Quadratic Equation MCQ Class 10 Mathematics

Please refer to Chapter 4 Quadratic Equation MCQ Class 10 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 10 Mathematics. Students should refer to MCQ Questions for Class 10 Mathematics with Answers to score more marks in Grade 10 Mathematics exams. Students should read the chapter Quadratic Equation and then attempt the following objective questions.

MCQ Questions Class 10 Mathematics Chapter 4 Quadratic Equation

The Quadratic Equation MCQ Class 10 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

Question. What is the relation between speed ,distance and time?
(a) speed = (distance )/time
(b) distance = (speed )/time
(c) time = speed x distance
(d) speed = distance x time

A

Question. Find the product of the roots of x2 + 8x – 16 = 0
(a) 8
(b) –8
(c) 16
(d) –16

D

Question. Let speed of the stream be x km/hr. then speed of the motorboat in upstream will be
(a) 20 km/hr
(b) (20 + x) km/hr
(c) (20 – x) km/hr
(d) 2 km/hr

C

Question. If the equation (1 + m2) x2 + (2mc) x + (c2 – a2) = 0 has equal roots, then
(a) c2 – a2 = 1 + m2
(b) c2 = a2 (1 + m2)
(c) c2a2 = (1 + m2)
(d) c2 + a2 = 1 + m2

B

Question. Which of the following satisfy the equation a2b2x2 + b2x – a2x – 1 = 0
(a) 1/a2
(b) 1/ b2
(c)  −1 / b2
(d) None of these

B

Question. If the equation x2 + 2(k + 2)x + 9k = 0 has equal roots, then k = ?
(a) 1 or 4
(b) –1 or 4
(c) 1 or – 4
(d) –1 or – 4

A

Question. If x2 + y2 = 25, xy = 12, then x =
(a) {3, 4}
(b) {3, –3}
(c) {3, 4, –3, –4}
(d) {–3, –3}

C

Question. The roots of the quadratic equation x2 – 0.04 = 0 are
(a) ± 0.2
(b) ± 0.02
(c) 0.4
(d) 2

A

Question. How much time boat took in downstream?
(a) 90 minute
(b) 15 minute
(c) 30 minute
(d) 45 minute

C

Question. If the product of roots of the equation x3 – 3x + k = 10 is –2, then the value of k is
(a) –2
(b) –8
(c) 8
(d) 12

C

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

D

Question. If the roots of 5x2 – kx + 1 = 0 are real and distinct, then
(a) −2√5 < k < 2√5
(b) k > 2√5 only
(c) k < −2√ 5 only
(d) either k > 2 √5 or k < −2√5

D

Question. If a – b, b – c are the roots of ax2 + bx + c = 0, then find the value of (a b)(b c)/c a
(a) b/ c
(b) c/ b
(c) ab/ c
(d) bc

B

Question. If x = √7 + 4√3 , then x +1/x=
(a) 4
(b) 6
(c) 3
(d) 2

A

Question. What will be the distance covered by Ajay’s car in two hours?
(a) 2(x +5)km
(b) (x – 5)km
(c) 2( x + 10)km
(d) (2x + 5)km

A

Question. If the roots of the equation px2 + 2qx + r = 0 and qx2 − 2√ pr x + q = 0 be real, then
(a) p = q
(b) q2 = pr
(c) p2 = qr
(d) r2 = pq

B

Question. Which of the following is not a quadratic equation?
(a) x2 – 2x + 2 (3 – x) = 0
(b) x (x + 1) + 1 = (x – 2) (x – 5)
(c) (2x – 1) (x – 3) = (x + 5) (x – 1)
(d) x3 – 4x2 – x + 1 = (x –2)3

B

Question. The equation 2x2 + 2(p + 1) x + p = 0, where p is real, always has roots that are
(a) Equal
(b) Equal in magnitude but opposite in sign
(c) Irrational
(d) Real

D

Question. If one root of 5x2 + 13x + k = 0 be the reciprocal of the other root, then the value of k is
(a) 0
(b) 1
(c) 2
(d) 5

D

Question. The condition for one root of the quadratic equation ax2 + bx + c = 0 to be twice the other, is
(a) b2 = 4ac
(b) 2b2 = 9ac
(c) c2 = 4a + b2
(d) c2 = 9a – b2

B

Question. If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is
(a) x2 – 6x + 6 = 0
(b) x2 + 6x – 6 = 0
(c) x2 – 6x – 6 = 0
(d) x2 + 6x + 6 = 0

A

Question. If one root of the quadratic equation ax2 + bx + c = 0 is the reciprocal of the other, then
(a) b = c
(b) a = b
(c) ac = 1
(d) a = c

D

Question. What is the speed of current ?
(a) 20 km/hour
(b) 10 km/hour
(c) 15 km/hour
(d) 25 km/hour

B

Question. The roots of the equation x +1/x=3.1/3x ≠0,  are
(a) 3, 1
(b) 3, 1/ 3
(c) 3, -1/ 3
(d) – 3, 1/ 3

B

Question. If (x-1/2)2−(x-3/2)2 =x+2 , then x =
(a) 3
(b) 2
(c) 4
(d) None of these

C

Question. If the equation (m2 + n2) x2 –2 (mp + nq) x + p2 + q2 = 0 has equal roots, then
(a) mp = nq
(b) mq = np
(c) mn = pq
(d) mq = √np

B

Question. If the ratio of the roots of the equation x2 + bx + c = 0 is the same as that of x2 + qx + r = 0, then
(a) r2b = qc2
(b) r2c = qb2
(c) c2r = q2b
(d) b2r = q2c

D

Question. If a and b are the roots of the quadratic equation x2 – 6x – 2 = 0 and if an = an – bn, then the value of  a10-2a/ 2a9  is
(a) 6.0
(b) 5.2
(c) 5.0
(d) 3.0

D

Fill in the Blanks :

Question. A quadratic equation cannot have more than …….. roots.

two

Question. If r, s are roots of ax2 + bx + c = 0, then is ……….

b2 −2ac /c2

Question. The equation ax2 + bx + c = 0, a ≠ 0 has no real roots, if ………

b2 < 4ac

Question. A quadratic equation ax2 + bx + c = 0 has two distinct real roots, if b2 – 4ac …………..

> 0

Question. The values of k for which the equation 2x2 + kx + x + 8 = 0 will have real and equal roots are ………….

7 and –9

Question. If a, b are the roots of x2 + x + 1 = 0, then a2 + b2 = ………..

–1

True Or False :

Question. For the expression ax2 + 7x + 2 to be quadratic, the possible values of a are non-zero real numbers.

True

Question. (x – 2) (x + 1) = (x – 1) (x + 3) is a quadratic equation.

False

Question. The roots of the equation (x – 3)2 = 3 are 3± 3

True

Question. A quadratic equation cannot be solved by the method of completing the square.

False

Question. Sum of the reciprocals of the roots of the equation x2 + px + q = 0 is 1/p.