MCQ Questions for Class 10 Maths Quadratic Equations with Answers

MCQ Questions for Class 10 Maths Quadratic Equations with Answers

Free PDF Download of CBSE Class 10 Maths Chapter 4 Quadratic Equations Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Quadratic Equations MCQs with Answers to know their preparation level.

Class 10 Maths MCQs Chapter 4 Quadratic Equations

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/Explanation

Answer: b
Explaination:Reason: Since it has degree 3.


2. The quadratic equation has degree
(a) 0
(b) 1
(c) 2
(d) 3

Answer/Explanation

Answer: c
Explaination:Reason: A quadratic equation has degree 2.


3. The cubic equation has degree
(a) 1
(b) 2
(c) 3
(d) 4

Answer/Explanation

Answer: c
Explaination:Reason: A cubic equation has degree 3.


4. A bi-quadratic equation has degree
(a) 1
(b) 2
(c) 3
(d) 4

Answer/Explanation

Answer: d
Explaination:Reason: A bi-quadratic equation has degree 4.


5. 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

Answer/Explanation

Answer: a
Explaination:Reason: We have x(x + 1) + 8 = (x + 2) (x - 2)
⇒ x² + x + 8 = x² - 4
⇒ x² + x + 8- x² + 4 = 0
⇒ x + 12 = 0, which is a linear equation.


6. The equation (x - 2)² + 1 = 2x - 3 is a
(a) linear equation
(b) quadratic equation
(c) cubic equation
(d) bi-quadratic equation

Answer/Explanation

Answer: b
Explaination:Reason: We have (x - 2)² + 1 = 2x - 3
⇒ x² + 4 - 2 × x × 2 + 1 = 2x - 3
⇒ x² - 4x + 5 - 2x + 3 = 0
∴ x² - 6x + 8 = 0, which is a quadratic equation.


9. 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/Explanation

Answer: d
Explaination:Reason: ∵ one root is 3 + √2
∴ other root is 3 - √2
∴ Sum of roots = 3 + √2 + 3 - √2 = 6
Product of roots = (3 + √2)(3 - √2) = (3)² - (√2)² = 9 - 2 = 7
∴ Required quadratic equation is x² - 6x + 7 = 0


10. 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/Explanation

Answer: d
Explaination:Reason: Here a = 2, b = k, c = 3
Since the equation has two equal roots
∴ b² - 4AC = 0
⇒ (k)² - 4 × 2 × 3 = 0
⇒ k² = 24
⇒ k = ± √24
∴ k= ± \pm \sqrt{4 \times 6} = ± 2√6


13. The sum of the roots of the quadratic equation 3×2 - 9x + 5 = 0 is
(a) 3
(b) 6
(c) -3
(d) 2

Answer/Explanation

Answer: c
Explaination:Reason: Here a = 3, b = -9, c = 5
∴ Sum of the roots =\frac{-b}{a}=-\frac{(-9)}{3}=3


17. If a, p are the roots of the equation (x - a) (x - b) + c = 0, then the roots of the equation (x - a) (x - P) = c are
(a) a, b
(b) a, c
(c) b, c
(d) none of these

Answer/Explanation

Answer: a
Explaination:Reason: By given condition, (x - a) (x - b) + c = (x - α) (x - β)
⇒ (x - α) (x - β) - c = (x - a) (x - b)
This shows that roots of (x - α) (x - β) - c are a and b


18. 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

Answer/Explanation

Answer: a
Explaination:Reason: Correct sum = 8 + 2 = 10 from Mohan
Correct product = -9 x -1 = 9 from Sohan
∴ x² - (10)x + 9 = 0
⇒ x² - 10x + 9 = 0
⇒ x² - 9x - x + 9
⇒ x(x - 9) - 1(x - 9) = 0
⇒ (x-9) (x-l) = 0 .
⇒ Correct roots are 9 and 1.


