Permutations an...

If $\displaystyle\sum^m_{k=1}(k^2+1)k!=1999(2000!)$, then m is?

If $24 + 37 = 7,12 + 18 = 3$, then 54+21=?

In the following number series,one number is wrong.find out the ?

1,2,8,33,149,765,4626

How many Pythagorean triangles are there with integer sides and one leg is Ramanujan Number 1729 .

The number of the three digits numbers having only two consecutive digits identical is:

$10$ IIT and $2$ NIT students sit at random in a row, and then number of ways in which exactly $3$ IIT students sit between $2$ NIT students is

The number of 5 letter words formed  using letters of word "CALCULUS" is  

Find the missing number, if a certain rule is followed

Direction: In a given question, one number is missing in the series. you have to understand the pattern of the series and insert the number 
JN    28   27    GP
CE   12   45    TU
LR     ?     ?     MS

The area of the triangle whose co-ordinates are $(2012, 7), (2014, 7)$ and $(2014, a)$ is $1 \,sq$ unit. The sum of possible values of $a$ is