Mathematics
Multiple Choice Questions (MCQ)
MCQ | Class 10 | Chapter 4
QUADRATIC EQUATIONS
- MCQ Based on the general quadratic equations.
- MCQ Based on the different methods of solving Quadratic Equations.
- MCQ Based on the Nature of roots of Quadratic Equations.
- MCQ Based on the Discriminant.
- MCQ Based from the Quadratic Formula.
Features
- In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations.
- Solution Hints are also given to some difficult problems.
- Each MCQ contains four options from which one option is correct.
- On the right hand side column of the pdf Answer option is given.
Action Plan
- First of all students should Learn and write all basic points and Formulas related to the Quadratic Equations.
- Start solving the NCERT Problems with examples.
- Solve the important assignments on the Quadratic Equations.
- Then start solving the following MCQ.
MCQ | CHAPTER 4 | CLASS 10
QUADRATIC EQUATIONS
Q 1) Which one of the following is not a quadratic equation?
(a) (x + 2)22 = 2(x + 3)
(b) x22 + 3x = (–1) (1 – 3x)22
(c) (x + 2) (x – 1) = x2 – 2x – 3
(d) x3 – x2 + 2x + 1 = (x + 1)3
Ans: c
Q 2) The sum of two numbers is 27 and product is 182. The numbers are:
(a) 12 and 13
(b) 13 and 14
(c) 12 and 15
(d) 13 and 24
(a) 12 and 13
(b) 13 and 14
(c) 12 and 15
(d) 13 and 24
Ans: b
Q 3) The quadratic equation x2 + 7x – 60 has
(a) two equal roots
(b) two real and unequal roots
(b) no real roots
(c) two equal complex roots
(b) two real and unequal roots
(b) no real roots
(c) two equal complex roots
Ans: b
Q 4) A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
(a) 30 km/hr
(b) 40 km/hr
(c) 50 km/hr
(d) 60 km/hr
(a) 30 km/hr
(b) 40 km/hr
(c) 50 km/hr
(d) 60 km/hr
Ans: b
Q 5) The quadratic equation 2x2 – √5x + 1 = 0 has
(a) two distinct real roots
(b) two equal real roots
(c) no real roots
(d) more than 2 real roots
(b) two equal real roots
(c) no real roots
(d) more than 2 real roots
Ans: c
Q 6) The quadratic equation has degree
(a) 0
(b) 1
(c) 2
(d) 3
(a) 0
(b) 1
(c) 2
(d) 3
Ans: c
Q 7) A bi-quadratic equation has degree
(a) 1
(b) 2
(c) 3
(d) 4
(a) 1
(b) 2
(c) 3
(d) 4
Ans: d
Q 8) 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
(a) linear equation
(b) quadratic equation
(c) cubic equation
(d) bi-quadratic equation
Ans: a
Q 9) The roots of the quadratic equation 6x² – x – 2 = 0 are
Ans: c
Q 10) The quadratic equation whose roots are 1 and -1/2 is
(a) 2x² + x – 1 = 0
(b) 2x² – x – 1 = 0
(c) 2x² + x + 1 = 0
(d) 2x² – x + 1 = 0
Ans: b
Q 11) 
(a) 4
(b) 3
(c) 3.5
(d) -3
Ans: b
Q 12) The roots of the quadratic equation 
Ans: c
Q 13) The sum of the roots of the quadratic equation 3x2 – 9x + 5 = 0 is
(a) 3
(b) 6
(c) – 3
(d) 2
Ans: a
Q 14) If one root of the equation x² + px + 12 = 0 is 4, while the equation x² + px + q = 0 has equal roots, the value of q is
a) 49 / 4
a) 49 / 4
b) 4 / 49
c) 4
d) 49
Ans: a
Ans: a
Q 15) The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, the other two sides of the triangle are equal to:
(a) Base = 10cm and Altitude = 5cm
(b) Base = 12cm and Altitude = 5cm
(c) Base = 14cm and Altitude = 10cm
(d) Base = 12cm and Altitude = 10cm
(a) Base = 10cm and Altitude = 5cm
(b) Base = 12cm and Altitude = 5cm
(c) Base = 14cm and Altitude = 10cm
(d) Base = 12cm and Altitude = 10cm
Ans: b
Q 16) If α and β are the roots of the equation 2x2 – 3x – 6 = 0. Then the equation whose roots are and is
