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Match the columns. {:("Column-I","Colu...

Match the columns.
`{:("Column-I","Column-II"),("(p)Number of line (s)passing through two given points is" ,(1) "Nine"),("(Q)Number of rays(s) can be drawn with same intial point is",(2)"Zero"),("(R )The number of points of intersection of three parallel lines is" ,(3) "One"),("(S)Number of diagonals in a six sided polygon is" ,(4) "Infinite"):}`

A

`(P)rarr(3),(Q)rarr(4),(R )rarr(2),(S)rarr(1)`

B

`(P)rarr(3),(Q)rarr(1),(R )rarr(2),(S)rarr(4)`

C

`(P)rarr(4),(Q)rarr(2),(R )rarr(1),(S)rarr(3)`

D

`(P)rarr(4),(Q)rarr(3),(R )rarr(2),(S)rarr(1)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of matching the columns, we will analyze each statement in Column I and find the corresponding answer in Column II. ### Step 1: Analyze Statement (p) **Statement (p):** Number of lines passing through two given points. - When we have two distinct points, there is exactly **one line** that can be drawn through both points. - **Match:** (p) matches with (3) "One". ### Step 2: Analyze Statement (Q) **Statement (Q):** Number of rays that can be drawn with the same initial point. - A ray has a fixed starting point and extends infinitely in one direction. From a single point, we can draw an infinite number of rays in different directions. - **Match:** (Q) matches with (4) "Infinite". ### Step 3: Analyze Statement (R) **Statement (R):** The number of points of intersection of three parallel lines. - Parallel lines never intersect, so the number of intersection points among three parallel lines is **zero**. - **Match:** (R) matches with (2) "Zero". ### Step 4: Analyze Statement (S) **Statement (S):** Number of diagonals in a six-sided polygon. - The formula for finding the number of diagonals in a polygon is given by: \[ \text{Number of diagonals} = \frac{n(n-3)}{2} \] where \( n \) is the number of sides. For a six-sided polygon (hexagon): \[ \text{Number of diagonals} = \frac{6(6-3)}{2} = \frac{6 \times 3}{2} = \frac{18}{2} = 9 \] - **Match:** (S) matches with (1) "Nine". ### Final Matches: - (p) → (3) "One" - (Q) → (4) "Infinite" - (R) → (2) "Zero" - (S) → (1) "Nine" ### Summary of Matches: - (p) → (3) - (Q) → (4) - (R) → (2) - (S) → (1)
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