**Directions(1-10):** Comparing x and y and select a required option.

- I.8x^2 – 46x +63 = 0

II.2y^2 – 17y + 35 = 0x>=yx > yy >= xy > xNo relation.Option C

From I: I.8x^2 – 46x +63 = 0

=>8x^2 – 28x – 18x + 63 = 0

=>(2x-7)(4x-9) = 0

=>x = 7/2,9/4

From II:

II.2y^2 – 17y + 35 = 0

=>2y^2 – 10y – 7y + 35 = 0

=>(2y-7)(y-5) = 0

=>y = 7/2,5

y >= x - I.x^2 + 11x + 28 = 0

II.y^2 + 17y + 72 = 0y > xy >= xNo relation.x > yx>=yOption D

From I: I.x^2 + 11x + 28 = 0

=>x2 + 4x + 7x + 28 = 0

=>(x+7)(x+4) = 0

=> x = -7,-4

From II: II.y^2 + 17y + 72 = 0

=>y^2 + 9y + 8y + 72 = 0

=>(y+9)(y+8) = 0

=> y = -9,-8

x > y - I.x^2 – 5x + 6 = 0

II.y^2 + 2y – 63 = 0y >= xx > yy > xNo relation.x>=yOption D

From I:

I.x^2 – 5x + 6 = 0

=>x^2 – 3x – 2x + 6 = 0

=>(x-3)(x-2) = 0

=> x= 3,2

From II:

II.y^2 + 2y – 63 = 0

=>y^2 + 9y – 7y – 63 = 0

=>(y+9)(y-7)= 0

=> y = -9,7

No relation. - I.12x^2 – 31x + 20 = 0

II.10y^2 – 11y + 3 = 0y > xNo relation.x>=yy >= xx > yOption E

From I:

I.12x^2 – 31x + 20 = 0

=>12x^2 – 16x – 15x + 20 = 0

=>(3x – 4)(4x – 5) = 0

=> x = 4/3,5/4

From II:

II.10y^2 – 11y + 3 = 0

=>10y^2 – 5y – 6y + 3 = 0

=>(5y-3)(2y-1) = 0

=>y = 3/5,1/2

x>y - I.x^2 – 3x – 54 = 0

II.y^2 – 19y + 90 = 0x > yNo relation.x>=yy > xy >= xOption E

From I:

I.x^2 – 3x – 54 = 0

=>x^2 – 9x + 6x – 54 = 0

=>(x-9)(x+6) = 0

=>x = 9, -6

From II:

II.y^2 – 19y + 90 = 0

=>y^2 – 9y – 10y + 90 = 0

=>(y-9)(y-10) = 0

=>y = 9,10

y>=x - I.7x+3y = 40

II.5x+6y = 44No relation.x > yy >= xy > xx>=yOption A

On solving both the equations, we get

x = y = 4

No relation. - I.x^2 – 15x + 56 = 0

II.y^2 + 2y – 63 = 0y > xx>=yy >= xNo relation.x > yOption B

From I:

I.x^2 – 15x + 56 = 0

=>x^2 – 7x – 8x + 56 = 0

=>(x-7)(x-8) = 0

=>x = 7,8

From II:

II.y^2 + 2y – 63 = 0

=>y^2 + 9y – 7y – 63 = 0

=>(y+9)(y-7)= 0

=> y = -9,7

x >= y - I.7x + 8y = 80

II.9x – 5y = 57x>=yy >= xx > yNo relation.y > xOption C

On solving both the equations,we get

x = 8 y = 3

x>y - I.x^2 – 3x – 18 = 0

II.y^2 + 8y + 15 = 0y >= xx>=yx > yy > xNo relation.Option B

From I:

I.x^2 – 3x – 18 = 0

=>x^2 + 3x – 6x – 18 = 0

=>(x+3)(x-6) = 0

=>x = -3,6

From II:

II.y^2 + 8y + 15 = 0

=>y^2 + 5y + 3y + 15 = 0

=>(y+3)(y+5)= 0

=>y = -3,-5

x>=y - I.x^2 – 2x – 15 = 0

II.y^2 + 4y – 12 = 0x > yNo relation.y > xy >= xx>=yOption B

From I:

I.x^2 – 2x – 15 = 0

=>x^2 – 5x + 3x – 15 = 0

=>(x-5)(x+3)=0

=>x = 5,-3

From II:

II.y^2 + 4y – 12 = 0

=>y^2 + 6y – 2y – 12 = 0

=>(y+6)(y-2)= 0

=>y = -6,2

No relation.