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CBSE Class 10  >  Class 10 Test  >  Mathematics (Maths)   >  Assertion & Reason Test: Quadratic Equation - Class 10 MCQ

Quadratic Equation - Free Assertion & Reason Questions with Solutions


MCQ Practice Test & Solutions: Assertion & Reason Test: Quadratic Equation (10 Questions)

You can prepare effectively for Class 10 Mathematics (Maths) Class 10 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Assertion & Reason Test: Quadratic Equation". These 10 questions have been designed by the experts with the latest curriculum of Class 10 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 20 minutes
  • - Number of Questions: 10

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Assertion & Reason Test: Quadratic Equation - Question 1
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): The degree of quadratic equation is always 2. Hence, x2 – 1 = 0 is pure quadratic equation.

Reason (R): An equation of the form ax2 + c = 0 is known as pure quadratic equation.

Detailed Solution: Question 1

An equation that can be expressed in the form ax2 + c = 0, where a and c are real numbers and a = 0 is a pure quadratic equation. Or the quadratic equation having only second degree variable is called a pure quadratic equation.

Assertion & Reason Test: Quadratic Equation - Question 2
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): The product of two successive positive integral multiples of 5 is 300, then the two numbers are 15 and 20.

Reason (R): The product of two consecutive integrals is a multiple of 2.

Detailed Solution: Question 2

15 and 20 are the correct two successive positive integral multiples whose product is 300. So, this Assertion is true.

The reason is also true as n(n+1) is divisible by 2 always for all natural number n.

Therefore, Both A and R are true and R is not correct explanation for A.

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Assertion & Reason Test: Quadratic Equation - Question 3
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): In the expression: x can’t have values 3 and – 5

Reason (R): If discriminant D = b2 – 4ac > 0 then the roots of the quadratic equation ax2 + bx + c = 0 are real and unequal.

Detailed Solution: Question 3

In the expression:

we can’t have values of 3 and – 5

As we will get forms in the expression which has no solution.

So, the assertion is correct.

D = b2 – 4ac > 0 then the roots of the quadratic equation ax2 + bx + c = 0 are real and unequal. The reason perfectly explains the roots of the equation whose D > 0. But it doesn’t explains the assertion.

Therefore, Both A and R are true and R is not correct explanation for A.

Assertion & Reason Test: Quadratic Equation - Question 4
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): The equation 8x2 + 3kx + 2 = 0 has equal roots than the value of k is ±

Reason (R): The equation ax2 + bx + c = 0 has equal roots if D = b2 – 4ac = 0.

Detailed Solution: Question 4

Reason perfectly explains the nature of roots when D = 0 for any quadratic equation.

Let us apply the reason on the equation,

8x2 + 3kx + 2 = 0

D = b2 – 4ac = 0

⇒ (3k)2 – 4(8) (2) = 0

⇒ 9k2 – 64 = 0

⇒

Assertion & Reason Test: Quadratic Equation - Question 5
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Directions: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): Values of x are a for the quadratic equation 2x2 + ax – a2 = 0.

Reason (R): For a quadratic equation ax2 + bx + c = 0, the roots are given by
x = (-b ± √(b2 - 4ac)) / 2a.

Detailed Solution: Question 5

The Reason (R) statement correctly states the quadratic formula for roots of the equation ax2 + bx + c = 0, which is:

x = (-b ± √(b2 - 4ac)) / 2a.

Let us apply this formula to the equation 2x2 + ax – a2 = 0:

Here, a = 2, b = a, and c = -a2.

Roots are:

x = (-a ± √(a2 - 4 × 2 × (-a2))) / (2 × 2)
= (-a ± √(a2 + 8a2)) / 4
= (-a ± √(9a2)) / 4
= (-a ± 3a) / 4

Therefore the roots are:

(-a + 3a) / 4 = 2a / 4 = a / 2

and

(-a - 3a) / 4 = -4a / 4 = -a

So the roots are x = a/2 and x = -a, which means the assertion that values of x are a is incorrect.

Hence, Assertion (A) is false, but Reason (R) is true.

Assertion & Reason Test: Quadratic Equation - Question 6
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): Sum of ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Then the difference between their ages is 16.

Reason (R): For quadratic equation ax2 + bx + c = 0,

Detailed Solution: Question 6

Present age of 1st friend = x years

Present age of 2nd friend = 20 – x years

4 years ago, age of 1st friend = x – 4

Age of 2nd friend = 16 – x years

According to the question,

(x – 4)(16 – x) = 48

⇒ 16 x – x2 – 48 + 4x = 48

⇒ x2 – 20x + 112 = 0

⇒ D = b2 – 4ac = (–20)2 – 4(1)(112) = – 48

Roots of the equation would be imaginary which is not possible for ages.

Hence, the situation is wrong.

Therefore, A is false but R is true.

Assertion & Reason Test: Quadratic Equation - Question 7
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): The roots of the quadratic equation x2 + 2x + 2 = 0 are imaginary.

Reason (B): If discriminant D = b2 – 4ac < 0 then the roots of the quadratic equation ax2 + bx + c = 0 are imaginary.

Detailed Solution: Question 7

Let us apply the reason on the equation,

x2 + 2x + 2 = 0

D = b2 – 4ac = (2)2 – 4(1)(2) = 4 – 8 = – 4

is unreal.

No real value is possible in this case.

Therefore, Both A and R are true and R is the correct explanation for A.

Assertion & Reason Test: Quadratic Equation - Question 8
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): If we solve the equation of the form 9(x+2) – 6.(3)(x+1) + 1 = 0, then x = – 2.

Reason (R): The equation of the form x2a + xb + b = 0 can’t be solved by quadratic formula.

Detailed Solution: Question 8

9(x+2) – 6.(3)(x+1) + 1 = 0

9x.92 – 6.3x.31 + 1 = 0

Or 81(3x)2 – 18.3x + 1 = 0

Let 3x = y So the equation becomes, 81y2 – 18y + 1 = 0 Which is a quadratic equation and its zeroes are 1/9, 1/9

Which contradicts the reason.

Therefore, A is true but R is false

Assertion & Reason Test: Quadratic Equation - Question 9
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): The equation has no root.

Reason (R): x - 1 ≠ 0, then only above equation is defined.

Detailed Solution: Question 9

Both A and R are true and R is the correct explanation of A.

x = 1

However at x = 1 the expression is not defined.

Hence the above equation has no real roots.

Assertion & Reason Test: Quadratic Equation - Question 10
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : The equation x2 + 3x+1 = (x - 2)2 is a quadratic equation.

Reason : Any equation of the form ax2 + bx + c = 0 where a ≠ 0 , is called a quadratic equation.

Detailed Solution: Question 10

We have, x2 + 3x + 1 = (x - 2)2 = x2 - 4x + 4

⇒ x2 + 3x + 1 = x2 - 4x + 4

⇒ 7x - 3 = 0 ,

it is not of the form ax2 + 6x + c = 0

So, A is incorrect but R is correct.

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About this Class 10 Practice Test

This test contains 10 MCQs on Assertion & Reason Test: Quadratic Equation with detailed solutions for each question. It is part of the Mathematics (Maths) Class 10 course on EduRev, designed to align with the current Class 10 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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