For a real number x let [x] denote the largest integer less than or equal to x and `{x}=x-[x]` Let n be a positive integer. Then `int_0^n cos(2pi)[x]{x})dx` is equal to

For a real number x let [x] denote the largest integer les than or eqaul to x and {x} =x -[x]. Let n be a positive integer. Then int_(0)^(1) cos(2pi[x]{x})dx is equal to

For a real number x let [x] denote the largest integer less than or equal to x and {x}=x-[x] . The possible integer value of n for which int_(1)^(n)[x]{x}dx exceeds 2013 is

For a real number x let [x] denote the largest integer less than or equal to x and {x}=x-[x] . The possible integer value of n for which int_(1)^(n)[x]{x}dx exceeds 2013 is

Let [x] denotes the greatest integer less than or equal to x and f(x)= [tan^(2)x] .Then

Let [x] denotes the greatest integer less than or equal to x and f(x)=[tan^(2)x] . Then

For a real number x let [x] denote the largest number less than or equal to x. For x in R let f (x)=[x] sin pix . Then

for a real number x, let [x] denote the largest unteger less than or equal to x , and let {x} = x-[x] . The number of solution x to the equation [x] {x} =5 with 0 le xle 2015 is -

For a real number x, let [x] denote the greatest integer less than or equal to x. Then f(x)=(tan(pi[x-pi]))/(1+[x]^(2)) is :