(a) 6x² – 3x + 2 = 0
(b) 6x² + 3x – 2 = 0
(c) 6x² – 3x – 2 = 0
(d) x² + 3x – 2 = 0
(b) 6x² + 3x – 2 = 0
(c) 6x² – 3x – 2 = 0
(d) x² + 3x – 2 = 0
Ans: b
Q 17) 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
(a) 12, 13
(b) 13,14
(c) 11,12
(d) 14,15
Ans: a
Q 18) 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
(a) 1
(b) -1
(c) 2
(d) -2
Ans: b
Q 19) 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
(a) p = 3
(b) p = 5
(c) p = 7
(d) p = 1
Ans: c
Q 20) 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
(a) 7 years, 49 years
(b) 5 years, 25 years
(c) 1 years, 50 years
(d) 6 years, 49 years
Ans: a
Q 21) Equation of (x + 1)2 – x2 = 0 has number of real roots equal to:
(a) 1
(b) 2
(c) 3
(d) 4
(b) 2
(c) 3
(d) 4
Ans: a
Q 22) The roots of 100x2 – 20x + 1 = 0 is:
(a) 1/20 and 1/20
(b) 1/10 and 1/20
(c) 1/10 and 1/10
(d) None of the above
(a) 1/20 and 1/20
(b) 1/10 and 1/20
(c) 1/10 and 1/10
(d) None of the above
Ans: c
Q 23) If 1/ 2 is a root of the quadratic equation x2 – mx – 5/4 = 0, then value of m is:
(a) 2
(b) -2
(c) -3
(d) 3
(a) 2
(b) -2
(c) -3
(d) 3
Ans: b
Q 24) 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
(a) P = 0
(b) p = – 2
(c) p = ± 2
(d) p = 2
Ans: d
Q 25) The roots of quadratic equation 2x2 + x + 4 = 0 are:
(a) Positive and negative
(b) Both Positive
(c) Both Negative
(d) No real roots
(a) Positive and negative
(b) Both Positive
(c) Both Negative
(d) No real roots
Ans: d
Q 26) If α and β are the roots of 4x2 + 3x + 7 = 0, then the value of is 
a) -3/4
b) -3/7
c) 3/7
d) 7/4
b) -3/7
c) 3/7
d) 7/4
Ans: b
Q 27) The sum of the reciprocals of Rehman’s ages 3 years ago and 5 years from now is 1/3. The present age of Rehman is:
(a) 7
(b) 10
(c) 5
(d) 6
(a) 7
(b) 10
(c) 5
(d) 6
Ans: a
Q 28) If one root of equation 4x2 – 2x + k – 4 = 0 is reciprocal of the other. The value of k is:
(a) – 8
(b) 8
(c) – 4
(d) 4
(b) 8
(c) – 4
(d) 4
Ans: b
Q 29) 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
Ans: d
Q 30) Which of the following equations has 2 as a root?
(a) x2 – 4x + 5 = 0
(b) x2 + 3x – 12 = 0
(c) 2x2 – 7x + 6 = 0
(d) 3x2 – 6x – 2 = 0
(a) x2 – 4x + 5 = 0
(b) x2 + 3x – 12 = 0
(c) 2x2 – 7x + 6 = 0
(d) 3x2 – 6x – 2 = 0
Ans: c
Q 31) A quadratic equation ax2 + bx + c = 0 has no real roots, if
(a) b2 – 4ac > 0
(b) b2 – 4ac = 0
(c) b2 – 4ac < 0
(d) b2 – ac < 0
Ans: c
Q 32) The equation which has the sum of its roots as 3 is
(a) 2x2 – 3x + 6 = 0
(b) –x2 + 3x – 3 = 0
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(d) 3x2 – 3x + 3 = 0
(a) 2x2 – 3x + 6 = 0
(b) –x2 + 3x – 3 = 0
(d) 3x2 – 3x + 3 = 0
Ans: b
Q 33) The roots of 100x2 – 20x + 1 = 0 is:
(a) 1/20 and 1/20
(b) 1/10 and 1/20
(c) 1/10 and 1/10
(d) None of the above
(a) 1/20 and 1/20
(b) 1/10 and 1/20
(c) 1/10 and 1/10
(d) None of the above
Ans: c
Q 34) The equation (x + 1)2 – 2(x + 1) = 0 has
(a) two real roots
(b) no real roots
(c) one real root
(d) two equal roots
(a) two real roots
(b) no real roots
(c) one real root
(d) two equal roots
Ans: a
Q 35) 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
(a) x² + 3x – 5 = 0
(b) x² + x3 + 2 = 0
(c) 3 + x + x² = 0
(d) x² – 9 = 0
Ans: b
Q 36) The maximum number of roots for a quadratic equation is equal to
(a) 1
(b) 2
(c) 3
(d) 4
(a) 1
(b) 2
(c) 3
(d) 4
Ans: b
Q 37) Values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is
(a) 0 only
(b) 4
(c) 8 only
(d) 0, 8
(a) 0 only
(b) 4
(c) 8 only
(d) 0, 8
Ans: d
