MCQs for Class 10 Maths Chapter 4 Quadratic Equations.
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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.
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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 + 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
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 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
Answer: (c) p = 16
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
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 x2-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 p2x2 – 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 x2 (a2 + b2) + 2x (ac + bd) + c2 +d2 = 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 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
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 ax2 + 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 x2 – 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 4x2-2x+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 9x2 – 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 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
Answer: (c)1/10 and 1/10
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
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 2x2 + 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 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
Answer: (a)42 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
Answer: (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
Answer:(a) q2/4p
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 9x2 + 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 2x2 -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 b2 – 4ac for equation 3x2 – 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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