If `A=1/3[(1,2,2),(2,1,-2),(x,2,y)]` satisfies `A^T A=I` , then `x+y=` (a) 3 (b) 0 (c) -3 (d) 1

If 3A=[(-1,-2,-2),(2,1,-2),(x,-2,y)] such that A A^T=I , then which of the following are correct? (A) x+2y=4 (B) x-y=1 (C) x^2+y^2=-3 (D) x^2+y^2=5

The roots of the equation det [(1-x, 2, 3),(0,2-x,0),(0,2,3-x)]=0 are (A) 1 and 2 (B) 1 and 3 (C) 2 and 3 (D) 1,2, and 3

If x=(1+t)/(t^3),y=3/(2t^2)+2/t , then x((dy)/(dx))^3-(dy)/(dx) is equal to (a) 0 (b) -1 (c) 1 (d) 2

If 3A=[-1-2-2 2 1-2x-2y] such that A.A^T=I , then which of the following are correct? x+2y=4 (b) x-y=1 x^2+y^2=-3 (d) x^2+y^2=5

If (1-i)x+(1+i)y=1-3i , then (x,y) is equal to (a) (2,-1) (b) (-2,1) (c) (-2,-1) (d) (2,1)

If y=3^(x-1)+3^(-x-1) , then the least value of y is (a) 2 (b) 6 (c) 2//3 (d) 3//2

The total number of matrices A = [{:(0, 2y, 1), (2x, y, -1), (2x, -y, 1):}] (x, y in R, x ne y) for which A^(T)A = 3I_(3) is

If x=a t^2,y=2a t , then (d^2y)/(dx^2) is equal to (a) -1/(t^2) (b) 1/(2a t^2) (c) -1/(t^3) (d) 1/(2a t^3)

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) none of these

If x+i y=(1+i)(1+2i)(1+3i),\ t h e n\ x^2+y^2 is: (a) . 0 (b) . 1 (c) . 100 (d) . none of these