Column I, Column II `(I-A)^n` is if `A` is idempotent, p. `2^(n-1)(l-A)` `(I-A)^n` is if `A` is involuntary, q. `I-n A` `(I-A)^n` is if `A` is nilpotent of index 2, r. `A` If `A` is orthogonal, then `(A^T)^(-1)` , s. `I-A`

If A is a nilpotent matrix of index 2, then for any positive integer n ,A(I+A)^n is equal to (a) A^(-1) (b) A (c) A^n (d) I_n

Find the value of i^n+i^(n-1)+i^(n-2)+i^(n-3) for all n in Ndot

If Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. I-(2^n-1)Z d. none of these

If (i)^-n =1(ninN) ,then least value of n will be

If i=sqrt-1 and n is a positive integer, then i^(n)+i^(n+1)+i^(n+3_ is equal to

If I_n = int sin^n x dx then nI_n - (n - 1)I_(n-2) = f(x)+c where f(x) =

Find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) for all n in Ndot

IF i^(2) =-1, then the value of sum _(i-1) ^(200) i^(n) is-

If m, n in R , then the value of I(m,n)=int_(0)^(1) t^(m)(1+t)^(n)dt is -

n whole are randomly chosen and multiplied Column I, Column II The probability that the last digit is 1,3,7, or 9 is, p. (8^n-4^n)/(10^n) The probability that the last digit is 2,4,6, or 8 is, q. (5^n-4^n)/(10^n) The probability that the last digit is 5 is, r. (4^n)/(10^n) The probability that the last digit is zero is, s. (10^n-8^n-5^n+4^n)/(10^n)