Integers part 2

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

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

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

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

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

Show that the following integers are cubes of negative integers. Also find the integer whose cube is the given integer. -5832 (ii) -2744000

Complex numbers whose real and imaginary parts x and y are integers and satisfy the equation 3x^(2)-|xy|-2y^(2)+7=0

The product of 12% of an integer and 20% of the next integer is 61.2. Find the integer.

Compare the integers : -2 and 0