**Directions: In the following questions, two equations numbered are given in variables x and y. You have to solve both the equations and find out the relationship between x and y. Then give answer accordingly.**

- I. 3x
^{2} + 22 x + 24 = 0

II. 2y^{2} + 11y + 12 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relation cannot be established

View Answer

** Option E**

Solution:

3x^{2} + 22 x + 24 = 0

3x^{2} + 18x + 4x + 24 = 0

Gives x = -4/3, -6

2y^{2} + 11y + 12 = 0

2y^{2} + 8y + 3y + 12 = 0

Gives y = -4, -3/2

Put all values on number line and analyze the relationship

-6…..-4…. -3/2….-4/3

- I. 20x
^{2} – 31x + 12 = 0

II. 4y^{2} + 5y – 6 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relation cannot be established

View Answer

** Option C**

Solution:

20x^{2} – 31x + 12 = 0

20x^{2} – 16x – 15x + 12 = 0

Gives x = 3/4, 4/5

4y^{2} + 5y – 6 = 0

4y^{2} + 5y – 6 = 0

Gives y = -2, 3/4

Put all values on number line and analyze the relationship

-2…. 3/4… 4/5

- I. 3x
^{2} + 14x – 5 = 0

II. 4y^{2} + 5y – 6 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relation cannot be established

View Answer

** Option E**

Solution:

3x^{2} + 14x – 5 = 0

3x^{2} + 15x – x – 5 = 0

Gives x = -5, 1/3

4y^{2} + 5y – 6 = 0

4y^{2} + 5y – 6 = 0

Gives y = -2, 3/4

Put all values on number line and analyze the relationship

-5….-2….. 1/3…. 3/4

- I. 2x
^{2} – 15x + 7 = 0

II. 8y^{2} + 6y – 5 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relation cannot be established

View Answer

** Option C**

Solution:

2x^{2} – 15x + 7 = 0

2x^{2} – 14x – x + 7 = 0

Gives x = 1/2, 7

8y^{2} + 6y – 5 = 0

8y^{2} – 4y + 10y – 5 = 0

Gives y = -5/4, 1/2

Put all values on number line and analyze the relationship

-5/4…. 1/2 …. 7

- I. 3x
^{2} + 16x + 20 = 0

II. 3y^{2} – 14y – 5 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relation cannot be established

View Answer

** Option B**

Solution:

3x^{2} + 16x + 20 = 0

3x^{2} + 6x + 10x + 20 = 0

Gives x = -2, -10/3

3y^{2} – 14y – 5 = 0

3y^{2} – 15y + y – 5 = 0

Gives y = -1/3, 5

Put all values on number line and analyze the relationship

-10/3… -2…. -1/3…. 5

- I. 3x
^{2} + 7x – 6 = 0

II. 6y^{2} – 35y + 50 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relation cannot be established

View Answer

** Option B**

Solution:

3x^{2} + 7x – 6 = 0

3x^{2} + 9x – 2x – 6 = 0

Gives x = -3, 2/3

6y^{2} – 35y + 50 = 0

6y^{2} – 15y – 20y + 50 = 0

Gives y = 5/2, 10/3

Put all values on number line and analyze the relationship

-3… 2/3… 5/2…. 10/3

- I. 7x
^{2} – 11x – 6 = 0

II. 6y^{2} + 13y + 5 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relation cannot be established

View Answer

** Option A**

Solution:

7x^{2} – 11x – 6 = 0

7x^{2} – 14x + 3x – 6 = 0

Gives x = -3/7, 2

6y^{2} + 13y + 5 = 0

6y^{2} + 3y + 10y + 5 = 0

Gives y = -5/3, -1/2

Put all values on number line and analyze the relationship

-5/3…. -1/2…. -3/7….. 2

- I. 3x
^{2} + 4x – 39 = 0

II. 3y^{2} – 5y – 78 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relation cannot be established

View Answer

** Option E**

Solution:

3x^{2} + 4x – 39 = 0

3x^{2} – 9x + 13x – 39 = 0

Gives x = -13/3, 3

3y^{2} – 5y – 78 = 0

3y^{2} – 18y + 13y – 78 = 0

Gives y = -13/3, 6

Put all values on number line and analyze the relationship

-13/3…. 3…. 6

- I. 4x
^{2} + 13x + 9 = 0

II. 3y^{2} – 7y – 20 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relation cannot be established

View Answer

** Option E**

Solution:

4x^{2} + 13x + 9 = 0

4x^{2} + 4x + 9x + 9 = 0

Gives x = -9/4, -1

3y^{2} – 7y – 20 = 0

3y^{2} – 12y + 5y – 20 = 0

Gives y = -5/3, 4

Put all values on number line and analyze the relationship

-9/4…. -5/3…. -1….4

- I. 4x
^{2} + 13x + 10 = 0

II. 4y^{2} – 7y – 15 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relation cannot be established

View Answer

** Option D**

Solution:

4x^{2} + 13x + 10 = 0

4x^{2} + 8x + 5x + 10 = 0

Gives x = -2, -5/4

4y^{2} – 7y – 15 = 0

4y^{2} – 12y + 5y – 15 = 0

Gives y = -5/4, 3

Put all values on number line and analyze the relationship

-2… -5/4…. 3

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