Integer part 10

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

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

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

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

What will be the sign of the product if we multiply together (i) 8 negative integers and 1 positive integers? (ii) 21 negative integers and 3 positive integers? (iii) 199 negative integers and 10 positive integers?

Two numbers a and b are selected successively without replacement in that order from the integers 1 to 10.The probability that a/b is an integer, is

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

How many integers are there from 1,002 to 10,001?

If the sum of two integers is -10 and one of them is 2, then the other is