Assertion and Reason Questions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables PDF

Assertion And Reason Questions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables are available in this Maths article. Assertion And Reason Questions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables are very useful to solve the problems easily. This article helps the students to know 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 for these problems 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 Pair of Linear Equations in Two Variables

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): A pair of linear equations in two variables can have a unique solution.

Reason (R): Two intersecting lines always meet at exactly one point.

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 equations 2x + 3y = 5 and 4x + 6y = 10 represent coincident lines.

Reason (R):

The ratios of corresponding coefficients are equal.

a1a2=b1b2=c1c2

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): Two parallel lines have no common solution.

Reason (R): Parallel lines never intersect each other.

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): If two linear equations intersect at one point, then the system is consistent.

Reason (R): A consistent system has at least one solution.

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 equations x + y = 4 and 2x + 2y = 8 have infinitely many solutions.

Reason (R): Both equations represent the same straight line.

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 substitution method can be used to solve a pair of linear equations.

Reason (R): In the substitution method, one variable is replaced using the value from another equation.

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): If a1a2≠b1b2then the pair of linear equations has a unique solution.

Reason (R): The lines intersect at one point when their slopes are different.

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): A pair of inconsistent equations has no solution.

Reason (R): Inconsistent equations represent intersecting lines.

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: (C). A is true, but R is false.

Question 9:

Assertion (A): The elimination method removes one variable to solve equations.

Reason (R): The coefficients of one variable are made equal before subtraction or addition.

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 10:

Assertion (A): The graphical solution of two equations is the point where the lines intersect.

Reason (R): The intersection point satisfies both equations simultaneously.

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): The equations 3x + 2y = 7 and 6x + 4y = 12 are inconsistent.

Reason (R): The ratios of coefficients satisfy:a1a2=b1b2≠c1c2

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): Coincident lines have infinitely many common points.

Reason (R): Coincident lines overlap completely.

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 equations x − y = 2 and 2x − 2y = 4 represent the same line.

Reason (R): One equation is obtained by multiplying the other equation by 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 14:

Assertion (A): The pair of equations x + y = 3 and x + y = 5 has no solution.

Reason (R): The lines represented by the equations are parallel.

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): A system of equations can be solved graphically.

Reason (R): The common point of the graphs gives the solution of the equations.

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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