### Class 10 Maths Chapter 4 Quadratic Equations MCQs

Class 10 Maths MCQs for Chapter 4 (Quadratic Equations) are available online here with answers. All these objective questions are prepared as per the latest CBSE syllabus and NCERT guidelines. MCQs for Class 10 Maths Chapter 4 are prepared according to the new exam pattern. Solving these multiple-choice questions will help students to score good marks in the board exams.

## Class 10 Maths MCQs for Quadratic Equations

1. Equation of (x+1)Â²-xÂ²=0 has number of real roots equal to:

(a) 1

(b) 2

(c) 3

(d) 4

2. The roots of 100xÂ² â€“ 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. 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

4. If Â½ is a root of the quadratic equation xÂ²-mx-5/4=0, then value of m is:

(a) 2

(b) -2

(c) -3

(d) 3

5. 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 Altitude=5cm

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

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

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

6. The roots of quadratic equation 2×2 + x + 4 = 0 are:

(a) Positive and negative

(b) Both Positive

(c) Both Negative

(d) No real roots

7. The sum of the reciprocals of Rehmanâ€™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

8. 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

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

(a) -8

(b) 8

(c) -4

(d) 4

10. Which one of the following is not a quadratic equation?

(a) (x + 2)Â² = 2(x + 3)

(b) xÂ² + 3x = (â€“1) (1 â€“ 3x)Â²

(c) (x + 2) (x â€“ 1) = xÂ² â€“ 2x â€“ 3

(d) xÂ³ â€“ xÂ² + 2x + 1 = (x + 1)Â³

11. Which of the following equations has 2 as a root?

(a) xÂ² â€“ 4x + 5 = 0

(b) xÂ² + 3x â€“ 12 = 0

(c) 2xÂ² â€“ 7x + 6 = 0

(d) 3xÂ² â€“ 6x â€“ 2 = 0

12. A quadratic equation axÂ² + bx + c = 0 has no real roots, if

(a) bÂ² â€“ 4ac > 0

(b) bÂ² â€“ 4ac = 0

(c) bÂ² â€“ 4ac < 0

(d) bÂ² â€“ ac < 0

13. The product of two consecutive positive integers is 360. To find the integers, this can be represented in the form of quadratic equation as

(a) xÂ² + x + 360 = 0

(b) xÂ²+ x â€“ 360 = 0

(c) 2xÂ² + x â€“ 360

(d) xÂ²â€“ 2x â€“ 360 = 0

14. The equation which has the sum of its roots as 3 is

(a) 2xÂ²â€“ 3x + 6 = 0

(b) â€“xÂ² + 3x â€“ 3 = 0

(c) âˆš2xÂ² â€“ 3/âˆš2x + 1 = 0

(d) 3xÂ² â€“ 3x + 3 = 0

15. The quadratic equation 2×2 â€“ âˆš5x + 1 = 0 has

(a) two distinct real roots

(b) two equal real roots

(c) no real roots

(d) more than 2 real roots

16. The equation (x + 1)Â² â€“ 2(x + 1) = 0 has

(a) two real roots

(b) no real roots

(c) one real root

(d) two equal roots

17. The quadratic formula to find the roots of a quadratic equation ax2 + bx + c = 0 is given by

(a) [-b Â± âˆš(bÂ²-ac)]/2a

(b) [-b Â± âˆš(bÂ²-2ac)]/a

(c) [-b Â± âˆš(bÂ²-4ac)]/4a

(d) [-b Â± âˆš(bÂ²-4ac)]/2a

18. The quadratic equation x2 + 7x â€“ 60 has

(a) two equal roots

(b) two real and unequal roots

(b) no real roots

(d) two equal complex roots

19. The maximum number of roots for a quadratic equation is equal to

(a) 1

(b) 2

(c) 3

(d) 4

20. Equation (x+1)Â² â€“ xÂ² = 0 has _____ real root(s).

(A) 1

B) 2

(C) 3

(D) 4

21. Which constant should be added and subtracted to solve the quadratic equation 4×2 âˆ’ âˆš3x + 5 = 0 by the method of completing the square?

