# MCQ Questions For Class 10 Quadratic Equation

Quadratic Equation Class 10 MCQ is one of the best strategies to prepare for the CBSE Class 10 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more MCQ on Quadratic Equation class 10, which will help them all through their board test.

Class 10 Math MCQ with answers are given here to chapter 4 Quadratic Equation. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 10 Mathematics syllabus. By Solving these Class 10 MCQs, you will be able to analyze all of the concepts quickly in the chapter and get ready for the Class 10 Annual exam.

Learn Quadratic Equation Class 10 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 10 Mathematics Quadratic Equation MCQ with answers given below

Question 1. If one root of the equation a(b – c)x2 + b(c – a)x + c(a – b) = 0 is 1, then the other root is ___.
(A) b(c – a) / a(b – c)
(A) a(b – c) / c(a – b)
(A) a(b – c) / c(a – b)
(A) b(c – a) / a(b – c)

D

Question 2. If the roots of the equation (a – b)x2 + (b – c)x + (c – a) = 0 are equal. Then _______.
(A) 2b = a + c
(B) 2a = b + c
(C) 2c = a + b
(D) 1/b = 1/a = 1/c

B

Question 3. The roots of ax2 + bx + c = 0, a ≠ 0 are real and unequal, if b2 – 4ac is _______.
(A) = 0
(B) > 0
(C) < 0,
(D) ≥ 0

B

Question 4. If x = √2 +√2 +√2 + ……….. , then _______.
(A) x = 1
(B) 0 < x < 1
(C) x is infinite
(D) x = 2

D

Question 5. If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q is equal to
(A) 8
(B) –8
(C) 16
(D) –16

C

Question 6. If one of roots of 2x2 + ax + 32 = 0 is twice the other root, then the value of a is ________.
(A) −3 √2
(B) 8 √2
(C) 12 √2
(D) −2 √2

C

Question. 7 For what value of a, the roots of the equation 2x2 + 6x + a = 0, satisfy the condition(α/β)+(β/α) < 2 (where a and b are the roots of equation).
(A) a < 0
(B) –1 < a < 0
(C) –1 < a < 1
(D) None of these

D

Question 8. One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x2 correctly as –6 and 1 respectively. The correct roots are ____.
(A) 3, –2
(B) –3, 2
(C) –6, –1
(D) 6, –1

D

Question 9. If √x −1 − √x +1+1=0 , then 4x is equal to ________.
(A) 4 √−1
(B) 0
(C) 5
(D) 1/4×1

C

Question 10. If the roots of the equation (a2 + b2) x2 – 2b(a + c)x + (b2 + c2) = 0 are equal, then ________.
(A) 2b = a + c
(B) b2 = ac
(C) b = 2ac/a+b
(D) b = ac

B

Question 11. Roots of the quadratic equation x2 + x – (a + 1)(a + 2) = 0 are ________.
(A) –(a + 1), (a + 2)
(B) (a + 1), –(a + 2)
(C) (a + 1), (a + 2)
(D) –(a + 1), –(a + 2)

B

Question 12. The roots of the equation 3x + 5 (x)1/2 = √2 can be found by solving ________.
(A) 9x2 + 28x + 25 = 0
(B) 9x2 + 30x + 25 = 0
(C) 9x2 + 28x – 25 = 0
(D) 16x2 + 22x – 30 = 0

A

Question 13. In the equation

the roots are equal when m = __.
(A) 1/2
(B) − 1/2
(C) 0
(D) 1

B

Question 14. Two numbers whose sum is 12 and the absolute value of whose difference is 4 are the roots of the equation ________.
(A) x2 – 12x + 30 = 0
(B) x2 – 12x + 32 = 0
(C) 2x2 – 6x + 7 = 0
(D) 2x2 – 24x + 43 = 0

B

Question 15. The roots of the equation x2/3 + x1/3 – 2 = 0 are ________.
(A) 1, –8
(B) 1, –2
(C) 2/3, 1/3
(D) –2, –8

A

Question 16. In the Maths Olympiad of 2020 at Animal Planet, two representatives from the donkey’s side, while solving a quadratic equation, committed the following mistakes.
(i) One of them made a mistake in the constant term and got the roots as 5 and 9.
(ii) Another one committed an error in the coefficient of x and he got the roots as 12 and 4. But in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the quadratic equation.
(A) x2 + 4x + 14 = 0
(B) 2x2 + 7x – 24 = 0
(C) x2 – 14x + 48 = 0
(D) 3x2 – 17x + 52 = 0

C

Question 17. ₹ 6500 were divided equally among a certain number of persons. If there had been 15 more persons, each would have got ₹ 30 less. Find the original number of persons.
(A) 50
(B) 60
(C) 45
(D) 55

A

Question 18. In a bangle shop, if the shopkeeper displays the bangles in the form of a square then he is left with 38 bangles. If he wanted to increase the size of square by one unit each side of the square he found that 25 bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was ________.
(A) 1690
(B) 999
(C) 538
(D) Can’t be determined

B

Question 19. A man walks a distance of 48 km in a given time. If he walks 2 km/hr faster, he will perform the journey 4 hrs before. His normal rate of walking, is ________.
(A) 3 km/hr (B) 4 km/hr
(C) – 6 km/hr or 4 km/hr
(D) 5 km/hr

B

Question 20. Read the statements carefully.
Statement – I : The quadratic equation ax2 + bx + c = 0 has two distinct real roots, if b2 – 4ac ≥ 0.
Statement – II : The quadratic equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
(A) Both Statement – I and Statement – II are true.
(B) Statement – I is true but Statement – II is false.
(C) Statement – I is false but Statement – II is true.
(D) Both Statement – I and Statement – II are false.

