Table of Contents
Chapter 4 of Class 10 Maths focuses on Quadratic Equations, a fundamental concept in algebra. This chapter introduces students to the standard form of quadratic equations, methods of solving them, and their real-life applications. Class 10 Maths Chapter 4 on Quadratic Equations MCQs are very important for testing your understanding of the main ideas. MCQs help you learn better, improve problem-solving skills, and understand quadratic equations more deeply. By practicing MCQs, you can strengthen your knowledge, gain confidence, and prepare well for exams. These questions cover different parts of quadratic equations, helping you master the chapter and do well in mathematics.
Class 10 Maths Chapter 4 Quadratic Equations MCQs with Answers
1. 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
Answer: (c) 1/10 and 1/10
Explanation: Given, 100x² – 20x + 1=0
100x² – 10x – 10x + 1 = 0
10x(10x – 1) -1(10x – 1) = 0
(10x – 1)² = 0
Therefore, x = 1/10
2. Equation of (x+1)² – x² = 0 has number of real roots equal to:
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (a) 1
Explanation: (x+1)² – x² = 0
x² + 2x + 1 – x² = 0
2x + 1 = 0
x = -1/2
Hence, there is one real root.
3. The sum of two numbers is 27 and the product is 182. The numbers are:
(a) 12 and 13
(b) 13 and 14
(c) 12 and 15
(d) 13 and 24
Answer: (b) 13 and 14
Explanation: Let x be one number
Another number = 27 – x
Product of two numbers = 182
x(27 – x) = 182
x² – 27x + 182 = 0
(x – 13)(x – 14) = 0
x = 13 or x = 14
4. If ½ 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
Answer: (b) -2
Explanation: Given x = ½ is a root of x² – mx – 5/4 = 0
(½)² – m(½) – 5/4 = 0
1/4 – m/2 – 5/4 = 0
Therefore, m = -2
5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, the other two sides are:
(a) Base = 10 cm and Altitude = 5 cm
(b) Base = 12 cm and Altitude = 5 cm
(c) Base = 14 cm and Altitude = 10 cm
(d) Base = 12 cm and Altitude = 10 cm
Answer: (b) Base = 12 cm and Altitude = 5 cm
Explanation: Let the base be x cm
Altitude = (x – 7) cm
Using Pythagoras theorem: x² + (x – 7)² = 13²
Solving, we get x = 12
Therefore, base = 12 cm and altitude = 5 cm
6. The roots of quadratic equation 2x² + x + 4 = 0 are:
(a) Positive and negative
(b) Both positive
(c) Both negative
(d) No real roots
Answer: (d) No real roots
Explanation: 2x² + x + 4 = 0
Solving the equation, we get imaginary roots.
Therefore, no real roots.
7. 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
Answer: (a) 7
Explanation: Let x be the present age of Rehman
Age 3 years ago = x – 3
Age 5 years from now = x + 5
Sum of reciprocals = 1/3
Solving, we get x = 7
8. 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
Answer: (c) no real roots
Explanation: Solving the quadratic equation, we find b² – 4ac < 0
Therefore, no real roots.
9. The value of 6+√6+√6+… is:
(a) 4
(b) 3
(c) 3.5
(d) -3
Answer: (b) 3
Explanation: Let x be the value
√(6 + x) = x
Solving, we get x = 3
10. 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. Find the speed of the train.
(a) 30 km/hr
(b) 40 km/hr
(c) 50 km/hr
(d) 60 km/hr
Answer: (b) 40 km/hr
Explanation: Let x km/hr be the speed
Time = 360/x
(x + 5)(360 – 1/x) = 360
Solving, we get x = 40
11. If one root of equation 4x² – 2x + k – 4 = 0 is the reciprocal of the other, the value of k is:
(a) -8
(b) 8
(c) -4
(d) 4
Answer: (b) 8
Explanation: If one root is the reciprocal of the other, then the product of roots will be 1.
α x 1/α = (k-4)/4
Therefore, k-4 = 4
k = 8
12. Which one of the following is not a quadratic equation?
(a) (x + 2)² = 2(x + 3)
(b) x² + 3x = (–1)(1 – 3x)²
(c) (x + 2)(x – 1) = x² – 2x – 3
(d) x³ – x² + 2x + 1 = (x + 1)³
Answer: (c) (x + 2)(x – 1) = x² – 2x – 3
Explanation: A quadratic equation has a degree of 2.
By verifying the options, option (c) simplifies to a linear equation, not a quadratic equation.
13. 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
Answer: (c) 2x² – 7x + 6 = 0
Explanation: Substitute x = 2 into the options:
Only option (c) satisfies the equation, making x = 2 a root.
14. 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
Answer: (c) b² – 4ac < 0
Explanation: A quadratic equation has no real roots if the discriminant (b² – 4ac) is less than 0.
15. The product of two consecutive positive integers is 360. To find the integers, this can be represented in the form of quadratic equation as:
(a) x² + x + 360 = 0
(b) x² + x – 360 = 0
(c) 2x² + x – 360
(d) x² – 2x – 360 = 0
Answer: (b) x² + x – 360 = 0
Explanation: Let x and (x + 1) be the two consecutive integers.
x(x + 1) = 360
x² + x – 360 = 0
16. The equation which has the sum of its roots as 3 is:
(a) 2x² – 3x + 6 = 0
(b) –x² + 3x – 3 = 0
(c) √2x² – 3/√2x + 1 = 0
(d) 3x² – 3x + 3 = 0
Answer: (b) –x² + 3x – 3 = 0
Explanation: The sum of the roots of a quadratic equation ax² + bx + c = 0 is given by –b/a.
For option (b), the sum is 3.
17. 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
Answer: (c) no real roots
Explanation: Solving the quadratic equation, we find b² – 4ac < 0.
Therefore, no real roots.
18. The quadratic formula to find the roots of a quadratic equation ax² + bx + c = 0 is given by:
(a) [-b ± √(b² – ac)]/2a
(b) [-b ± √(b² – 2ac)]/a
(c) [-b ± √(b² – 4ac)]/4a
(d) [-b ± √(b² – 4ac)]/2a
Answer: (d) [-b ± √(b² – 4ac)]/2a
Explanation: The quadratic formula to find the roots of a quadratic equation ax² + bx + c = 0 is given by [-b ± √(b² – 4ac)]/2a.
19. The quadratic equation x² + 7x – 60 has:
(a) two equal roots
(b) two real and unequal roots
(c) no real roots
(d) two equal complex roots
Answer: (b) two real and unequal roots
Explanation: Given, x² + 7x – 60 = 0
Solving, we find b² – 4ac > 0.
Therefore, the equation has two real and unequal roots.
20. The maximum number of roots for a quadratic equation is equal to:
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (b) 2
Explanation: The maximum number of roots for a quadratic equation is 2 since its degree is 2.
