Differentiation...

Ten points lie in a plane so that no three of them are collinear. The number of lines passing through exactly two of these points are dividing the plane into two regions each containing four of the remaining points is 

Area of the triangle formed by the points $$(0,0),(2,0)$$ and $$(0,2)$$ is

If $$y = \dfrac {1}{1 + x + x^{2}}$$, then $$\dfrac {dy}{dx}$$ is equal to

Out of $$7$$ consonants and $$4$$ vowels, words are formed each having $$3$$ consonants and $$2$$ vowels. The number of such words that can be formed is

Find the term independent of $$x$$ in $${ \left( \cfrac { 3 }{ 2 } { x }^{ 2 }-\cfrac { 1 }{ 3x }  \right)  }^{ 9 }$$.

Consider an incomplete pyramid of balls on a square base having $$18$$ layers; and having $$13$$ balls on each side of the top layer. Then the total number $$N$$ of balls in that pyramid satisfies

If $$f(x)=\left| \log { \left| x \right|  }  \right| $$, then

Choose $$3, 4, 5$$ points other than vertices respectively on the sides $$AB, BC$$ and $$CA$$ of a $$\triangle ABC$$. The number of triangles that can be formed by using only these points as vertices, is

If $$ y^x = 2^x , $$ then $$ \dfrac {dy}{dx} $$ is equal to :

If $$\alpha ,\beta , \gamma $$ are three consecutive integers. If these integers are raised to first, second and third positive powers respectively, and added then they form a perfect square, the square root of which is equal to the sum of these integers. Also, $$\alpha < \beta < \gamma $$. Then, $$\gamma$$ is equals to: