Is `x < y` ?
(1) `1/x < 1/y`
(2) `x/y < 0`

Simplify xy [(x + y) ((1) / (x) - (1) / (y)) + (2x) / (y)]

If (1)/(1 + x+ x ^(2) + x ^(3)) then y _(2) (0) =

y = e ^ (xx) x tan ^ (- 1) x, showthat (1 + x ^ (2)) y_ (2) -2 (1-x + x ^ (2)) y_ (1) + (1 -x ^ (2)) y = 0

The sum of first n terms of the series 1 + (1 + x) y+ (1 + x + x^(2)) y^(2) + (1 + x + x^(2) + x^(3))y^(3) + ……….. is

The geometric mean of (x _(1) , x _(2), x _(3), ... X _(n)) is X and the geometric mean of (y _(1), y _(2), y _(3),... Y _(n)) is Y. Which of the following is/are correct ? 1. The geometric mean of (x _(1) y _(1), x _(2) y _(2) . x _(3) y _(3), ... x _(n) y _(n)) is XY. 2. The geometric mean of ((x _(1))/( y _(1)) , ( x _(2))/( y _(2)), (x _(3))/( y _(3)) , ... (x _(n))/( y _(n))) is (X)/(Y). Select the correct answer using the code given below:

if (x_ (1), y_ (1)), (x_ (2), y_ (2)), (x_ (3), y_ (3)) are vertices equilateral triangle such that (x_ (1) -2) ^ (2) + (y_ (1) -3) ^ (2) = (x_ (2) -2) ^ (2) + (y_ (2) -3) ^ (2) = (x_ (3) - 2) ^ (2) + (y_ (3) -3) ^ (2) then x_ (1) + x_ (2) + x_ (3) +2 (y_ (1) + y_ (2) + y_ (3) ))

If y = (x +1)/( (x -1) ( x -2)) find y".

If x_(1), x_(2), x_(3) and y_(1),y_(2), y_(3) are in arithmetic progression with the same common difference then the points (x_(1),y_(1)) (x_(2),y_(2)) (x_(3), y_(3)) are:

If x_(1), x_(2), x_(3) are in A.P. and y_(1), y_(2), y_(3) are in A.P. then the points (x_(1), y_(1)), (x_(2), y_(2)), (x_(3), y_(3))

If X_(1) = (x_(1), y_(1)) and X_(2) = (x_(2),y_(2)) are two optimal solutions of a L.P.P., then