**Directions (Q. 1–4): 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 value of x and y. Give answer**

**1) if x > y**

**2) if x >= y**

**3) if x < y**

**4) if x <= y**

**5) if x = y or relationship between x and y cannot be determined.**

1.

I. x^2 + x – 20 = 0

II. y^2 + 13y + 40 = 0

2.

I. x^2 – 11x + 30 = 0

II. y^2 – 13y + 40 = 0

3.

I. x^2 + 10x + 25 = 0

II. 5y^2 – 2 15 y + 9 = 0

4.

I. 10x^2 – 29x – 21 = 0

II. y^2 + 13y – 68 = 0

**Directions (Q. 5–7): What value should come in the place of question mark (?) in the following number series?**

**5. 362, 452, 550, 656, ?**

1) 770

2) 772

3) 670

4) 870

5) 790

**6. 25, 28, 26, ?, 27, 30**

1) 28

2) 32

3) 34

4) 29

5) 36

**7. 9, 12, 30, 99, ?**

1) 406

2) 418

3) 408

4) 416

5) 424

**Directions (Q. 8–10): What value should come in the place of question mark (?) in the following questions?**

**8. 168.781 – 112.412 – 8.409 – 1.150 = ?**

1) 44.81

2) 46.81

3) 40.81

4) 47.81

5) 46.61

**9. [(3√27) + 2√27) * (27√27 + 26√27)] – 159√27 = ?**

1) 1431

2) 1331

3) 1421

4) 1441

5) 1231

**10. 8.5% of 160 – 0.42% of 750 = ?**

1) 11.45

2) 12.45

3) 13.45

4) 9.45

5) 10.45

1.2

I. x^2 + 5x – 4x – 20 = 0

(x – 4) (x + 5) = 0

x = 4, – 5

II. y^2 + 8y + 5y + 40 = 0

(y + 8) (y + 5) = 0

y = –8, – 5

x >= y

2.5

I. x^2 – 6x – 5x + 30 = 0

(x – 5) (x – 6) = 0

x = 5, 6

II. y^2 – 8y – 5y + 40 = 0

(y – 8) (y – 5) = 0

y = 8, 5

No relationship between ‘x’ and ‘y’ exits.

3. 3;

I. (x + 5)^2 = 0

x = –5

II. (√5y – √3)^2 = 0

x = √3/√5

4. 5

I. 10x^2 – 35x + 6x – 21 = 0

(5x + 3) (2x – 7) = 0

x = -3/5, 7/2

II. y^2 + 17y – 4y – 68 = 0

(y – 4) (y + 17) = 0

y = 4, –17

No relationship between x and y exists.

5. 1;

6. 4

7. 3

8. 2

? = 46.81

9. 1

? = (3 + √27)(53√27) - 159√27

= 159√27 + 53 * 27 - 159√27 = 1431

10. 5

? = 8.5/100 * 160 - 0.42/100 * 750

= 13.6 - 3.15 = 10.45

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