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) x
22 + 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
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
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
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
Ans: c
Q 6) The quadratic equation has degree
(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
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
Ans: a
Q 9) The roots of the quadratic equation 6x² – x – 2 = 0 are
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
Q 13) The sum of the roots of the quadratic equation 3
x2 – 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
b) 4 / 49
c) 4
d) 49
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
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
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
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
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
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
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
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
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
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
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
Ans: d
Q 26) If α and β are the roots of 4
x2 + 3x + 7 = 0, then the value of is
a) -3/4
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
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
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
Ans: c
Q 31) A quadratic equation a
x2 + bx + c = 0 has no real roots, if
(a) b
2 – 4ac > 0
(b) b
2 – 4ac = 0
(c) b
2 – 4ac < 0
(d) b
2 – ac < 0
Ans: c
Q 32) The equation which has the sum of its roots as 3 is
(a) 2
x2 – 3x + 6 = 0
(b) –
x2 + 3x – 3 = 0
\:%20\:%20\sqrt{2}x^{2}-\frac{3}{\sqrt{2}}x+1)
(d) 3
x2 – 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
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
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
Ans: b
Q 36) The maximum number of roots for a quadratic equation is equal to
(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
Ans: d
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