Assertion Reasoning Quiz

Question 1 of 7

Assertion (A): The equation of the line making intercepts \( 2 \) and \( 3 \) on the x-axis and y-axis respectively is \( 3x + 2y = 6 \).

Reason (R): The equation of a line making intercepts \( a \) and \( b \) on the x- and y-axes respectively is given by the intercept form \( \frac{x}{a} + \frac{y}{b} = 1 \).

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.

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Question 2 of 7

Assertion (A): The acute angle between the lines \( y = x \) and \( y = 0 \) is \( 45^\circ \).

Reason (R): The acute angle \( \theta \) between two lines with slopes \( m_1 \) and \( m_2 \) is given by \( \tan \theta = \left|\frac{m_2 - m_1}{1 + m_1 m_2}\right| \).

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.

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Question 3 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.

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Question 4 of 7

Assertion: If the \(x\)-axis acts as a plane mirror, the image of the point \((2,3)\) is \((-2,3)\).
Reason: Reflection in the \(x\)-axis keeps the \(x\)-coordinate unchanged and reverses the sign of the \(y\)-coordinate.

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.

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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.

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Question 6 of 7

Assertion (A): The points \( (1, 5) \), \( (2, 3) \), and \( (-2, -11) \) are collinear.

Reason (R): Three points A, B, and C are collinear if and only if the slope of AB is equal to the slope of BC.

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.

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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.

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Assertion Reasoning Quiz