3

(d) 4

Answer: (c) 3

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9. If ½ is a root of the quadratic equation x^{2}-mx-5/4=0, then value of m is:

(a)2

(b)-2

(c)-3

(d)3

Answer: (b)-2

10. A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

(a) 3

(b) 8

(c) 4

(d) 7

Answer: (b) 8

11. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, the other two sides of the triangle are equal to:

(a)Base=10cm and Altitiude=5cm

(b)Base=12cm and Altitude=5cm

(c)Base=14cm and Altitude=10cm

(d)Base=12cm and Altitude=10cm

Answer: (b)Base=12cm and Altitude=5cm

12. If p^{2}x^{2} – q2 = 0, then x =?

(a) ± q/p

(b) ±p/q

(c) p

(d) q

Answer:(a)± q/p

13. If 7th and 13th term of an A.P. are 34 and 64 respectively, then its 18th term is

(a) 87

(b) 88

(c) 89

(d) 90

Answer:(c) 89

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14. Which constant must be added and subtracted to solve the quadratic equation 9x² + 34 x – √2 = 0 by the method of completing the square?

(a) 18

(b) 164

(c) 14

(d) 964

Answer: (b) 164

15. If x^{2} (a^{2} + b^{2}) + 2x (ac + bd) + c^{2 }+d^{2} = 0 has no real roots, then

(a) ad≠bc

(b) ad<bc

(c) ad>bc

(d) all of these

Answer: (d) all of these

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16. Which of the following equations has no real roots?

(a) x² – 4x + 3√2 = 0

(b) x² + 4x – 3√2 = 0

(c) x² – 4x – 3√2 = 0

(d) 3x² + 4√3 +4 = 0

Answer: (a) x² – 4x + 3√2 = 0

17. A bi-quadratic equation has degree

(a) 1

(b) 2

(c) 3

(d) 4

Answer: (d) 4

18. The sum of the reciprocals of Rehman’s ages 3 years ago and 5 years from now is 1/3. The present age of Rehman is:

(a)7

(b)10

(c)5

(d)6

Answer: (a)7

19. The polynomial equation x (x + 1) + 8 = (x + 2) {x – 2) is

(a) linear equation

(b) quadratic equation

(c) cubic equation

(d) bi-quadratic equation

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Answer: (a) linear equation

20. Two candidates attempt to solve a quadratic equation of the form x^{2} + px + q = 0. One starts with a wrong value of p and finds the roots to be 2 and 6. The other starts with a wrong value of q and finds the roots to be 2 and – 9. Find the correct roots of the equation :

(a) 3, 4

(b) – 3, – 4

(c) 3, – 4

(d) – 3, 4

Answer: (b) – 3, – 4

21. If the equation x^{2} – kx + 1, have no real roots, then

(a) –2 < k < 2

(b) –3 < k < 3

(c) k > 2

(d) k < –2

Answer:(a) –2 < k < 2

22. Values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is

(a) 0 only

(b) 4

(c) 8 only

(d) 0, 8

Answer: (d) 0, 8

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23. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

(a)30 km/hr

(b)40 km/hr

(c)50 km/hr

(d)60 km/hr

Answer: (b)40 km/hr

24. Value of D when root of ax^{2} + bx + c = 0 are real and unequal will be

(a) D ≥ 0

(b) D > 0

(c) D < 0

(d) D = 0

Answer:(b) D > 0

25. Roots of quadratic equation x^{2} – 3x = 0 , will be

(a) 3

(b) 0, –3

(c) 0, 3

(d) none of these

Answer: (c) 0, 3

26. If one root of equation 4x^{2}-2x+k-4=0 is reciprocal of other. The value of k is:

(a)-8

(b)8

(c)-4

(d)4

Answer: (b)8

27. Rohini had scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?

(a) 14

(b) 16

(c) 15

(d) 18

Answer: (c) 15

28. The equation (x – 2)2 + 1 = 2x – 3 is a

(a) linear equation

(b) quadratic equation

(c) cubic equation

(d) bi-quadratic equation

Answer: (b) quadratic equation

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29. The roots of the equation 9x^{2} – bx + 81 = 0 will be equal, if the value of b is

