**Directions(1-10):** Find the values of x and y, compare their values and choose a correct option.

- (i) x² = 81

(ii) y² – 18y + 81 = 0

y > xy > xx >= yy >= xNo relation existsOption D

(i)x² = 81

x = ± 9

(ii)Y² – 18y + 81 = 0

(y – 9)² = 0

y = 9, 9

x ≤ y - (i) 4x² – 24x + 32 = 0

(ii) y² – 8y + 15 = 0

y > xy >= xx >= yNo relation existsy > xOption D

(i)4x² – 24x + 30 = 0

4x² – 16x – 8x + 32 = 0

4x (x – 4) –8 (x–4) = 0

x = 4, 2

(ii) y² – 8y + 15 = 0

y² – 5y – 3y + 15 = 0

y(y – 5)–3 (y – 5) = 0

y = 5, 3

No relation exists - (i) x² – 21x + 108 = 0

(ii) y² – 17y + 72 = 0

y > xy > xx >= yNo relation existsy >= xOption C

(i)x² – 21x + 108 = 0

x² – 9x – 12x + 108 = 0

x(x – 9) – 12 (x – 9) = 0

x = 9, 12

(ii) y² – 17y + 72 = 0

y² – 8y – 9y + 72 = 0

y (y – 8) – 9 (y – 8) = 0

y = 8,9

x ≥ y - (i) x² – 11x + 30 = 0

(ii) y² – 15y + 56 = 0

y > xx >= yy > xy >= xNo relation existsOption C

(i)x² – 11x + 30 = 0

x² – 6x – 5x + 30 = 0

x(x – 6) – 5(x – 6) = 0

x = 6, 5

(ii)y² – 15y + 56 = 0

y² – 7y – 8y + 56 = 0

y (y – 7) – 8 (y – 7) = 0

y = 7, 8

x < y - (i) x^2 + 12x + 35 =0

(ii) 5y^2 + 33y + 40 =0

y >= xy > xx >= yy > xNo relation existsOption A

(i) 𝑥^2 + 12𝑥 + 35 = 0

𝑥^2 + 7𝑥 + 5𝑥 + 35 = 0

𝑥(𝑥 + 7) + 5(𝑥 + 7) = 0

(𝑥 + 7)(𝑥 + 5) = 0

𝑥 = −7 , −5

(ii) 5𝑦 2 + 33y + 40 = 0

5𝑦 2 + 25𝑦 + 8𝑦 + 40 = 0

5𝑦(𝑦 + 5) + 8(𝑦 + 5) = 0

(𝑦 + 5)(5𝑦 + 8) = 0

𝑦 = − 8/5 , −5

𝑦 ≥ x - (i) 4x^2 + 9x + 5 =0

(ii) 3y^2 + 5y + 2 =0

y > xy >= xNo relation existsx >= yy > xOption B

(i) 4𝑥^2 + 9𝑥 + 5 = 0

4𝑥^2 + 4𝑥 + 5𝑥 + 5 = 0

4𝑥(𝑥 + 1) + 5(𝑥 + 1) = 0

(4𝑥 + 5)(𝑥 + 1) = 0

𝑥 = −1 , − 5/4

(ii) 3𝑦^2 + 5y + 2 = 0

3𝑦^2 + 3y + 2y + 2 = 0

3𝑦(𝑦 + 1) + 2(𝑦 + 1) = 0

(3𝑦 + 2)(𝑦 + 1) = 0

𝑦 = − 2/3 , −1

𝑦 ≥ x - (i) x^2 − 11x + 24 = 0

(ii) y^2 − 12y + 27 = 0

y > xy > xx >= yy >= xNo relation existsOption E

(i) 𝑥^2 − 11𝑥 + 24 = 0

𝑥^2 − 8𝑥 − 3𝑥 + 24 = 0

𝑥(𝑥 − 8) − 3(𝑥 − 8) = 0

(𝑥 − 3)(𝑥 − 8) = 0

𝑥 = 3 , 8

(ii) 𝑦^2 − 12y + 27 = 0

𝑦^2 – 9𝑦 − 3𝑦 + 27 = 0

𝑦(𝑦 − 9) − 3(𝑦 − 9) = 0

(𝑦 − 9)(𝑦 − 3) = 0

𝑦 = 9 , 3

No relation exists - (i) 4𝑥^2 − 21𝑥 + 20 = 0

(ii) 3y^2 − 19y + 30 = 0

y > xy >= xy > xNo relation existsx >= yOption D

(i) 4𝑥^2 − 21𝑥 + 20 = 0

4𝑥^2 − 16𝑥 − 5𝑥 + 20 = 0

4𝑥(𝑥 − 4) − 5(𝑥 − 4) = 0

(4𝑥 − 5)(𝑥 − 4) = 0

𝑥 = 5/4 , 4

(ii) 3𝑦^2 − 19𝑦 + 30 = 0

3𝑦^2 – 9𝑦 − 10𝑦 + 30 = 0

3𝑦(𝑦 − 3) − 10(𝑦 − 3) = 0

(3𝑦 − 10)(𝑦 − 3) = 0

𝑦 = 10/3 , 3

No relation exists - (i) 𝑥^2 − 20𝑥 + 96 = 0

(ii) 𝑦^2 = 64

y > xNo relation existsx >= yy >= xy > xOption C

(i) 𝑥^2 − 20𝑥 + 96 = 0

𝑥^2 − 12𝑥 − 8𝑥 + 96 = 0

(𝑥 − 12) − 8(𝑥 − 12) = 0

(𝑥 − 12)(𝑥 − 8) = 0

𝑥 = 12,8

(ii) 𝑦^2 = 64

𝑦 = ±8

𝑥 ≥ 𝑦 - (i) x³ = 512

(ii) y² = 64

x >= yy >= xy > xNo relation existsy > xOption A

(i) x³ = 512

x = 8

(ii) y² = 64

y = √64 = ± 8

x ≥ y