Assertion and Reason Questions for Class 10 Maths Chapter 4 Quadratic Equations PDF

Assertion And Reason Questions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables are available in this Maths article. These questions are very useful for solving problems easily. This article helps students understand the key questions and answers about Pair of Linear Equations in Two Variables. Pair of linear equations in two variables help us solve problems with two unknowns using equations, graphs, and real-life situations. Our subject experts have provided detailed solutions based on the CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination. A free downloadable PDF is also available for easy practice and revision.

Important Assertion And Reason Questions on Quadratic Equations

Directions: In the following questions a statement of assertion (A) is followed by a statement of reason(R). Mark the correct choice as:

Choose the correct option for the following questions:

• (A). Both Assertion (A) and Reason (R) are true, and Reason is the correct explanation of Assertion.

• (B). Both Assertion (A) and Reason (R) are true, but Reason is not the correct explanation of Assertion.

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

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

Question 1:
Assertion (A): An equation of the formax2+bx+c=0, where  a≠0, is called a quadratic equation.

Reason (R): The highest power of the variable in a quadratic equation is 2.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 2:

Assertion (A): The equationx2−5x+6=0has roots 2 and 3.

Reason (R): The equation can be factorised as:x2−5x+6=(x−2)(x−3)

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 3:

Assertion (A): A quadratic equation can have at most two real roots.

Reason (R): The degree of a quadratic equation is 2.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 4:

Assertion (A): The roots of the equationx2+4x+4=0are equal.

Reason (R): The discriminant of the equation is zeroD=b2−4ac

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 5:

Assertion (A): The equationx2+1=0has no real roots.

Reason (R): The discriminant of the equation is negative.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 6:

Assertion (A): The roots of the equation2x2−7x+3=0are rational.

Reason (R): The discriminant of the equation is a perfect square.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 7:

Assertion (A): Completing the square is a method used to solve quadratic equations.

Reason (R): In this method, the quadratic expression is converted into a perfect square trinomial.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 8:

Assertion (A): The quadratic formula can solve every quadratic equation.

Reason (R): The quadratic formula gives the roots directly in terms of coefficients.

x=−b±b2−4ac2a}

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 9:

Assertion (A): The sum of the roots of ax2+bx+c=0is:−ba

Reason (R): The product of the roots is:ca

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (B). Both A and R are true, but R is not the correct explanation of A.

Question 10:

Assertion (A): The equationx2−9=0has roots 3 and−3.

Reason (R): The equation can be factorised as:x2−9=(x−3)(x+3)

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 11:

Assertion (A): A quadratic equation may have imaginary roots.

Reason (R): If the discriminant is negative, the roots are not real.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 12:

Assertion (A): The equationx2−4x+4=0has equal roots.

Reason (R): The equation is a perfect square.

x2−4x+4=(x−2)2

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 13:

Assertion (A): The roots of  x2−2x−3=0 are 3 and−1.

Reason (R): The equation can be factorised as:x2−2x−3=(x−3)(x+1)

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 14:

Assertion (A): The graph of a quadratic equation is a parabola.

Reason (R): A quadratic equation contains the square of the variable.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 15:

Assertion (A): The equationx2−16=0has roots 4 and−4.

Reason (R): The equation represents the difference of two squares.

x2−16=(x−4)(x+4)

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

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