Assertion Reasoning Quiz

Question 1 of 7

Assertion: The roads represented by \(y=2x+3\) and \(y=2x-5\) are parallel.
Reason: The perpendicular distance between the roads is \(\dfrac{8}{\sqrt5}\) units.

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

Select one option. Answers are shown after the test.

Question 2 of 7

Assertion (A): The line \( y = 2x + 3 \) is perpendicular to the line \( x + 2y = 5 \).

Reason (R): Two non-vertical lines are perpendicular if \( m_1 + m_2 = 0 \).

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

Select one option. Answers are shown after the test.

Question 3 of 7

Assertion (A): The lines \( x + y = 1 \), \( x - y = 1 \), and \( 2x = 2 \) are concurrent.

Reason (R): Three lines are said to be concurrent if they pass through a common point.

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

Select one option. Answers are shown after the test.

Question 4 of 7

Assertion: A line of slope \(3\) makes an acute angle of \(45^\circ\) with a line of slope \(\dfrac12\).
Reason: Both the slopes are positive.

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

Select one option. Answers are shown after the test.

Question 5 of 7

Assertion: The line \(x=4\) has an undefined slope.
Reason: For any two distinct points on \(x=4\), the difference of their \(x\)-coordinates is zero.

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

Select one option. Answers are shown after the test.

Question 6 of 7

Assertion (A): The lines represented by the equations \( 2x - 3y = 5 \) and \( 4x - 6y = 7 \) are parallel to each other.

Reason (R): Two non-vertical lines are parallel if and only if their slopes are equal (\( m_1 = m_2 \)).

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

Select one option. Answers are shown after the test.

Question 7 of 7

Assertion (A): The y-intercept of the line \( 2x - 3y = 6 \) is \( 2 \).

Reason (R): The equation \( y = mx + c \) represents a line with slope \( m \) and y-intercept \( c \).

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

Select one option. Answers are shown after the test.

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