`"^(21)C_0` +` "^(21)C_1 `+ `"^(21)C_2` +……+`"^(21)C_19` + `"^(21)C_(20)` is equal to

The sum S = ""^(20)C_(2) + 2*""^(20)C_(3) + 3 *""^(20)C_(4) + ...+ 19 * ""^(20)C_(20) is equal to

The value of (.^(21)C_(1) - .^(10)C_(1)) + (.^(21)C_(2) - .^(10)C_(2)) + (.^(21)C_(3) - .^(10)C_(3)) + (.^(21)C_(4) - .^(10)C_(4)) + "…." + (.^(21)C_(10) - .^(10)C_(10)) is

int_-1^1(x^19+x^21)dx is equal to :

If A = [(1,0),(1/2,1)] , then A^100 is equal to

Solve: 1/(22) + (21)/(22)

If A = ([2,1],[1,2]) , then A (Adj A) equals :

If A = [(2,2),(-2,1)] , Find A^(-1) .

If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}| and C_(ij)=(-1)^(i+j) M_(ij), "where " M_(ij) is a determinant obtained by deleting ith row and jth column then then |{:(C_(11),C_(12),C_(13)),(C_(21),C_(22),C_(23)),(C_(31),C_(32),C_(33)):}|=Delta^(2). Suppose a,b,c, in R, a+b+c gt 0, A =bc -a^(2),B =ca-b^(2) and c=ab-c^(2) and |{:(A,B,C),(B,C,A),(C,A,B):}| =49 then the valu of a^(3)+b^(3)+c^(3) -3abc is