The determinant `|[^xC_1 ,^xC_2 ,^xC_3],[^yC_1 ,^yC_2 ,^yC_3],[^zC_1 ,zC_2 ,zC_3]|` is equal to-

Evaluate: |[^xC_1, ^xC_2, ^xC_3],[^yC-1, ^yC_2, ^yC_3],[^zC_1, ^zC_2, ^zC_3]|

The determinant |^(^^)xC_(1),^(x)C_(2),^(x)C_(3)^(^^)yC_(1),^(y)C_(2),^(y)C_(3)sim zC_(1),zC_(2),zC_(3)] is equal to-

Evaluate det[[x_(C_(1)),x_(C_(2)),x_(C_(3))y_(C_(1)),y_(C_(2)),yC_(3)z_(C_(1)),z_(C_(2)),z_(C_(3))]]

int xc^(2e)dx

Without expanding show that : |(""^xC_r,""^xC_(r+1),""^xC_(r+2)),(""^yC_r,""^yC_(r+1),""^yC_(r+2)),(""^zC_r,""^zC_(r+1),""^zC_(r+2))|=|(""^xC_r,""^(x+1)C_(r+1),""^(x+2)C_(r+2)),(""^yC_r,""^(y+1)C_(r+1),""^(y+2)C_(r+2)),(""^zC_r,""^(z+1)C_(r+1),""^(z+2)C_(r+2))|

find out missing term ZA_5,Y _4 B, XC_6 , W_3,D, ? .

If x, y and r are positive integers , then : ""^xC_r+""^rC_(r-1)""^yC_1+^xC_(r-2)""^yC_2+..........+""^yC_r =

If a,b,g,d,e and f are in GP,then the value of [[a^(2),d^(2),xb^(2),e^(2),yc^(2),f^(2),z]| depends on

Using properties of determinants, prove that |(a^2+2a, 2a+1,1), (2a+1, a+2, 1), (3,3,1)| = (a-1)^3