If `D=|1 1 1 1 1+x1 1 1 1+y|"f o r"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

If D = |(1,1,1),(1,1 +x,1),(1,1,1 +y)| " for " x!= 0, y != 0 , then D is divisible by

x^(2n-1)+y^(2n-1) is divisible by x+y

If n in N,x^(2n-1)+y^(2n-1) is divisible by x+y if n is

If the six digit number 15 x 1y 2 is divisible by 44 then (x + y) is equal to :

Using mathematical induction, prove that for x^(2n-1)+y^(2n-1) is divisible by x+y for all n in N

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

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 .

P(x) is a least degree polynomial such that (P(x)-1) in divisible by (x-1)^(2) and (P(x)-3) is divisible by ((x+1)^2) ,then (A) graph of y=P(x) ,is symmetric about origin (B) y=P(x) ,has two points of extrema (C) int_(-1)^(2)P(x)dx=0 for exactly one value of lambda . (D) int_(-1)^(2)P(x)dx=0 for exactly two values of lambda