(A) 9/16

(B) 3/16

(C) 3/4

(D) âˆš3/4

22. If 1/2 is a root of the equation x2 + kx â€“ (5/4) = 0 then the value of k is

(A) 2

(B) â€“ 2

(C) 3

(D) â€“3

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

(A) 3

(B) 8

(C) 4

(D) 7

### Class 10 Maths Chapter 4 Quadratic Equations MCQs

24. The product of two successive integral multiples of 5 is 300. Then the numbers are:

(A) 25, 30

(B) 10, 15

(C) 30, 35

(D) 15, 20

25. If pÂ²xÂ² â€“ qÂ² = 0, then x =?

(A) Â± q/p

(B) Â±p/q

(C) p

(D) q

26. 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

(D) all of these

27. 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

28. 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 Â½ Days

(C) 13 days

(D) 15days

29. If 12 is a root of the equation xÂ² + kx â€“ 54 = 0 then the value of k is

(a) 2

(b) -2

(c) 1/4

(d) 1/2

30. Values of k for which the quadratic equation 2xÂ² â€“ kx + k = 0 has equal roots is

(a) 0 only

(b) 4

(c) 8 only

(d) 0, 8

31. The quadratic equation 2xÂ² â€“ âˆš5x + 1 = 0 has

(a) two distinct real roots

(b) two equal real roots

(c) no real roots

(d) more than 2 real roots

32. Which constant must be added and subtracted to solve the quadratic equation 9xÂ² + 34 x â€“ âˆš2 = 0 by the method of completing the square?

(a) 1/8

(b) 1/64

(c) 1/4

(d) 9/64

33. (xÂ² + 1)Â² â€“ xÂ² = 0 has

(a) four real roots

(b) two real roots

(c) no real roots

(d) one real roots

34. The quadratic equation has degree

(a) 0

(b) 1

(c) 2

(d) 3

35. The cubic equation has degree

(a) 1

(b) 2

(c) 3

(d) 4

36. A bi-quadratic equation has degree

(a) 1

(b) 2

(c) 3

(d) 4

37. The polynomial equation x (x + 1) + 8 = (x + 2) {x â€“ 2) is

(a) linear equation

(b) quadratic equation

(c) cubic equation

(d) bi-quadratic equation

37. The equation 2xÂ² + kx + 3 = 0 has two equal roots, then the value of k is

(a) Â±âˆš6

(b) Â± 4

(c) Â±3âˆš2

(d) Â±2âˆš6

39. Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are

(a) 9,1

(b) -9,1

(c) 9, -1

(d) -9, -1

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

(a) P = 0

(b) p = -2

(c) p = Â±2

(d) p = 2

41. If one root of the quadratic equation 2xÂ² + kx â€“ 6 = 0 is 2, the value of k is

(a) 1

(b) -1

(c) 2

(d) -2

42 . The roots of the quadratic equation

(a) a, b

(b) -a, b

(c) a, -b

(d) -a, -b

43. If -5 is a root of the quadratic equation 2xÂ² + px â€“ 15 = 0, then

(a) p = 3

(b) p = 5

(c) p = 7

(d) p = 1

44. If the roots of the equations axÂ² + 2bx + c = 0 and bxÂ² â€“ 2âˆšac x + b = 0 are simultaneously real, then

(a) b = ac

(b) bÂ²= ac

(c) aÂ²= be

(d) cÂ²= ab

45. The roots of the equation (b â€“ c) xÂ² + (c â€“ a) x + (a â€“ b) = 0 are equal, then

(a) 2a = b + c

(b) 2c = a + b

(c) b = a + c

(d) 2b = a + c

46. A chess board contains 64 equal squares and the area of each square is 6.25 cmÂ². A border round the board is 2 cm wide. The length of the side of the chess board is

(a) 8 cm

(b) 12 cm

(c) 24 cm

(d) 36 cm

47. One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his sonâ€™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

48. The sum of the squares of two consecutive natural numbers is 313. The numbers are

(a) 12, 13

(b) 13,14

(c) 11,12

(d) 14,15

49. The roots of the equation 7xÂ² + x â€“ 1 = 0 are

(a) real and distinct

(b) real and equal

(c) not real

(d) none of these

50. The equation 12xÂ² + 4kx + 3 = 0 has real and equal roots, if

(a) k = Â±3

(b) k = Â±9

(c) k = 4

(d) k = Â±2

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