19. If a and p are the roots of the equation 2x² - 3x - 6 = 0. The equation whose roots are \frac{1}{\alpha} and \frac{1}{\beta} is
(a) 6x² - 3x + 2 = 0
(b) 6x² + 3x - 2 = 0
(c) 6x² - 3x - 2 = 0
(d) x² + 3x-2 = 0

Answer/Explanation

Answer: b
Explaination:
MCQ Questions for Class 10 Maths Quadratic Equations with Answers 11


20. 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/Explanation

Answer: d
Explaination:Reason: here α = \frac{1}{β}
∴ αβ = 1
⇒ \frac{2}{p} = 1
∴ p = 2


21. If one root of the quadratic equation 2x² + kx - 6 = 0 is 2, the value of k is
(a) 1
(b) -1
(c) 2
(d) -2

Answer/Explanation

Answer: b
Explaination:Reason: Scice x = 2 is a root of the equation 2x² + kx -6 = 0
∴ 2(2)² +k(2) - 6 = 0
⇒ 8 + 2k - 6 = 0
⇒ 2k = -2
∴ k = -1


22. The roots of the quadratic equation
MCQ Questions for Class 10 Maths Quadratic Equations with Answers 6
(a) a, b
(b) -a, b
(c) a, -b
(d) -a, -b

Answer/Explanation

Answer: d
Explaination:
MCQ Questions for Class 10 Maths Quadratic Equations with Answers 12


23. The roots of the equation 7x² + x - 1 = 0 are
(a) real and distinct
(b) real and equal
(c) not real
(d) none of these

Answer/Explanation

Answer: a
Explaination:Reason: Here a = 2, b = 1, c = -1
∴ D = b² - 4ac = (1)² - 4 × 2 × (-1) = 1 + 8 = 9 > 0
∴ Roots of the given equation are real and distinct.


24. The equation 12x² + 4kx + 3 = 0 has real and equal roots, if
(a) k = ±3
(b) k = ±9
(c) k = 4
(d) k = ±2

Answer/Explanation

Answer: a
Explaination:Reason: Here a = 12, b = 4k, c = 3
Since the given equation has real and equal roots
∴ b² - 4ac = 0
⇒ (4k)² - 4 × 12 × 3 = 0
⇒ 16k² - 144 = 0
⇒ k² = 9
⇒ k = ±3


25. If -5 is a root of the quadratic equation 2x² + px - 15 = 0, then
(a) p = 3
(b) p = 5
(c) p = 7
(d) p = 1

Answer/Explanation

Answer: c
Explaination:Reason: Since - 5 is a root of the equation 2x² + px -15 = 0
∴ 2(-5)² + p (-5) - 15 = 0
⇒ 50 - 5p -15 = 0
⇒ 5p = 35
⇒ p = 7


26. If the roots of the equations ax² + 2bx + c = 0 and bx² - 2√ac x + b = 0 are simultaneously real, then
(a) b = ac
(b) b2 = ac
(c) a2 = be
(d) c2 = ab

Answer/Explanation

Answer: b
Explaination:Reason: Given equations have real roots, then
D1 ≥ 0 and D2 ≥ 0
(2b)² - 4ac > 0 and (-2√ac)² - 4b.b ≥ 0
4b² - 4ac ≥ 0 and 4ac - 4b2 > 0
b² ≥ ac and ac ≥ b²
⇒ b² = ac


27. 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/Explanation

Answer: d
Explaination:Reason: Since roots are equal
∴ D = 0 => b² - 4ac = 0
⇒ (c - a)² -4(b - c) (a - b) = 0
⇒ c² - b² - 2ac -4(ab -b² + bc) = 0 =>c + a-2b = 0 => c + a = 2b
⇒ c² + a² - 2ca - 4ab + 4b² + 4ac - 4bc = 0
⇒ c² + a² + 4b² + 2ca - 4ab - 4bc = 0
⇒ (c + a - 2b)² = 0
⇒ c + a - 2b = 0
⇒ c + a = 2b


28. A chess board contains 64 equal squares and the area of each square is 6.25 cm². 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

Answer

Answer: c


29. 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

Answer: a


30. 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

Answer

Answer: a


31. Which of the following is not a quadratic equation? [NCERT Exemplar Problems]
(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/Explanation

Answer: c
Explaination:
2x² + 3 + 2√6 x + x² = 3x² - 5x
2√6x + 5x + 3 = 0


32. 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/Explanation

Answer: c
Explaination:
∵ x - a is one of the factors one root = a.


33. 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, 1

Answer/Explanation

Answer: b
Explaination:
Given equation is x² - 9x + 20 = 0
⇒ x² - 5x - 4x + 20 = 0
⇒ x(x - 5) - 4(x - 5) = 0
⇒ (x - 5) (x - 4) = 0
⇒ either x - 5 = 0 and x - 4 = 0
⇒ x = 5 and x = 4
∴ x = 4 and 5 are the roots/solution of the given quadratic equation.


