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} + 22x + 24 = 0,

II. 3y^{2} – 8y – 16 = 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} + 22 x + 24 = 0

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

Gives x = -4/3, -6

3y^{2} – 8y – 16 = 0

3y^{2} – 12y + 4y – 16 = 0

So y = -4/3, 4

Plot on number line

-6…. -4/3……. 4

- I. 5x
^{2} – 18x – 8 = 0,

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

5x^{2} – 18x – 8 = 0

5x^{2} – 20x + 2x – 8 = 0

So x = -2/5, 4

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

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

Gives y = -4, -3/2

Plot on number line

-4… -3/2…. -2/5….. 4

- I. x
^{2} – 652 = 504,

II. y = √1156

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:

x^{2} – 652 = 504

x^{2} = 1156

So x = 34, -34

y = √1156 = 34

Plot on number line

-34… 34

- I. 9/√x + 8/(√x +1) = 5,

II. 12/√y – 4/√y = 2

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:

9/√x + 8/(√x +1) = 5

[9(√x +1) + 8√x]/[√x * (√x +1)] = 5

17√x + 9 = 5 (x + √x)

5x – 12√x – 9 = 0

5x – 15√x + 3√x – 9 = 0

5√x (√x – 3) + 3 (√x – 3) = 0

√x cannot be -3/3

So √x = 3, so x = 9

12/√y – 4/√y = 2

8/√y = 2

So √y = 4 or y = 16

So y > x

- I. 3x
^{2} – 6x – √3x + 2√3 = 0,

II. 2y^{2} – 3y – 2√2y + 3√2 = 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} – 6x – √3x + 2√3 = 0

3x (x- 2) – √3 (x – 2) = 0,

So x = 2, √3/3

2y^{2} – 3y – 2√2y + 3√2 = 0

y (2y – 3) – √2 (2y – 3) = 0

So y = 3/2, √2 (1.44)

plot on number line

√3/3(0.57)…….√2…..(3/2)……2

- I. x
^{2} – 2x – √5x + 2√5 = 0

II. y^{2} – 3y – √6y + 3√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:

x^{2} – 2x – √5x + 2√5 = 0

x (x – 2) – √5 (x – 2) = 0

So x = 2, √5 (2.23)

y^{2} – 3y – √6y + 3√6 = 0

y (y – 3) – √6 (y – 3) = 0

So y = 3, √6 (2.44)

Plot on number line

2…2.23……2.44…….3

- I. 8x
^{2} + 6x + 1 = 0,

II. 5y^{2} + 8y – 4 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relationship cannot be determined

View Answer

** Option E**

Solution:

8x^{2} + 6x + 1 = 0

8x^{2} + 4x + 2x + 1 = 0

So x = -1/4, -1/2

5y^{2} + 8y – 4 = 0

5y^{2} + 10y – 2y – 4 = 0

So y = -2, 2/5

- I. 4x
^{2} – 23x + 30 = 0,

II. 4y^{2} – 3y – 45 = 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:

4x^{2} – 23x + 30 = 0

4x^{2} – 15x – 8x + 30 = 0

So x = 15/4, 2

4y^{2} – 3y – 45 = 0

4y^{2} + 12y – 15y – 45 = 0

So y = -3, 15/4

Put on number line

-3…. 2…. 15/4

- I. 5x
^{2} – 7x – 6 = 0,

II. 3y^{2} – 2y – 8 = 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} – 7x – 6 = 0

5x^{2} – 10x + 3x – 6 = 0

So x = -3/5, 2

3y^{2} – 2y – 8 = 0

3y^{2} – 6y + 4y – 8 = 0

So y = -4/3, 1

Plot on number line

-4/3……-3/5….. 1….. 2

- I. 3x
^{2} + 2x – 21 = 0,

II. 3y^{2} – 19y + 28 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relationship cannot be determined

View Answer

** Option D**

Solution:

3x^{2} + 2x – 21 = 0

3x^{2} + 9x – 7x – 21 = 0

Gives x = -3, 7/3

3y^{2} – 19y + 28 = 0

3y^{2} – 12y – 7y + 28 = 0

So y = 7/3, 4

Put on number line

-3……7/3……4

6/10

how u solved 4, 5 and 6 ??

at the time of solving i cant able to solve only 4,5,6

5,6 IS EASY ..no need to aware..but u have to know the roots until 10…

nice ques mam

thanku 🙂

ty….good qsn

thank u mam

thank u mam :))

thank mam 4,5,and 6 are good que