If `x` is a positive number, then which of the following fractions has the greatest value? `x/x` (b) `x/(x+1)` (c) `(x+1)/x` (d) `(x+2)/(x+3)`

If 0 < x < 1 , which of the following is greatest ? x (b) x^2 (c) 1/x (d) 1/(x^2)

If x=10 and y=0.1, which of the following is the greatest? x^(2)+y^(2)( b) x^(2)-y^(2)( c) x^(2)backslash y^(2) (d) (x^(2))/(y^(2))

If x,y,z be three positive numbers such that xyz^(2) has the greatest value (1)/(64) , then the value of (1)/(x)+(1)/(y)+(1)/(z) is

If x is a positive real number and the exponents are rational numbers,show that: ((x^(a))/(x^(b)))^(a+b-c)((x^(b))/(x^(c)))^(b+c-a)((x^(c))/(x^(a)))^(c+a-b)=1

Assuming that x is a positive real number and a,b,c are rational numbers,show that: ((x^(a))/(x^(b)))^((1)/(ab))((x^(b))/(x^(c)))^((1)/(bc))((x^(c))/(x^(a)))^((1)/(ac))=1

Assuming that x is a positive real number and a,b,c are rational numbers,show that: ((x^(b))/(x^(c)))^(a)((x^(c))/(x^(a)))^(b)((x^(a))/(x^(b)))^(c)=1

Assuming that x is a positive real number and a,b,c are rational numbers,show that: ((x^(a))/(x^(b)))^(a+b)((x^(b))/(x^(c)))^(b+c)((x^(c))/(x^(a)))^(c+a)=1

If [x] and {x} represetnt the integral and fractional parts of x, respectively,then the value of sum_(r=1)^(2000)({x+r})/(2000) is (a)x (b) [x]( c) {x} (d) x+2001