Permutations an...

The total number of ways of arranging the letters $$AAABBBCCDEF$$ in a row such that letters $$C$$ are separated from one another is

If $$64a^2+36b^2=400, ab=4 $$ , then $$8a+6b$$ is: 

There is a defined relationship between the pair of figure on either side of : :. Identify the relationship of the given pair and find be the missing figure.

The number of positive integral solutions of the equation $$x _ { 1 } x _ { 2 } x _ { 3 } x _ { 4 } x _ { 5 } = 1050$$ is

If the area of triangle formed by the points $$(2a,b),(a+b,2b+a)$$ and $$(2b,2a)$$ be $$\lambda$$ then the area of the triangle whose vertices are $$(a+b,a-b), (3b-a,b+3a)$$ and $$(3a-b,3b-a)$$ will be

If $$(1+x+x^2)^n=\displaystyle\sum^{2n}_{r=0}a_rx^r$$, then $$a_0a_{2r}-a_1a_{2r+1}+a_2a_{2r+2}-....=?$$

If repetitions are not allowed, the number of numbers consisting of $$4$$ digits and divisible by $$5$$ and formed out of $$0,1,2,3,4,5,6$$ is 

A Printer number the pages of a book starting with $$1$$ and used $$3193$$ digit in all. How many pages does the book have:

The number of permutations of letters of the word "PARALLAL" atken four at a time must be, 

$$\sum _{ k=1 }^{ 10 }{ k.k! } =$$