(a) ± 9

(b) ± 18

(c) ± 27

(d) ± 54

Answer: (d) ± 54

30. The sum of the reciprocals of Rehman’s ages 3 years ago and 5 years from now is 1/3. The present age of Rehman is:

(a)7

(b)10

(c)5

(d)6

Answer: (a)7

31. If 12 is a root of the equation x² + kx – 5/4 = 0 then the value of k is

(a) 2

(b) -2

(c) 1/4

(d) 1/2

Answer: (a) 2

32. Every quadratic polynomial can have at most

(a) three zeros

(b) one zero

(c) two zeros

(d) none of these

Answer: (c) two zeros

33. Satvik observed that in a clock, the time needed by the minute hand of a clock to show 3 PM was found to be 3 min less than t2/4 minutes at t minutes past 2 PM. Then t is equal to

(a) 14

(b) 15

(c) 16

(d) None of these

Answer: (a) 14

34. The equation (x – 2)² + 1 = 2x – 3 is a

(a) linear equation

(b) quadratic equation

(c) cubic equation

(d) bi-quadratic equation

Answer: (b) quadratic equation

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35. The roots of 100x^{2} – 20x + 1 = 0 is:

(a)1/20 and 1/20

(b)1/10 and 1/20

(c)1/10 and 1/10

(d)None of the above

Answer: (c)1/10 and 1/10

36. The quadratic equation whose one rational root is 3 + √2 is

(a) x^{2} – 7x + 5 = 0

(b) x^{2} + 7x + 6 = 0

(c) x^{2} – 7x + 6 = 0

(d) x^{2} – 6x + 7 = 0

Answer: (d) x^{2} – 6x + 7 = 0

37. For ax^{2} + bx + c = 0, which of the following statement is wrong?

(a) If b2 – 4ac is a perfect square, the roots are rational.

(b) If b2 = 4ac , the roots are real and equal.

(c) If b2 – 4ac is negative, no real roots exist.

(d) If b2 = 4ac , the roots are real and unequal.

Answer: (d) If b2 = 4ac , the roots are real and unequal.

38. Which of the following is not a quadratic equation?

(a) 2(x – 1)² = 4x² – 2x + 1

(b) 2x – x² = x² + 5

(c) (√2x + √3)² + x² = 3x² – 5x

(d) (x² + 2x)² = x4 + 3 + 4x³

Answer: (c) (√2x + √3)² + x² = 3x² – 5x

39. Which of the following is a quadratic equation?

(a) x² + 2x+ 1 = (4 – x)² + 3

(b) -2x² = (5 – x)[2x – 25]

(c) (k + 1)x² + 32 x = 7, where k = -1

(d) x³ – x² = (x – 1)³

Answer: (d) x³ – x² = (x – 1)³

40. A takes 6 days less than B to finish a piece of work. If both A and B together can finish the work in 4 days, find the time taken by B to finish the work.

(a)12 days

(b) 12 ½ Days

(c) 13 days

(d) 15days

Answer: (a)12 days

41. Which of the following has the sum of its roots as 3?

(а) 2x² – 3x + 6 = 0

(b) -x² + 3x + 3 = 0

(c) √2x² – 3√2x + 1 = 0

(d) 3x² – 3x + 3 = 0

Answer: (b) -x² + 3x + 3 = 0

42. The roots of quadratic equation 2x^{2} + x + 4 = 0 are:

(a)Positive and negative

(b)Both Positive

(c)Both Negative

(d)No real roots

Answer: (d)no real roots

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43. Which of the following equations has two distinct real roots?

(a) 2x² – 3√2x + 94 = 0

(b) x² + x – 5 = 0

(c) x² + 3x + 2√2 = 0

(d) 5x² – 3x + 1 = 0

Answer: (b) x² + x – 5 = 0

44. Reduction of a rupee in the price of onion makes the possibility of buying one more kg of onion for Rs.56. Find the original price of the onion per kg?

