[" A rubber cube "C={(x,y,z)|0<=x,y,z<=1}" is cut by a sharp knife along the plane "x=y,y=z" and "],[z=x" if no piece is moved until all three cuts are made,then the number of pieces of "],[[" (A) "6," (B) "7," (C) "8," (D) "27]]

If a + b + c != 0 then the number solutions (x,y,z) to the system (b + c)(y + z) - ax = b - c (c + a)(z + x) - by = c - a (a + b) (x + y) - cz = a - b is

for every point (x,y,z) on the y-axis: (A) x=0,y=0 (B) x=0,z=0 (C) y=0,z=0 (D) y!=0,x=0,z=0

for every point (x,y,z) on the y-axis: (A) x=0,y=0 (B) x=0,z=0 (C) y=0,z=0 (D) y!=0,x=0,z=0

If x+y+z=0 prove that |a x b y c z c y a z b x b z c x a y|=x y z|a b cc a bb c a|

Let x, y, z are distinct cube roots of unity and the value of |[x,y-z,z-y],[x-z,y,z-x],[x-y,y-x,z]|=K then |K|

For every point (x\ , y ,\ z) on the x- axis (except the origin) a. x=0,\ y=0,\ z!=0 b. x=0,\ z=0,\ y!=0 c. y=0,\ z=0,\ x!=0 d. x=y=z=0

Direction: Read the following Caselet DI carefully and answer the following questions. 3 cubes P, Q, and R are cut from the cubes A, B, and C respectively. The length of the side of cube P is given by the equation x - 12x + 36 = 0 and the length of the side of cube A is 2 cm more than cube P. The length of the side of cube Q is given by the equation y + 21y - 46 = 0 and the length of the side of cube B is 3 cm more than cube Q. The length of the side of cube R is given by the equation z - 10z + 25 = 0 and the length of the side of cube C is 4 cm more than cube R. Here x, y, and z are in centimeter. The average length of side of cube P, B, and C is how much percent more or less than the average length of side of cube A, Q, and R?