If `D=|(1, 1, 1), (1, 1+x, 1), (1, 1, 1+y)|` for `x!=0, y!=0` then `D` is (1) divisible by neither x nor y (2) divisible by both x and y (3) divisible by x but not y (4) divisible by y but not x

Let P(x) and Q(x) be two polynomials.Suppose that f(x) = P(x^3) + x Q(x^3) is divisible by x^2 + x+1, then (a) P(x) is divisible by (x-1),but Q(x) is not divisible by x -1 (b) Q(x) is divisible by (x-1), but P(x) is not divisible by x-1 (c) Both P(x) and Q(x) are divisible by x-1 (d) f(x) is divisible by x-1

Assume that neither x nor y is equal to 0, to permit division by x and by y. 48:2x is equivalent to 144:600 . What is x?

Assume that neither x nor y is equal to 0, to permit division by x and by y. What is the ratio x:y:z ? (1) x+y=2z (2) 2x+3y=z

If X-Y=[1 1 1 1 1 0 1 0 0] and X+Y=[3 5 1-1 1 4 11 8 0] , find X and Y .

Prove the following by the principle of mathematical induction: \ x^(2n-1)+y^(2n-1) is divisible by x+y for all n in NNdot

Let X={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9} , Let R_1 be a relation on X given by R_1={(x ,\ y): x-y is divisible by 3} and R_2 be another relation on X given by R_2={(x ,\ y):{x ,\ y}sub{1,\ 4,\ 7} or {x ,\ y}sub{2,\ 5,\ 8} or {x ,\ y}sub{3,\ 6,\ 9}}dot Show that R_1=R_2 .

If A=[[0,1],[-1,0]], find x\ a n d \ y such that (x I+y A)^2=A

The normal to the curve x^2=4y passing (1,2) is (A) x + y = 3 (B) x y = 3 (C) x + y = 1 (D) x y = 1

If D1=|1 1 1 x^2 y^2 z^2 x y z| and D2=|1 1 1y z z xx y x y z| , without expanding prove that D1=D2 .

The normal at the point (1,1) on the curve 2y+x^2=3 is (A) x + y = 0 (B) x y = 0 (C) x + y +1 = 0 (D) x y = 0