**Directions(1-10):** Comparing the values of x and y and then choose a required option.

- I.x^2 + 40x + 399 = 0

II.y^2 + 43y + 462 = 0x >= yNo relationy >= xx >= yy > xOption D

From I: x^2 + 40x + 399 = 0

=> x^2 + 21x + 19x + 399 = 0

=>(x+21)(x+19) = 0

=> x = – 21, – 19

From II: y^2 + 43y + 462 = 0

=>y^2 + 22y + 21y + 462 = 0

=> (y+22)(y+21) = 0

=> y = – 22, – 21

x >= y - I.19x + 14y = 80

II.12x – 7y = 3y > xx >= yx >= yNo relationy >= xOption A

On solving both the equations, we get the values

x = 2

y = 3

y > x - I.2x^2 – 12x + 16 = 0

II.2y^2 = 5y + 12x >= yy > xy >= xNo relationx >= yOption D

From I: 2x^2 – 12x + 16 = 0

=> 2x^2 – 8x – 4x + 16 = 0

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

=> x = 2,4

From II: 2y^2 = 5y + 12

=> 2y^2 – 8y + 3y + 12 = 0

=> (2y+3)(y-4) = 0

=> y = 4,-3/2

No relation - I.x^2 + [12+5(5)^1/2]x + 60(5)^1/2 = 0

II.y^2 + 9(5)^1/2y + 100 = 0y >= xx >= yy > xx >= yNo relationOption A

From I: x^2 + [12+5(5)^1/2]x + 60(5)^1/2 = 0

=> x^2 + 12x + 5(5)^1/2x + 60(5)^1/2 = 0

=> (x+12)[x+5(5)^1/2] = 0

=> x = -12, -5(5)^1/2

From II: y^2 + 9(5)^1/2y + 100 = 0

=> y^2 + 5(5)^1/2y + 4(5)^1/2y + 100 = 0

=> [y+5(5)^1/2][y+4(5)^1/2] = 0

=> y = -5(5)^1/2, -4(5)^1/2

y >= x - I.2x^2 – 11x + 15 = 0

II.4y^2 = 2y + 20y >= xx >= yx >= yNo relationy > xOption C

From I: 2x^2 – 11x + 15 = 0

=> 2x^2 – 6x – 5x + 15 = 0

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

=> x = 3,5/2

From II: 4y^2 = 2y + 20

=> 2y^2 – y – 10 = 0

=> (y+2)(2y – 5) = 0

=> y = -2,5/2

x >= y - I.x^2 + 33x + 272 = 0

II.y^2 + y – 306 = 0No relationx >= yy > xx >= yy >= xOption A

From I: x^2 + 33x + 272 = 0

=> x^2 + 17x + 16x + 272 = 0

=> (x+17)(x+16) = 0

=> x = -17,-16

From II: y^2 + y – 306 = 0

=> y^2 + 18y – 17y -306 = 0

=> (y+18)(y-17) = 0

=> y = -18,17

No relation - I.12x + 7y = 133

II.17x – 9y = 56y > xNo relationx >= yx >= yy >= xOption B

On solving both the equations, we get the same values of x and y.

x = y = 7

No relation - I.x^2 + 15x + 56 = 0

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

From I: x^2 + 15x + 56 = 0

=> x^2 + 8x + 7x + 56 = 0

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

=> x = -8,-7

From 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 + 31x + 238 = 0

II.y^2 + 35y + 306 = 0No relationx >= yy >= xx >= yy > xOption D

From I: x^2 + 31x + 238 = 0

=> x^2 + 17x + 14x + 238 = 0

=> (x+14)(x+17) = 0

=> x = -14, -17

From II: y^2 + 35y + 306 = 0

=>y^2 + 17y + 18y + 306 = 0

=> (y+17)(y+18) = 0

=> y = -17, -18

x >= y - I.3x^2 – 14x + 16 = 0

II.2y^2 = 5y + 18y >= xNo relationy > xx >= yx >= yOption B

From I: 3x^2 – 14x + 16 = 0

=>3x^2 – 8x – 6x + 16 = 0

=> (3x-8)(x-2) = 0

=> x = 2,8/3

From II: 2y^2 = 5y + 18

=> 2y^2 – 9y + 4y – 18 = 0

=> (y+2)(2y – 9) = 0

=> y = -2,9/2

No relation