In the relation `x > y+z ,\ x+y > p\ a n d\ z < p` which of the following is true? (a) `y > p` (b) `x+y > z` (c) `y+p > x` (d) insufficient data

The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

If a,x,b are in A.P.,a,y,b are in G.P. and a,z,b are in H.P. such that x=9z and a>0, b>0, then (a) y=3z. (b) x=3y (c) 2y= x+z (d) none of these

The determinant |[x p+y, x, y], [y p+z, y, z],[0,x p+y, y p+z]|=0 if (a) x y z are in AP (b) x y z are in GP (c) x y z are in HP (d) xy yz zx are in AP

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

The minimum value of P=b c x+c a y+a b z , when x y z=a b c , is