(a) 7

(b) 1

(c) 7, -8

(d) 8

Answer: (d) 8

45. (x² + 1)² – x² = 0 has

(a) four real roots

(b) two real roots

(c) no real roots

(d) one real roots

Answer: (c) no real roots

46. If p = 1 and q = –2 are roots of equation x^{2} – px + q = 0 , then quadratic equation will be

(a) x^{2} + 2x –1= 0

(b) x^{2} – x – 2 = 0

(c) x^{2} – 2x + 1= 0

(d) x^{2} + x + 2 = 0

Answer:(b) x2 – x – 2 = 0

47. A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?

(a) 42 km/hr

(b) 44 km/hr

(c) 46 km/hr

(d) 48 km/hr

Answer: (a)42 km/hr

48. The equation 2x^{2} + kx + 3 = 0 has two equal roots, then the value of k is

(a) ±√6

(b) ± 4

(c) ±3√2

(d) ±2√6

Answer: (d) ±2√6

49. If px^{2} + qx + r = 0 has equal roots, value of r will be

(a) q^{2}/4p

(b) -q^{2}/4p

(c) 4p/q^{2}

(d) none

Answer:(a) q^{2}/4p

50. Which constant must be added and subtracted to solve the quadratic equation 9x² + 34 x – √2 = 0 by the method of completing the square?

(a) 1/8

(b) 1/64

(c) 1/4

(d) 9/64

Answer: (b) 1/64

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51. The sum of two numbers is 27 and product is 182. The numbers are:

(a)12 and 13

(b)13 and 14

(c)12 and 15

(d)13 and 24

Answer: (b)13 and 14

52. Which of the following are the roots of the quadratic equation, x2 – 9x + 20 = 0 by factorisation?

(a) 3,4

(b) 4, 5

(c) 5, 6

(d) 6, 7

Answer: (b) 4, 5

53. If equation 9x^{2} + 6px + 4 = 0 has equal roots, then both roots are equal to

(a) ^{+}-⅔

(b) ^{+}-3

(c) ^{+}-3/2

(d) 0

Answer: a) +-⅔

54. The cubic equation has degree

(a) 1

(b) 2

(c) 3

(d) 4

Answer: (c) 3

55. Find the two consecutive odd positive integers, sum of whose square is 290

(a) 15, 17

(b) 9, 11

(c) 13, 15

(d) 11, 13

Answer: (d) 11, 13

56. The sum of the roots of the quadratic equation 3×2 – 9x + 5 = 0 is

(a) 3

(b) 6

(c) -3

(d) 2

Answer: (c) -3

57. Value(s) of k for which the quadratic equation 2x^{2} -kx + k = 0 has equal roots is

(a) 0

(b) 4

(c) 8

(d) 0 and 8

Answer: (d) 0 and 8

58. The value of b^{2} – 4ac for equation 3x^{2 }– 7x – 2 = 0 is

(a) 49

(b) 0

(c) 25

(d) 73

Answer: (d) 73

59. The roots of the equation (b – c) x2 + (c – a) x + (a – b) = 0 are equal, then

(a) 2a = b + c

(b) 2c = a + b

(c) b = a + c

(d) 2b = a + c

Answer: (d) 2b = a + c

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60.The equation x2 – px + q = 0 p, q ε R has no real roots if :

(a) p2 > 4q

(b) p2 < 4q

(c) p2 = 4q

(d) None of these

Answer: (b) p2 < 4q

61. The value of b2 – 4ac for equation 3×2 – 7x – 2 = 0 is

(a) 49

(b) 0

(c) 25

(d) 73

Answer: (d) 73

62. If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then

(a) P = 0

(b) p = -2

(c) p = ±2

(d) p = 2

Answer: (d) p = 2

63. If -5 is a root of the quadratic equation 2×2 + px – 15 = 0, then

(a) p = 3

(b) p = 5

(c) p = 7

(d) p = 1

Answer: (c) p = 7

64. One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. Their present ages are

(a) 7 years, 49 years

(b) 5 years, 25 years

(c) 1 years, 50 years

(d) 6 years, 49 years

Answer:(a) 7 years, 49 years

65. If (x – a) is one of the factors of the polynomial ax2 + bx + c, then one of the roots of ax² + bx + c = 0 is

(a) 1

(b) c

(c) a

(d) none of these

Answer: (c) a

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