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Directions:1-5) ** In the following questions, two equations numbered are given in variables a and b. ****You**** have to solve both the equations and find out the relationship between a and b. Then give answer accordingly-**

1.

I.3a^{2} – 8a – 28 = 0

II.3b^{2} – 44b + 140 = 0

2.

I.2a^{2} – 27a + 81 = 0

II.3b^{2} – 50b + 168 = 0

3.

I.2a^{2} – 27a + 81 = 0

II.3b^{2} – 50b + 168 = 0

4.

I.3a^{2} – 14a – 24 = 0

II.3b^{2} + 32b + 64 = 0

5.

I.4a2 + a – 18 = 0

II.4b2 – 11b – 45 = 0

Directions:6-10) ** In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the relation between x and y.**

6.

I. 5x^{2} – 176x – 333 = 0

II. 49y^{2} – 84y + 36 = 0

7.

I. x^{2} + 13√2x + 84 = 0

II. 12y^{2} – 20y + 8 = 0

8.

I. 20x^{2} – 108x + 144 = 0

II. y^{2} – 26y + 168 = 0

9.

I. x^{2 }– 32x + 252 = 0

II. 25y^{2} – 90y + 72 = 0

10.

I. x^{2} – 56x + 783 = 0

II. 12y^{2} + 82y + 140 = 0

**Check your Answers below:**

Directions:1-5)

**In the following questions, two equations numbered are given in variables a and b.****You****have to solve both the equations and find out the relationship between a and b. Then give answer accordingly-**##### 1. Question

I.3a

^{2}– 8a – 28 = 0

II.3b^{2}– 44b + 140 = 0

Ans:4

3a^{2}– 8a – 28 = 0

3a^{2}+ 6a – 14a – 28 = 0

Gives a = -2, 14/3

3b^{2}– 44b + 140 = 0

3b^{2}– 30b -14b + 140 = 0

Gives b = 14/3, 10

a ≤ b##### 2. Question

I.2a

^{2}– 27a + 81 = 0

II.3b^{2}– 50b + 168 = 0Ans:4

2a^{2}– 27a + 81 = 0

2a^{2}– 18a – 9a + 81 = 0

Gives a = 9/2, 9

3b^{2}– 50b + 168 = 0

3b^{2}– 36b – 14b + 168 = 0

Gives b = 14/3, 12

Cannot be determined##### 3. Question

I.2a

^{2}– 27a + 81 = 0

II.3b^{2}– 50b + 168 = 0

Ans:5

2a^{2}– 27a + 81 = 0

2a^{2}– 18a – 9a + 81 = 0

Gives a = 9/2, 9

3b^{2}– 50b + 168 = 0

3b^{2}– 36b – 14b + 168 = 0

Gives b = 14/3, 12

Cannot be determined##### 4. Question

I.3a

^{2}– 14a – 24 = 0

II.3b^{2}+ 32b + 64 = 0Ans:1

3a^{2}– 14a – 24 = 0

3a^{2}– 18a + 4a – 24 = 0

Gives a = -4/3, 6

3b^{2}+ 32b + 64 = 0

3b^{2}+ 24b + 8b + 64 = 0

Gives b= -8, -8/3

a > b##### 5. Question

I.4a2 + a – 18 = 0

II.4b2 – 11b – 45 = 0Ans:5

4a^{2}+ a – 18 = 0

4a^{2}– 8a + 9a – 18 = 0

Gives a = -9/4, 2

4b^{2}– 11b – 45 = 0

4b^{2}– 20b + 9b – 45 = 0

Gives b= -9/4, 5Cannot be determined

Directions:6-10)

**In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the relation between x and y.**##### 6. Question

I. 5x

^{2}– 176x – 333 = 0II. 49y

^{2}– 84y + 36 = 0Ans:5

I. 5x^{2}– 176x – 333 = 0=> (x – 37)(5x + 9) = 0

=> x = 37, -9/5

II. 49y

^{2}– 84y + 36 = 0=> (7y – 6)

^{2 }= 0=>7y – 6 = 0

=> y = 6/7

Hence, relationship between x and y cannot be determined.

##### 7. Question

I. x

^{2}+ 13√2x + 84 = 0II. 12y

^{2}– 20y + 8 = 0Ans:3

I. x^{2}+ 13√2x + 84 = 0=> (x + 6√2)(x + 7√2) = 0

=> x = -6√2, -7√2

II. 12y

^{2}– 20y + 8 = 0=> 3y

^{2}– 5y + 2 = 0=> (3y – 2)(y – 1) = 0

=> y = 2/3, 1

Hence, x < y

##### 8. Question

I. 20x

^{2}– 108x + 144 = 0II. y

^{2}– 26y + 168 = 0Ans:3

I. 20x^{2}– 108x + 144 = 0=>5x

^{2}– 27x + 36 = 0=> (5x – 12)(x – 3) = 0

=> x = 12/5, 3

II. y

^{2}– 26y + 168 = 0=> (y – 12)(y – 14) = 0

=> y = 12, 14

Hence, x < y

##### 9. Question

I. x

^{2 }– 32x + 252 = 0II. 25y

^{2}– 90y + 72 = 0Ans:1

I. x^{2 }– 32x + 252 = 0=> (x – 18)(x – 14) = 0

=> x = 18, 14

II. 25y

^{2}– 90y + 72 = 0=> (5y – 12)(5y – 6) = 0

=> y = 12/5, 6/5

Hence, x > y

##### 10. Question

I. x

^{2}– 56x + 783 = 0II. 12y

^{2}+ 82y + 140 = 0Ans:1

I. x^{2}– 56x + 783 = 0=> (x – 29)(x – 27) = 0

=> x = 29, 27

II. 12y

^{2}+ 82y + 140 = 0=> 6y

^{2}+ 41y + 70 = 0=> (2y + 7)(3y + 10) = 0

=> y = -7/2, -10/3

Hence, x > y