Differentiation...

A box contains 5 pairs of shoes. If 4 shoes are selected, then the number of ways in which exactly one pair of shoes obtained is :

The number of intersection points of diagonals of $$2009$$ sides polygon, which lie  inside the polygon.

The midpoints of the sides of a triangle are $$\left(1,1\right),\left(4,3\right)$$ and $$\left(3,5\right)$$. The area of the triangle is ___ square units.

Ten persons, amongst whom are $$A$$,$$B$$ and $$C$$ to speak at a function. The number of ways in which it can be done if $$A$$ wants to speak before $$B$$ AND $$B$$ wants to speak before $$C$$ is 

Let $$p=\dfrac{1}{1\times2}+\dfrac{1}{3\times4}+\dfrac{5}{1\times6}+.......+\dfrac{1}{2013\times2014}$$ and $$Q=\dfrac{1}{1008\times2014}+\dfrac{1}{1009\times2013}+.........+\dfrac{1}{2014\times1008}$$
then $$\dfrac{P}{Q}=$$

The number of ways in which a mixed doubles tennis game can be arranged between 10 players consisting of 6 men and 4 women is . 

If $$a{x^2} + 2hxy + b{y^2} = 0$$ then $$\frac{{dy}}{{dx}}$$ is equal to

solve that :- 

The number of permutation of the letters of the word $$HINDUSTAN$$ such that neither the pattern $$'HIN'$$ nor $$'DUS'$$ nor $$'TAN'$$ appears, are :

In the following question, groups of letters are  given. Find the odd one out.