The number of three digit numbers of the form xyz such that `x lt y , z le y and x ne0`, is

The number of whole number solutions of x + y + z = 20 is

Find the total number of positive integral solutions for (x ,y ,z) such that x y z=24. Also find out the total number of integral solutions.

If alpha, beta, gamma are the cube roots of a negative number p, then for any three real numbers x,y,z the value of (x alpha+y beta+ z gamma)/(x beta +y gamma+z alpha) is

The first three terms of a geometric sequence are x , y , z and these have the sum equal to 42 . If the middle term y is multiplied by 5//4 , the numbers x , (5y)/(4) , z now form an arithmetic sequence. The largest possible value of x is

Let RR be the set of all real numbers. Consider the following subsets of the plane RRxxRR :S = { (x,y) : y=x+1 and 0 lt x lt 2 } and T = { (x,y) : x-y is an integer }. Then which of the following is true ?

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,y,z be three numbers in G.P. such that 4 is the A.M. between x and y and 9 is the H.M. between y and z , then y is

Maximise Z=x+y subject to x-y lt 1, -x+y, le 0, x,y ge 0

x+y le 9. y gt x, x ge 0

Let N be the number of points (x, y, z) in space such that x+y+z=12 , where x, y, z in N . The number of divisors of N is equal to