Types of lines we can construct in xy-plane:
A. Vertical lines
B. Horizontal lines
C. Lines with +ve slope and +ve y-intercept
D. Lines with +ve slope and -ve y-intercept
E. Lines with -ve slope and +ve y-intercept
F. Lines with -ve slope and -ve y-intercept

NOTE: I'm going to use A, B, C, D, E and F for the respective lines

Total lines = \(35 = A + B + C + D + E + F\)

Given: \(C + D = 15\)
Now, C = \(\frac{1}{3}(15) = 5\)
Thus, \(D = 15 - 5 = 10\)

So, \(35 = 0 + B + 5 + 10 + E + F\)

Now, 23 lines have a y-intercept less than or equal to zero i.e. \(B + D + F = 23\)
Plugging \(D = 10\) from above;

\(B + 10 + F = 23\)
\(B + F = 13\)

Qs: Number of lines containing no point in the Quadrant I
This means all lines which have a -ve slope and -ve y-intercept i.e. Lines marked as \(F\)

Since, \(B + F = 13\)
Even if we assume that all the lines which are marked as \(B\) have y-intercept as \(0\) (in order to maximise \(F\)), still we have \(F\) (lines with -ve slope and -ve y-intercept) as \(13\) only

Col. A: 13
Col. B: 15

Col. A < Col. B
Hence, option B

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