Straight Lines ...

If $$A$$ and $$B$$ are two points having co-ordinates $$(3,4)$$ and $$(5,-2)$$ respectively and $$P$$ is a point such that $$PA=PB$$ and area of triangle $$PAB=10$$ square units, then the co-ordinates of $$P$$ are

The letters of word 'ZENITH' are written in all positive ways. If all these words are written in the order of a dictionary, then the rank of the word 'ZENITH' is

The next number in the pattern 62, 37, 12 ____ is

the area of a triangle with vertices $$ (-3, 0),(3,0) $$ and $$ (0, k) $$ is $$ 9 $$ sq units. then the value of $$ k $$ will be 

The number of distinct rational numbers x such that $$\displaystyle 0 < x < 1$$ and $$\displaystyle x = \frac{p}{q}r$$, where $$\displaystyle p,q \epsilon \left \{ 1,2,3,4,5,6 \right \}$$,is

The number of rectangles that can be obtained by joining four of the twelve vertices of a $$12$$ sided regular polygon is

Three vertices are chosen randomly from the seven vertices of a regular $$7$$ -sided polygon. The probability that they form the vertices of an isosceles triangle is

The number of ways in which three numbers in A.P. can be seleced from the set of first n natural number if n is odd is

If the difference of the number of arrangements of three things from a certain number of dissimilar things and the number of selections of the same number of things from them exceeds $$ 100$$, then the least number of dissimilar things is

If four points are $$A(6,3),B(-3,5),C(4,-2)$$ and $$P(x,y),$$ then the ratio of the areas of $$\triangle PBC$$ and $$\triangle ABC$$ is: