Assertion & Reason Test: Quadratic Equation - Class 10 MCQ

# Assertion & Reason Test: Quadratic Equation - Class 10 MCQ

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## 10 Questions MCQ Test - Assertion & Reason Test: Quadratic Equation

Assertion & Reason Test: Quadratic Equation for Class 10 2024 is part of Class 10 preparation. The Assertion & Reason Test: Quadratic Equation questions and answers have been prepared according to the Class 10 exam syllabus.The Assertion & Reason Test: Quadratic Equation MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Assertion & Reason Test: Quadratic Equation below.
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Assertion & Reason Test: Quadratic Equation - Question 1

### 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 for Assertion & Reason Test: Quadratic Equation - 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

### 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 for Assertion & Reason Test: Quadratic Equation - 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

### 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 – 5Reason (R): If discriminant D = b2 – 4ac > 0 then the roots of the quadratic equation ax2 + bx + c = 0 are real and unequal.

Detailed Solution for Assertion & Reason Test: Quadratic Equation - 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

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 for Assertion & Reason Test: Quadratic Equation - 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

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 a quadratic equation 2x2 + ax – a2 = 0.

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

Detailed Solution for Assertion & Reason Test: Quadratic Equation - Question 5
Reason is correct as the formula to find roots of an equation is x =

let us verify the reason on the equation

2x2 + ax – a2 = 0

That means a are not the zeroes.

Therefore, A is false but R is true.

Assertion & Reason Test: Quadratic Equation - Question 6

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 for Assertion & Reason Test: Quadratic Equation - 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

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 for Assertion & Reason Test: Quadratic Equation - 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

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 for Assertion & Reason Test: Quadratic Equation - 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

Therefore, A is true but R is false

Assertion & Reason Test: Quadratic Equation - Question 9

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 for Assertion & Reason Test: Quadratic Equation - 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

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 for Assertion & Reason Test: Quadratic Equation - 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.