CBSE Class 10 Mathematics Quadratic Equations MCQs Set 02

Question: 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
Answer: b

Question: 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
Answer: c

Question: Find two consecutive positive odd numbers, the sum of whose squares is 514.
a) 11, 13
b) 15, 17
c) 11, 9
d) 13, 15
Answer: b

Question: 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
Answer: d

Question: 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
Answer: c

Question: 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
Answer: a

Question: If x = √2 +√2 +√2 + ........... , then _______.
a) x = 1
b) 0 < x < 1
c) x is infinite
d) x = 2
Answer: d

Question: In the quadratic equation 9x² + ax - 2 = 0 , find the value of a for which x = 1/3 is its solution.
a) -2
b) 3
c) -4
d) 6
Answer: b

Question: 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
Answer: a

Question: 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
Answer: b

Question: 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)
Answer: d

Question: 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
Answer: d

Question: 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
Answer: b

Question: Which of the following quadratic polynomials can be factorized into a product of real linear factors?
a) 2x² - 5x + 9
b) 2x² + 4x -5
c) 3x² + 4x + 6
d) 5x² - 3x + 2
Answer: b

Question: 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
Answer: b

Question: 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
Answer: a

Question: The ratio of the length and breadth of a rectangular photo frame is 3 : 2. Find its length if its area is 864 cm² .
a) 34 cm
b) 26 cm
c) 24 cm
d) 36 cm
Answer: d

Question: 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
Answer: c

Question: ₹ 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
Answer: a

Question: If a and Rare the roots of the equation x² -8x + p = 0 such that α² + β² = 40 , find the value of 'p'.
a) 8
b) 10
c) 12
d) 14
Answer: c

Question: 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)
Answer: b

Question: 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
Answer: b

Question: Find two consecutive integers whose product is 600.
a) 30, 20
b) 50, 12
c) 15, 40
d) 24, 25
Answer: d

Question: If √x −1 − √x +1+1=0 , then 4x is equal to ________.
a) 4 √−1 
b) 0
c) 5
d) 1/4x1
Answer: c

Question: 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
Answer: b

Question: 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
Answer: b

Question: Find the value of 'k' for which x² - 4x + k = 0 has coincident roots.
a) 4
b) -4
c) 0
d) -2
Answer: a

Question: The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2x16/21 , find the fraction.
a) 3/7
b) 7/3
c) 4/3
d) 3/4
Answer: a

Question: 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
Answer: c

Question: 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.
Answer: a

 Question: 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
Answer: b

Question: 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
Answer: d

Question: 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
Answer: a

Question: 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
Answer: b

Question: 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
Answer: c

Question: Find the sum of the roots of x² + x - 210 = 0
a) -2
b) 29
c) 20
d) -1
Answer: d

Question: Find the product of the roots of the quadratic equation 9m2 + 24 m+16 = 0 .
a) 4/3
b) 9/16
c) 16/9
d) 3/4
Answer: c

 Question: 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.
Answer: b

Question: 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
Answer: a

Question: 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.
Answer: c