CBSE Class 10 Mathematics Quadratic Equations MCQs Set E

Question. (x + 1)2 −x² = 0 has
(a) no real roots
(b) 1 real root
(c) 2 real roots
(d) 4 real roots

Answer: B

Question. 9x² + 12x + 4 = 0 have
(a) Real and Distinct roots
(b) No real roots
(c) Distinct roots
(d) Real and Equal roots

Answer: D

Question. Find two consecutive even numbers whose product is double that of the greater number.
(a) 1, 3
(b) 4, 6
(c) 2, 4
(d) 6, 8

Answer: C

Question. What are the roots of 17a² – 20a + 10 = 10a² + 2a + 7 ?
(a) 1/7 , 3
(b) 3 , -1/7
(c) -1/7 , 3
(d) -3 , – 1/7

Answer: A

Question. 5x² + 8x + 4 = 2x² + 4x + 6 is a
(a) quadratic equation
(b) cubic equation
(c) constant
(d) linear equation

Answer: A

Question. x² – 30x + 225 = 0 have
(a) Real roots
(b) No real roots
(c) Real and Equal roots
(d) Real and Distinct roots

Answer: C

Question. For what value of k, the equation 9x² – 24x + k = 0 has equal roots?
(a) 12
(b) 16
(c) 18
(d) 20

Answer: B

Question. A cyclist takes 2 hours less to cover a distance of 200 km, if he increases his speed by 5 km/hr. Then his original speed is
(a) 26 km/hr
(b) 20 km/hr
(c) 24 km/hr
(d) 25 km/hr

Answer: B

Question. Which of the following statements is true?
(a) x² + x + 1 = 0 has no real roots.
(b) x² – 4x + 3 = 0 and x² – x – 2 = 0 have two common roots.
(c) x² – 3x – 4 = 0 have real and equal roots.
(d) The roots of ax² + bx + c = 0,a ≠ 0 are reciprocal to each other if a ≠ c .

Answer: A

Question. The length and breadth of a rectangle are (3k + 1) cm and (2k – 1) cm respectively. Find the perimeter of the rectangle if its area is 144cm2 .
(a) 50 cm
(b) 10 cm
(c) 32 cm
(d) 25 cm

Answer: A

Question. The perimeter of a right triangle is 70cm and its hypotenuse is 29cm. The area of the triangle is
(a) 210 sq.cm
(b) 200 sq.cm
(c) 180 sq.cm
(d) 250 sq.cm

Answer: A

Question. If the quadratic equation bx² -2√acx + b = 0 has equal roots, then
(a) b²  = -ac
(b) 2b²  = ac
(c) b²  = ac
(d) b²  = 2ac

Answer: C

Question. The quadratic equation whose roots are is
(a) 6x² + 13x -5 = 0
(b) 6x² + 13x + 5 = 0
(c) 6x² -13x + 5 = 0
(d) 6x² -13x -5 = 0

Answer: D

Question. If one root of the equation 4x² -2x + (λ-4) = 0 be the reciprocal of the other, then the value of λ is
(a) 8
(b) 4
(c) – 8
(d) – 4

Answer: A

Question. 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

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. If the quadratic equation x² – 2x + k = 0 has equal roots, then value of k is
(a) 1
(b) 2
(c) 3
(d) 0

Answer: A

Question. If the roots of the equation (a² + b²)x² -2ab (a + c) x + c² + b² = 0 are equal, then
(a) b = ac
(b) b² = ac
(c) b = 2ac/a + c
(d) 2b = a + c

Answer: B

Question. Identify the quadratic equation from the following.
(a) P + 1/P = 1 , P ≠0
(b) P2 + 1/P = 1 , P ≠ 0
(c) x² – 1/x = 1, x ≠ 0
(d) x² + 2√x – 1 = 0

Answer: A

Question. 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

Answer: D

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. A quadratic equation αx² + 5x + β two roots x = 1/3 and x = -2 . Find the respective values of α and β .
(a) 3, 2
(b) 2, -5
(c)-3, 5
(d) 3, -2

Answer: D

Question. The value(s) of k for which the quadratic equation 2×2 + kx + 2 = 0 has equal roots, is
(a) 4
(b) ± 4
(c) – 4
(d) 0

Answer: B

Question. A quadratic equation ax² + bx + c = 0 has non – real roots, if
(a) b² -4ac > 0
(b) b² -4ac = 0
(c) b² -4ac < 0
(d) b² -ac = 0

Answer: C

Question. A quadratic equation ax² + bx + c = 0 has real and distinct roots, if
(a) b² -4ac > 0
(b) b² -4ac < 0
(c) b² -4ac = 0
(d) None of the options

Answer: A

Question. The value(s) of k, for which the roots of the equation 3x² + 2k + 27 = 0 are real and equal are
(a) k = 9
(b) k = ± 9
(c) k = –9
(d) k = 0

Answer: B

Assertion and Reason:
(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion (A): The equation 8x² + 3kx + 2 = 0 has equal roots, then the value of k is ± 8/3 .
Reason (R): The equation ax² + bx + c = 0 has equal roots if D = b² – 4ac = 0.

Answer: A

Question. Assertion (A): The roots of the quadratic equation x² + 2x + 2 = 0 are imaginary.
Reason (R): If discriminant D = b² – 4ac < 0, then the roots of quadratic equation ax² + bx + c = 0 are imaginary.

Answer: A

Question. Assertion : If roots of the equation x² – bx + c = 0 are two consecutive integers, then b² – 4c = 1.
Reason : If a, b, c are odd integer then the roots of the equation 4abc x² + (b² – 4ac) x – b = 0 are real and distinct.

Answer: B

Question. Assertion : A quadratic equation ax² + bx + c = 0, has two distinct real roots, if b² – 4ac > 0.
Reason : A quadratic equation can never be solved by using method of completing the squares.

Answer: C

Question. Assertion : (2x – 1)2 – 4x² + 5 = 0 is not a quadratic equation.
Reason : x = 0, 3 are the roots of the equation 2x² – 6x = 0.

Answer: B

Question. Assertion : Sum and product of roots of 2x² – 3x + 5 = 0 are 3/ 2 and 5/ 2 respectively.
Reason : If α and β are the roots of ax² + bx + c = 0, a ≠ 0, then sum of roots = α + β – b a = and product of roots αβ = c/a .

Answer: A

Question. Assertion : The equation 9x² + 3kx + 4 = 0 has equal roots for k = ± 4.
Reason : If discriminant ‘D’ of a quadratic equation is equal to zero then the roots of equation are real and equal.

Answer: A

Question. Assertion : 4x² – 12x + 9 = 0 has repeated roots.
Reason : The quadratic equation ax² + bx + c = 0 have repeated roots if discriminant D > 0.

Answer: C