Integer part1

If f(x)=(x^(3)+x+1)tan(pi[x]) (where, [x] represents the greatest integer part of x), then

Consider the function f(x)=cos^(-1)([2^(x)])+sin^(-1)([2^(x)]-1) , then (where [.] represents the greatest integer part function)

Let [x] denote the greatest integer part of a real number x, if M= sum_(n=1)^(40)[(n^(2))/(2)] then M equals

If f(x)=(x^(2)-[x^(2)])/(1+x^(2)-[x^(2)]) (where [.] represents the greatest integer part of x), then the range of f(x) is

Let f(x)=(x-[x])/(1+x-[x]),RtoA is onto then find set A. (where {.} and [.] represent fractional part and greatest integer part functions respectively) (a) (0,1/2] (b) [0,1/2] (c) [0,1/2) (d) (0,1/2)

If [x] and (x) are the integral part of x and nearest integer to x then solve (x)[x]=1

If x= (8 + 3 sqrt(7))^(n) , where n is a natural number, power that the integral part of x is an odd integer and also show that x - x^(2) + x[x] = 1 , where [.] denotes the greatest integer function .

The range of the function f defined by f(x)=[1/(sin{x})] (where [.] and {dot}, respectively, denote the greatest integer and the fractional part functions) is

Two integers are selected at random from the integers 1 to 9. If their sum is even, then find the probability that both integers are odd.

Two integers are selected at random from the integers 1 to 11. If their sum is even find the probability that both integers are odd.