For what vlaue of n is `|n-1|+1` equal to 0?

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+………+C_(n)x^(n) AA n in N and (C_(0)^(2))/(1)+(C_(1)^(2))/(2)+(C_(2)^(2))/(3)+……..+(C_(n)^(2))/(n+1)=(lambda(2n+1)!)/((n+1)!)^(2), then the vlaue of lambda is equal to

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+………+C_(n)x^(n) AA n in N and (C_(0)^(2))/(1)+(C_(1)^(2))/(2)+(C_(2)^(2))/(3)+……..+(C_(n)^(2))/(n+1)=(lambda(2n+1)!)/((n+1)!)^(2), then the vlaue of lambda is equal to

If the definite integral I=int_(0)^(pi)sin[x] dx=sum_(epsilon=0)^(n)a_(epsilon)sin epsilon . (where, [.] is the greatest integer function), then the vlaue of (a_(n)+n)/(pi) is equal to

If the definite integral I=int_(0)^(pi)sin[x] dx=sum_(epsilon=0)^(n)a_(epsilon)sin epsilon . (where, [.] is the greatest integer function), then the vlaue of (a_(n)+n)/(pi) is equal to

If A=[(1,0,0),(0,1,0),(3,4,-1)] and A^(n)=l , then value of n is equal to

If the product of n matrices [[1,n][0, 1] [[1, 2],[ 0 , 1]] [[1 , 3],[ 0, 1]][[1, n],[ 0 , 1]] is equal to the matrix [[1, 378], [0 , 1]] then the value of n is equal to

What is int_0^1 x(1-x)^n dx equal to