34. If (1 - p) is a root of the equation x² + px + 1 -p = 0, then roots are
(a) 0, 1
(b) -1, 1
(c) 0, -1
(d) - 1, 2

Answer/Explanation

Answer: c
Explaination:
(1 -p) is a root
∴ (1 - p)² + p(1 - p)+ 1 - p = 0
⇒ (1 - p)[1 - p + p + 1] = 0
⇒ (1 - p)(2) = 0
⇒ p=1
x²+x = 0
One root = 0 and another root = - 1
∴ roots are 0 and - 1.


35. If a, P are roots of the equation x² + 5x + 5 = 0, then equation whose roots are a + 1 and p + 1 is
(a) x² + 5x - 5 = 0
(b) x² + 3x + 5 = 0
(c) x² + 3x + 1 = 0
(d) none of these

Answer/Explanation

Answer: c
Explaination:
α + β = -5, αβ = 5.
Required equation is x² - (α + 1 + β + 1)x + (α + 1) (β + 1) = 0
⇒ x² - (α + β + 2)x + (αβ + α + β +1) = 0
⇒ x² - (-5 + 2)x + (5 - 5 + 1) = 0
⇒ x² + 3x + 1 = 0


36. Which of the following equations has two distinct real roots? [NCERT Exemplar Problems]
(a) 2x² - 3√2x + \frac{9}{4} =0
(b) x² + x - 5 = 0
(c) x² + 3x + 2√2 = 0
(d) 5x² - 3x + 1 = 0

Answer/Explanation

Answer: b
Explaination: (b) D > 0


37. Which of the following equations has no real roots ? [NCERT Exemplar Problems]
(a) x² - 4x + 3√2 =0
(b) x² + 4x - 3√2 = 0
(c) x² - 4x - 3√2 = 0
(d) 3x² + 4√3x + 4 = 0

Answer/Explanation

Answer: a
Explaination: (a) D < 0


38. (x² + 1)² - x² = 0 has [NCERT Exemplar Problems]
(a) four real roots
(b) two real roots
(c) no real roots
(d) one real root

Answer/Explanation

Answer: c
Explaination: (c) no real roots


39. If the difference of the roots of the equation x² - bx + c = 0 be 1, then
(a) b² - 4c + 1 = 0
(b) b² + 4c = 0
(c) b² - 4c - 1 - 0
(d) b² - 4c = 0

Answer/Explanation

Answer: c
Explaination:
Let roots are α and β
⇒ α - β = 1
∵ (α - β)² = (α + β)² - 4αβ
⇒ 1 = b² - 4c
⇒ b² - 4c - 1 = 0

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  • 2019-May-10 13:17:17
10th results
  • Sri kesav
  • 2019-May-10 09:58:50
Please tell me the correct date of AP ssc results
  • K. Sudhakar
  • 2019-May-10 09:58:43
Plz 10th result
  • V pawan durga sriniva
  • 2019-May-07 14:24:49
Please 10th cbsc results
  • V pawan durga sriniva
  • 2019-May-07 14:24:39
Please 10th cbsc results
  • Charan
  • 2019-May-07 14:24:21
Result ssc
  • Ayesha
  • 2019-May-07 14:24:17
At. What time did exam results will come?
  • Vadithya suresh
  • 2019-May-04 14:44:06
Results
  • VANKUDOTH pavan kalyan
  • 2018-May-30 10:16:07
Results
  • C H VAISHAVI
  • 2018-May-29 18:18:18
Cbse result by name
  • varunsai sanne
  • 2018-May-29 16:00:17
Xth results 2018
  • varunsai sanne
  • 2018-May-29 15:44:24
Xth results 2018
  • Yalagala Srihari
  • 2018-May-29 13:04:27
Exam results
  • Alpesh Dhamale
  • 2018-May-29 11:36:50
Nice article my baby wait for exam result i hope this year pass percentage may be increase
  • m. mohan rao
  • 2018-May-28 11:03:47
hi, s me cbse 10 class 2018 results
  • akshaya
  • 2018-May-26 10:22:07
at what time resilts are going to today
  • Velupala Ashwarya
  • 2018-May-15 11:01:52
My result
  • Ramu
  • 2018-May-12 16:09:34
good information