If `A=[(a,b),(0,a)]` is nth root of `I_(2)`, then choose the correct statements :
(i) if n is odd, a=1, b=0
(ii) if n is odd, a=-1, b=0
(iii) if n is even, a=1, b=0
(iv) if n is even, a=-1, b=0

If A=[a b0a] is nth root of I_2, then choose the correct statements: If n is odd, a=1,b=0 If n is odd, a=-1,b=0 If n is even, a=1,b=0 If n is even, a=-1,b=0 a. i, ii, iii, iv b. ii, iii, iv c. i, ii, iii, iv d. i, iii, iv

Let f: N->N be defined0 by: f(n)={(n+1)/2, if n is odd (n-1)/2, if n is even Show that f is a bijection.

Let f(x)=(x-1)^4(x-2)^n ,n in Ndot Then f(x) has (a) a maximum at x=1 if n is odd (b) a maximum at x=1 if n is even (c) a minimum at x=1 if n is even (d) a minima at x=2 if n is even

If A=[(2,-1),( 3,-2)] , then A^n= [(1, 0),( 0,1)] , if (a) n is an even natural number (b) [(1 ,0),( 0, 1)] , if n is an odd natural number (c) [(1 ,0),( 0, 1)] , if n in N (d) none of these

If omega be a nth root of unity, then 1+omega+omega^2+…..+omega^(n-1) is (a)0(B) 1 (C) -1 (D) 2

Number of ways in which three numbers in A.P. can be selected from 1,2,3,..., n is a. ((n-1)/2)^2 if n is even b. n(n-2)/4 if n is even c. (n-1)^2/4 if n is odd d. none of these

Find the equations of the circles the end points of whose diameter are as follows : (i) (0,6) and (6,0) (ii) (-1,3) and (2,4) (iii) (A+b,a-b) and (a-b,a+b) (iv) (0,0) and (2,2)

If A=[(i,0), (0,i)],\ n in N , then A^(4n) equals [(0,i), (i,0)] (b) [(0 ,0) ,(0, 0)] (c) [(1, 0) ,(0, 1)] (d) [(0,i) ,(i,0)]

If nth-order square matrix A is a orthogonal, then |adj(adjA)| is (a)always -1 if n is even (b) always 1 if n is odd (c) always 1 (d) none of these

If A=[(1,a),(0, 1)] , then A^n (where n in N) equals (a) [(1,n a),(0, 1)] (b) [(1,n^2a),(0, 1)] (c) [(1,n a),(0 ,0)] (d) [(n,n a),(0,n)]