Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - EmSAT Achieve MCQ

Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - EmSAT Achieve MCQ

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10 Questions MCQ Test Mathematics for EmSAT Achieve - Test: Linear Equations in Two Variables- Assertion & Reason Type Questions

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Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 1

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If x = 2, y = 1 is a solution of the equation 2x + 3y = k, then the value of k is 7.Reason : The solution of the line will satisfy the equation of the line.

Detailed Solution for Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 1
We know that the solution of the line will satisfy the equation of the line.

So, Reason is correct.

Since x = 2, y =1 is a solution of the given linear equation, we have 2 x 2 + 3 x 1 – k = 0 ⇒ 4 + 3 – k = 0 ⇒ k =7.

So, Assertion is also correct Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 2

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : There are infinite number of lines which passes through (3, 2).Reason : A linear equation in two variables has infinitely many solutions.

Detailed Solution for Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 2
We know that a linear equation in two variables has infinitely many solutions. So, Reason is correct.

Through a point infinite lines can be drawn.

Through (3, 2) infinite number of lines can be drawn.

Hence, Assertion is also correct.

But reason (R) is not the correct explanation of assertion (A).

Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).

Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 3

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 point (3, 0) lies on the graph of the linear equation 4x + 3y = 12.Reason : (3, 0) satisfies the equation 4x + 3y = 12.

Detailed Solution for Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 3
For Assertion: The given linear equation is 4x + 3y = 12 Substituting x = 3 and y = 0, we get LHS = 4 x 3 + 3 x 0 = 12 + 0 = 12 = RHS Since (3, 0) satisfies the equation 4x + 3y = 12, therefore point (3, 0) lies on the graph of the linear equation 4x + 3y = 12.

So, Reason and Assertion are both correct. Here, Reason is the correct explanation of Assertion.

Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 4

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

Assertion: x = 2 is a line parallel to the y-axis.

Reason: The equation of a line parallel to the y-axis is x = a.

Detailed Solution for Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 4
We know that equation of a line parallel to the y-axis is x = a. So, Reason (R) is true.

Also, x = 2 is a line parallel to the y-axis. So, Assertion (A) is true.

Thus, Reason (R) and Assertion (A) are true and Reason (R) is a correct explanation of Assertion (A).

Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 5

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

Assertion: y = 3x represents a line passing through the origin.

Reason: Any line parallel to the x-axis is y = a.

Detailed Solution for Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 5
Since x = 0 and y = 0 is not satisfying y = 3x, therefore it is passing through the origin.

So, Assertion (A) is true.

Also, we know that equation of a line parallel to the x-axis is y = a.

So, Reason (R) is also true.

But Reason is not the correct explanation of Assertion.

Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).

Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 6

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

Assertion : A linear equation 3x + 5y = 2 has a unique solution.

Reason : A linear equation in two variables has infinitely many solutions.

Detailed Solution for Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 6
We know that a linear equation in two variables has infinitely many solutions.

So, Reason is correct.

Hence, Assertion is not correct Correct option is (d) Assertion (A) is false but reason (R) is true.

Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 7

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

Assertion : If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, then the value of k is 10

Reason : A linear equation in two variables has infinitely many solutions.

Detailed Solution for Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 7
We know that a linear equation in two variables has infinitely many solutions. So, Reason is correct.

Since x = 2k -1 and y = k is solution of the given linear equation, we have 3 x (2k -1) -5k -7 = 0 ⇒ 6k -3 -5k -7 = 0 ⇒ k -10 = 0 ⇒ k = 10.

So, Assertion is also correct

But reason (R) is not the correct explanation of assertion (A).

Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).

Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 8

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

Assertion: x = 3 and y = 2 is a solution of the linear equation 2x + 3y = 12.

Reason: x = 4 and y = 2 is a solution of the linear equation x + 3y = 10.

Detailed Solution for Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 8
For Assertion: The given linear equation is 2x + 3y = 12 Substituting x = 3 and y = 2, we get LHS = 2 x 3 + 3 x 2 = 6 + 6 = 12 = RHS So, Assertion is correct.

For Reason: The given linear equation is x + 3y = 10 Substituting x = 4 and y = 2, we get LHS = 4 + 3 x 2 = 4 + 6 = 10 = RHS So, Reason is also correct. But reason (R) is not the correct explanation of assertion (A).

Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).

Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 9

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 graph of the linear equation 2x – y = 1 passes through the point (2, 3).

Reason : Every point lying on graph is not a solution of 2x – y = 1.

Detailed Solution for Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 9
For Assertion: The given linear equation is 2x – y = 1

Substituting x = 2 and y = 3, we get

LHS = 2 x 2 – 3 = 4 – 3 = 1 = RHS

Since (3, 0) satisfies the equation 4x + 3y = 12, therefore graph of the linear equation 2x – y = 1 passes through the point (2, 3).

So, Assertion is correct.

But Reason is not correct as every point lying on graph is a solution of

2x – y = 1.

Correct option is (c) Assertion (A) is true but reason (R) is false.

Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - 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: x + y = 3 is the equation of a line passing through the origin.

Reason: y = 2x is the equation of a line passing through the origin.

Detailed Solution for Test: Linear Equations in Two Variables- Assertion & Reason Type Questions - Question 10
For Assertion: The given linear equation is x + y = 3

Since x = 0 and y = 0 is not satisfying x + y = 3, therefore it is not passing through the origin.

So, Assertion is not correct.

Since x = 0 and y = 0 is not satisfying y = 2x, therefore it is passing through the origin.

So, Reason is correct. Correct option is (d) Assertion (A) is false but reason (R) is true.

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