# MCQs for Class 10 Maths Chapter 4 Quadratic Equations.

MCQs for Class 10 Maths Chapter 4 Quadratic Equations.: In this article, we have covered all the important MCQs for Free for Class 10 Term 1 2021-22 Board Exams. In accordance with the latest pattern, Padhle is here with MCQ Questions for Class 10.

# MCQs for Class 10 Maths Chapter 4 Quadratic Equations.

Maths Chapter 4

MCQ

1. Which of the following is not a quadratic equation

(a) x² + 3x – 5 = 0

(b) x² + x3 + 2 = 0

(c) 3 + x + x² = 0

(d) x² – 9 = 0

Answer: (b) x² + x3 + 2 = 0

2. The roots of 100x2 – 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

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

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

5. Positive value of p for which equation x2 + px + 64 = 0 and x2 – 8x + p = 0 will both have real roots will be

(a) p ≥ 16

(b) p ≤ 16

(c) p = 16

(d) none of these

6. The quadratic equation 2x2 – 3x + 5 = 0 has​

(a) Real and distinct roots

(b) Real and equal roots

(c) Imaginary roots

(d) All of the above

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

8. The cubic equation has degree

(a) 1

(b) 2

(c) 3

(d) 4

9. If ½ is a root of the quadratic equation x2-mx-5/4=0, then value of m is:

(a)2

(b)-2

(c)-3

(d)3

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

(a) 3

(b) 8

(c) 4

(d) 7

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

12. If p2x2 – q2 = 0, then x =?

(a) ± q/p

(b) ±p/q

(c) p

(d) q

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

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

15.  If x2 (a2 + b2) + 2x (ac + bd) + c2 +d2 = 0 has no real roots, then

(d) all of these

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

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

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

(a) linear equation

(c) cubic equation

20. Two candidates attempt to solve a quadratic equation of the form x2 + 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 x2 – 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

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

24. Value of D when root of ax2 + bx + c = 0 are real and unequal will be

(a) D ≥ 0

(b) D > 0

(c) D < 0

(d) D = 0

25. Roots of quadratic equation x2 – 3x = 0 , will be

(a) 3

(b) 0, –3

(c) 0, 3

(d) none of these

26.  If one root of equation 4x2-2x+k-4=0 is reciprocal of other. The value of k is:

(a)-8

(b)8

(c)-4

(d)4

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

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

(a) linear equation

(c) cubic equation

29. The roots of the equation 9x2 – bx + 81 = 0 will be equal, if the value of b is

(a) ± 9

(b) ± 18

(c) ± 27

(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

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

32. Every quadratic polynomial can have at most

(a) three zeros

(b) one zero

(c) two zeros

(d) none of these

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

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

(a) linear equation

(c) cubic equation

35. The roots of 100x2 – 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

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

(a) x2 – 7x + 5 = 0

(b) x2 + 7x + 6 = 0

(c) x2 – 7x + 6 = 0

(d) x2 – 6x + 7 = 0

Answer: (d) x2 – 6x + 7 = 0

37. For ax2 + 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

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 2x2 + x + 4 = 0 are:

(a)Positive and negative

(b)Both Positive

(c)Both Negative

(d)No real roots

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

45. (x² + 1)² – x² = 0 has

(a) four real roots

(b) two real roots

(c) no real roots

(d) one real roots

46. If p = 1 and q = –2 are roots of equation x2 – px + q = 0 , then quadratic equation will be

(a) x2 + 2x –1= 0

(b) x2 – x – 2 = 0

(c) x2 – 2x + 1= 0

(d) x2 + 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

48. The equation 2x2 + kx + 3 = 0 has two equal roots, then the value of k is

(a) ±√6

(b) ± 4

(c) ±3√2

(d) ±2√6

49.  If px2 + qx + r = 0 has equal roots, value of r will be

(a) q2/4p

(b) -q2/4p

(c) 4p/q2

(d) none

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

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

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

53.  If equation 9x2 + 6px + 4 = 0 has equal roots, then both roots are equal to

(a) +-⅔

(b) +-3

(c) +-3/2

(d) 0

54. The cubic equation has degree

(a) 1

(b) 2

(c) 3

(d) 4

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

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

(a) 3

(b) 6

(c) -3

(d) 2

57.  Value(s) of k for which the quadratic equation 2x2 -kx + k = 0 has equal roots is

(a) 0

(b) 4

(c) 8

(d) 0 and 8

58. The value of b2 – 4ac  for equation 3x2 – 7x – 2 = 0 is

(a) 49

(b) 0

(c) 25

(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

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

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

(a) 49

(b) 0

(c) 25

(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

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

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

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