How many integral solutions are there to x+y+z+t=29, when `xge1,y gt 1, z ge3 and t ge0`?

Let N be the number of integral solution of the equation x+y+z+w=15" where " x ge 0, y gt 5, z ge 2 and w ge 1 . Find the unit digit of N.

The number of integral solutions of equation x+y+z+t=29, when x >= 1, y >= 2, z>=2, 3 and t >= 0 is

The number of integral solutions of the inequation x+y+z le 100, (x ge 2, y ge 3, z ge 4) , is

The number of integers solutions for the equation x+y+z+t=20 , where x,y,z t are all ge-1 , is

Number of integral solutions of 2x+y+z=10 (xge0,yge0,Zge0) is

3x + 2y le 12, x ge 1, y ge 2

The number of the positive integral solutions (x,y, z) of the equation xyz = 24 is t, then the number of all possible factors of t is

If the number of integral solutions (x, y, z) of the equation xyz = 18 is t, then the value of (t)/(8) is

Using integration, find the area of the region {(x,y) : x^(2) +y^(2) le 1, x+y ge 1, x ge 0, y ge 0}

2x + y ge 6, x + 2y ge 8, x ge 0, y ge 0