Permutations an...

The coefficient of $$x^{18}$$ in the expansion of $$(1+x)(1-x)^{10}\{(1+x+x^2)^9\}$$ is?

The area of a triangle with vertices $$A(5,0),B(8,0)$$ and $$C(8,4)$$ in square units is 

Area of the triangle with vertices $$(-2,2), (1,5)$$ and $$(6,-1)$$ is 

If $$\dfrac{1}{6!}+\dfrac{1}{7!}=\dfrac{x}{8!}$$, then $$x=?$$

The vertices of a $$\triangle ABC$$ are $$A(3,8),B(-4,2)$$ and $$C(5,-1)$$. The area of $$\triangle ABC$$ is

The exponent of 3 in $$100!$$ is 

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

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