C

Question 21. If the roots of the equation x2 + 2cx + ab = 0 are real and unequal, then the equation x2 – 2(a + b)x + a2 + b2 + 2c2 = 0 has ________ roots.
(A) Real
(B) Equal
(C) No real
(D) Can’t be determined

C

Question 22. Swati can row her boat at a speed of 5 km/hr in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, find the speed of the stream.
(A) 5 km/hr
(B) 2 km/hr
(C) 3 km/hr
(D) 4 km/hr

B

Whoever needs to take the CBSE Class 10 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 10 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Quadratic Equation class 10 MCQ are ready by the subject specialists themselves.

Question 23. Which of the following equations has two distinct real roots?
(A) 2x2 – 3 √2x + 9/4 = 0
(B) x2 + x – 5 = 0
(C) x2 + 3x + 2 √2 = 0
(D) 5x2 – 3x + 1 = 0

B

Question 24. The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2×16/21 , find the fraction.
(A) 3/7
(B) 7/3
(C) 4/3
(D) 3/4

A

Question 25. Identify the correct statement.
(a) The roots of the quadratic equation 2y2 + 9y = 0 are 0 and -9/2.
(b) The value of ‘k’ for which 4m2 + k – 15 = 0 has a root m = 3 is 7.
(c) The quadratic equation 2 (4x -11)2 = 0 has two distinct roots.
(d) 7x2 – 12x – 18 = 0 is not a quadratic equation.

A

Question 26. Read the statement carefully and state ‘T’ for true and ‘F’ for false

(ii) A line segment AB of length 2 m is divided at C into two parts such that AC2 = AB·CB. The length of the part CB is 3 + √5 .
(iii) Every quadratic equation can have at most two real roots.
(iv) A real number a is said to be root of the quadratic equation ax2 + bx + c = 0, if aα2 + bα + c = 0.
(i)   (ii)  (iii)   (iv)
(A)   F     T      T      T
(B)   F     T     T      F
(C)   T     F     F      T
(D)   F     F     T      T

D

Question 27. Which of the following equations has 2 as a root?
(a) 2x2 – 7x + 6 = 0
(b) x2 – 4x + 5 = 0
(c) 3x2 – 6x – 2 = 0
(d) x2 + 3x -12 = 0

A

Question 28. Which of the following is the quadratic equation one of whose roots is 3 – 2√3 ?
(a) x2 + 6x – 3 = 0
(b) x2 – 6x – 3 = 0
(c) x2 + 6x + 3 = 0
(d) x2 – 6x + 3 = 0

B

Question 29. Which of the following is a quadratic equation?

D

Question 30. When are the roots of a quadratic equation real and equal?
(a) When the discriminant is positive.
(b) When the discriminant is zero.
(c) When the discriminant is negative.
(d) When the discriminant is non-negative.

B

Question 31. A two digit number is 4 times the sum of its digits and also 16 more than the product of digits. Find the number.
(a) 48
(b) 36
(c) 44
(d) 32

A

Question 32. If the product of the roots of x2 – 3x + k = 10 is – 2, what is the value of’ k’?
(a) -2
(b) 8
(c) 12
(d)-8

B

Question 33. The area of a rectangular cardboard is 80 cm2 . If its perimeter is 36 cm, find its length.
(a) 40 cm
(b) 10 cm
(c) 20 cm
(d) 8 cm

B

Question 34. Find the sum of the roots of x2 + x – 210 = 0
(a) -2
(b) 29
(c) 20
(d) -1

D

Question 35. What is the value of ‘k’ for which 2x2 – kx k has equal roots?
(a) 4 only
(b) 0 only
(c) 8 only
(d) 0, 8

D

Question 36. The sides of two square plots are (2x – 1)m and (5x + 4)m . The area of the second square plot is 9 times the area of the first square plot. Find the side of the larger plot.
(a) 15m
(b) 13m
(c) 31 m
(d) 39m

D

Question 37. If the roots of x2 + 4mx + 4m2 + m + 1 = 0 are real, which of the following is true?
(a) m = – 1
(b) m ≤ – 1
(c) m ≥ -1
(d) m ≥ 0

B

Question 38. Find the value of ‘p’ for which m = 1/√3 is a root of the eq/uation pm2 + ( √3 – √2)m – 1 = 0
(a) √3
(b) √2
(c) √6
(d) √7

C

Question 39. The perimeter and area of a rectangular park are 80 m and 400 m2 . What is its length?
(a) 20m
(b) 15m
(c) 30m
(d) 40m

A

Question 40. Find the common root of the equations x2 – 7x + 10 = 0 and x2 – 10x + 16 = 0.
(a) – 2
(b) 3
(c) 5
(d) 2

D

Question 41. What is the ratio of the sum and the product of roots of 7x2 – 12x + 18 = 0
(a) 7:12
(b) 2:3
(c) 3:2
(d) 7:18

B

Question 42. Find the present age of a boy whose age 12 years from now will be the square of his present age.
(a) 5 years
(b) 7 years
(c) 4 years
(d) 6 years

C

Question 43. If the equation ax – 5x + c = 0 has 10 as the sum of the roots and also as the product of the roots, which of the following is true?
(a) a – c = 5
(b) a = 2,c = 3
(c) a = 5, c =1
(d) a = 3, c = 2

A

Question 44. The quadratic equation ax2 + bx + c = 0 has no real root. Which of the following is true?
(a) b2 – 4ac < 0
(b) b2 – 4ac = 0
(c) b2 – 4ac > 0
(d) b2 + 4ac < 0

A

Question 45. What is the value of ‘k’ for which the roots of the quadratic equation 3x2 + 2kx + 27 = 0 are real and equal?
(a) 9 only
(b) -9 only
(c) 9 or-9
(d) Neither 9 nor-9.

C

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