**Directions: In each of these questions two ****equations numbered I and II are given. You have to ****solve both the equations and give answer.**

**1. I. x**^{2}-32x+256=0

^{2}-32x+256=0

** II. y**^{2}-33y+272=0

^{2}-33y+272=0

A. x < y

B. x ≤ y

C. x > y

D. x ≥ y

E. If either x=y or the relationship can’t be

established

** 2. ****I. 3x-4y+9=0**

** II.7x-7y-7=0**

A. x < y

B. x ≤ y

C. x > y

D. x ≥ y

E. If either x=y or the relationship can’t be

established

** 3. ****I. x**^{2}-2x-15=0

^{2}-2x-15=0

** II. y**^{2}-9y+14=0

^{2}-9y+14=0

A. x < y

B. x ≤ y

C. x > y

D. x ≥ y

E. If either x=y or the relationship can’t be

established

**4. ****I. 4x**^{2}-8x+3=0

^{2}-8x+3=0

** II. 4y**^{2}+8y+3=0

^{2}+8y+3=0

A. x < y

B. x ≤ y

C. x > y

D. x ≥ y

E. If either x=y or the relationship can’t be

established

** 5. **** ****I. 2x**^{2}-3x+1=0

^{2}-3x+1=0

** II. 2y**^{2}-4y+2=0

^{2}-4y+2=0

A. x < y

B. x ≤ y

C. x > y

D. x ≥ y

E. If either x=y or the relationship can’t be

established

**Directions: In each of these questions two ****equations numbered I and II are given. You have to ****solve both the equations and give answer.**

**6. I. 3x**^{2}+12x-180=0

^{2}+12x-180=0

** II. 2y**^{2}+4y-96=0

^{2}+4y-96=0

A. x < y

B. x ≤ y

C. If either x=y or the relationship can’t be

established

D. x > y

E. x ≥ y

** 7. ****I. 36x**^{2}+30x+6=0

^{2}+30x+6=0

** II.45y**^{2}+24y+3=0

^{2}+24y+3=0

A. x < y

B. x ≤ y

C. If either x=y or the relationship can’t be

established

D. x > y

E. x ≥ y

** 8. ****I. 2x**^{2}-9x+9=0

^{2}-9x+9=0

** II. y**^{2}-11y+24=0

^{2}-11y+24=0

A. x < y

B. x ≤ y

C. If either x=y or the relationship can’t be

established

D. x > y

E. x ≥ y

**9. ****I. x**^{2}-13x+40=0

^{2}-13x+40=0

** II. y**^{2}+9y+18=0

^{2}+9y+18=0

A. x < y

B. x ≤ y

C. If either x=y or the relationship can’t be

established

D. x > y

E. x ≥ y

** 10. **** ****I. 42x**^{2}-162x-24=0

^{2}-162x-24=0

** II. 12y**^{2}+24y-288=0

^{2}+24y-288=0

A. x < y

B. x ≤ y

C. If either x=y or the relationship can’t be

established

D. x > y

E. x ≥ y

## Answer-

- I. x
^{2}-32x +256 =0

=> (x-16)^{2}=0

=> x = 16,16

and II. y^{2}– 33y + 272 =0

=> (y-16)(y-17)=0

=> y =16,17

So, x ≤ y

**Hence, option B**

- Solving I and II, we get

x = 13 and y =12

So, x > y.**Hence, option C** - I. x
^{2}-2x -15 =0

=>x^{2}-5x +3x -15 =0

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

=> x= 5, -3

II. y^{2}– 9y +14 =0

=>y^{2}– 2y -7y +14 =0

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

=>y = 2,7

So, relation between x and y is not determined.

**Hence, option e.**

4.** C**

**B**

6.

From I,

x^{2} + 4x – 60 = 0

x^{2}– 6x + 10x – 60 = 0

x(x – 6)+10(x – 6) = 0

(x – 6)(x + 10) = 0

x = 6 or -10

From II,

y^{2} + 2y – 48 = 0

y^{2}– 6y + 8y – 48 = 0

y(y – 6)+8(y – 6) = 0

(y – 6)(y + 8) = 0

y = -8 or 6

So, no relationship can be established between x

and y. **Hence, option c.**

7.

From I,

6x^{2} + 5x + 1 = 0

6x^{2} + 3x + 2x + 1 = 0

3x(2x + 1) + 1(2x + 1) = 0

(3x + 1)(2x + 1) = 0

x = -1/3 or -1/2

From II,

15y^{2} + 8y + 1 = 0

15y^{2} + 5y + 3y + 1 = 0

5y(3y + 1) + 1(3y + 1) = 0

(5y + 1)(3y + 1) = 0

y = -1/5 or -1/3

So, y≥x. **Hence, option b.**

8.

From I,

2x^{2}– 6x – 3x + 9 = 0

2x(x – 3)-3(x – 3) = 0

(2x – 3)(x – 3) = 0

x = 3/2 or 3

From II,

y^{2}– 3y – 8y + 24 = 0

y(y – 3)-8(y – 3) = 0

(y – 3)(y – 8) = 0

y = 3 or 8

So, y ≥ x. **Hence, option b**

9.

From I,

x^{2}– 5x – 8x + 40 = 0

x(x – 5)-8(x – 5) = 0

(x – 5)(x – 8) = 0

x = 5 or 8

From II,

y^{2} + 3y + 6y + 18 = 0

y(y + 3)+6(y + 3) = 0

(y + 3)(y + 6) = 0

y = -3 or -6

So, x > y. **Hence, option d.**

10.

From I,

7x^{2}– 27x – 4 = 0

7x^{2}– 28x + x – 4 = 0

7x(x – 4) + 1(x – 4) = 0

(x – 4)(7x + 1) = 0

x = -1/7 or 4

From II,

y^{2} + 2y – 24 = 0

y^{2}– 4y + 6y – 24 = 0

y(y – 4)+6(y – 4) = 0

(y – 4)(y + 6) = 0

y = 4 or -6

So, no relationship can be established between x

and y. **Hence, option c.**