golu23 wrote:1)In the rectangular co-ordinate system does the line K intersect quadrant II?
a) The slope of K is-1/6
b) The y intercept of K is -6

The answer to this question lies in the facts that:
1. If slope of a line is positive then,
A) It'll always intersect 1st and 3rd quadrant.
B) It'll intersect 2nd quadrant if the y-intercept is positive.
C) It'll intersect 4th quadrant if the y-intercept is negative.
D) It'll not intersect 2nd or 4th quadrant and pass through origin if y-intercept is zero.

2. If slope of a line is negative then,
A) It'll always intersect 2nd and 4th quadrant.
B) It'll intersect 1st quadrant if the y-intercept is positive.
C) It'll intersect 3rd quadrant if the y-intercept is negative.
D) It'll not intersect 1st or 3rd quadrant and pass through origin if y-intercept is zero.

There is mathematical proof for all of these. But better way to understand them is draw various types of lines in the xy plane and try to visualize each of the cases individually. Let me know if you have any problem.

(1) Slope of k is -1/6
As the slope of k is negative it'll always intersect 2nd and 4th quadrant; SUFFICIENT.

(2) y-intercept of k is -6
If slope of k is negative it'll always intersect 2nd quadrant.
But if slope of k is positive then it'll not intersect 2nd quadrant as the y-intercept is negative; NOT sufficient.

The correct answer is A.

golu23 wrote: 2)If the speed of X meter/ seconds is equivalent to the speed of y km/second what is y in terms of X?
a)5x/18 b)6x/5 c)18x/5 d)16x e)3600000x

I think it should be y km/hr. Please check that.

1 m = 1/1000 km and 1 hr = 3600 sec
So, x m/s = x * 3600/1000 km/hr = [spoiler]18x/5 km/hr[/spoiler]

The correct answer is C.

We can also use the picking numbers approach here. We can pick any small value for x and then solve.