Short Quiz

Question 1 of 5

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.

Select one option. Answers are shown after the test.

Question 2 of 5

Assertion (A): The line passing through \( (2, 3) \) and \( (4, 5) \) is perpendicular to the line passing through \( (3, 4) \) and \( (5, 2) \).

Reason (R): Two non-vertical lines are perpendicular to each other if and only if the product of their slopes is \( 1 \) (i.e., \( m_1 m_2 = 1 \)).

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.

Select one option. Answers are shown after the test.

Question 3 of 5

Assertion (A): The distance of the point \( (0, 0) \) from the line \( 3x - 4y + 10 = 0 \) is \( 2 \).

Reason (R): The perpendicular distance of a line \( Ax + By + C = 0 \) from a point \( (x_1, y_1) \) is \( d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}} \).

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 4 of 5

Assertion (A): The equation of the line passing through \( (1, 2) \) with slope \( 3 \) is \( 3x - y - 1 = 0 \).

Reason (R): The equation of a line passing through the point \( (x_1, y_1) \) with slope \( m \) is \( y - y_1 = m(x - x_1) \).

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.

Select one option. Answers are shown after the test.

Question 5 of 5

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.

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular