If `{:X=[(3,-4),(1,-1)]:}`, the value of `X^n` is equal to

If lim _(xto1)(x^(1)+x^(2)+x^(3)+"..."+x^(n)-n)/(x-1)=820,(nin N) then the value of n is equal to

If X=[[1,1],[1,1]] , then X^n , for n in N is equal to

Let A=[(2, -1, 1),(-2, 3, -1),(-4, 4, -x)] be a matrix. If A^(2)=A , then the value of x is equal to

Let A=[(2, -1, 1),(-2, 3, -1),(-4, 4, -x)] be a matrix. If A^(2)=A , then the value of x is equal to

If x-(1)/(x)=1, then the value of x^(3)-(1)/(x^(3)) is equal to (a)2(b)3(c)4(d)8

If int_((1)/(3))^(3)(tan^(-1)x)/(x)dx=(pi)/(8)" lnk , then value of (k)/(4) is equal to

If N is any four digit number say x_(1),x_(2),x_(3),x_(4) then the maximum value ofis equal to (N)/(x_(1)+x_(2)+x_(3)+x_(4)) is equal to

If N is any four digit number say x_1, x_2, x_3, x_4 , then the maximum value ofis equal to N/(x_1+x_2+x_3+x_4) is equal to

The value of int(dx)/(x^n(1+x^n)^(1/ n)) is equal to

If X={4^(n)-3n-1n in N} and Y={9(n-1):n in N} , then X uu Y is equal to