Short Quiz

Question 1 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 2 of 5

The slope of the line passing through the points \((3,-2)\) and \((-1,4)\) is

A \(\dfrac{3}{2}\) B \(-\dfrac{2}{3}\) C \(-\dfrac{3}{2}\) D \(\dfrac{2}{3}\)

Select one option. Answers are shown after the test.

Question 3 of 5

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 4 of 5

Assertion: A taxi charges a fixed booking fee of ₹50 and ₹12 per kilometre. If \(x\) is the distance in kilometres and \(y\) is the total fare, then \(y=12x+50\).
Reason: In \(y=mx+c\), the \(y\)-intercept \(c\) is the value of \(y\) when \(x=0\).

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 5

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.

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