**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. 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. 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

- I. 3x
^{2} + 23x + 30 = 0

II. 3y^{2} – 4y – 4 = 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} + 23x + 30 = 0

3x^{2} + 18x + 5x + 30 = 0

Gives x = -5/3, -6

3y^{2} – 4y – 4 = 0

3y^{2} – 6y + 2y – 4 = 0

Gives y = 2, -2/3

Put all values on number line and analyze the relationship

-6…. -5/3….. -2/3…… 2

- I. 6x
^{2} + 5x – 1 = 0,

II. 3y^{2} – 11y + 6 = 0

A) If X > Y

B) If X < Y

C) If X ≥ Y

D) If X ≤ Y

E) If X = Y or relation cannot be established

View Answer

** Option B**

Solution:

6x^{2} + 5x – 1 = 0

6x^{2} + 6x – x – 1 = 0

Gives x = -1, 1/6

3y^{2} – 11y + 6 = 0

3y^{2} – 9y – 2y + 6 = 0

Gives y = 2/3, 3

Put on number line

-1… 1/6… 2/3… 3

- I. 3x
^{2} + 4x – 4 = 0,

II. 4y^{2} + 5y – 6 = 0

A) If X > Y

B) If X < Y

C) If X ≥ Y

D) If X ≤ Y

E) If X = Y or relation cannot be established

View Answer

** Option E**

Solution:

3x^{2} + 4x – 4 = 0

3x^{2} + 6x – 2x – 4 = 0

Gives x = -2, 2/3

4y^{2} + 5y – 6 = 0

4y^{2} + 5y – 6 = 0

Gives y = -2, 3/4

Put on number line

-2…. 2/3… 3/4

When x=2/3, x>y(= -2) and x<y(= 3/4)

So cant be determined

- I. 5x
^{2} – 36x – 32 = 0,

II. 3y^{2} – 17y – 6 = 0

A) If X > Y

B) If X < Y

C) If X ≥ Y

D) If X ≤ Y

E) If X = Y or relation cannot be established

View Answer

** Option E**

Solution:

5x^{2} – 36x – 32 = 0

5x^{2} + 4x – 40x – 32 = 0

Gives x = -4/5, 8

3y^{2} – 17y – 6 = 0

3y^{2} + y – 18y – 6 = 0

Gives y= -1/3, 6

Put on number line

-4/5…. -1/3… 6… 8

- I. 3x
^{2} – 25x + 52 = 0,

II. 15y^{2} – 38y – 40 = 0

A) If X > Y

B) If X < Y

C) If X ≥ Y

D) If X ≤ Y

E) If X = Y or relation cannot be established

View Answer

** Option A**

Solution:

3x^{2} – 25x + 52 = 0

3x^{2} – 12x – 13x + 52 = 0

Gives x = 4, 13/3

15y^{2} – 38y – 40 = 0

15y^{2} + 12y – 50y – 40 = 0

Gives y = -4/5, 10/3

Put on number line

-4/5… 10/3… 4… 13/3

- I. 6x
^{2} + x – 2 = 0,

II. 2y^{2} + 11y + 14 = 0

A) If X > Y

B) If X < Y

C) If X ≥ Y

D) If X ≤ Y

E) If X = Y or relation cannot be established

View Answer

** Option A**

Solution:

6x^{2} + x – 2 = 0

6x^{2} + 4x – 3x – 2 = 0

Gives x = -2/3, 1/2

2y^{2} + 11y + 14 = 0

2y^{2} + 4y + 7y + 14 = 0

Gives y = -7/2, -2

- I. 3x
^{2} + 14x – 5 = 0,

II. 3y^{2} – 19y + 6 = 0

A) If X > Y

B) If X < Y

C) If X ≥ Y

D) If X ≤ Y

E) If X = Y or relation cannot be established

View Answer

** Option D**

Solution:

3x^{2} + 14x – 5 = 0

3x^{2} + 15x – x – 5 = 0

Gives x = -5, 1/3

3y^{2} – 19y + 6 = 0

3y^{2} – 18y – y + 6 = 0

Gives y = 1/3, 6

Put on number line

-5…. 1/3… 6

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