## Simplification And Quadratic Equation Quiz

Direction (1-5): What value will come in place of the question mark (?) in the following questions ?

- 624 ÷ 26 × 3 + 110 =?

(1) 182 (2) 172 (3) 118 (4) 108 (5) None of these

- 456 – 559 = ? – 213 + 1118

(1) 34 (2) 2118 (3) 179 (4) 11118 (5) None of these

- 567 – 4824 ÷ 134 = ? × 9

(1) 33 (2) 59 (3) 37 (4) 57 (5) None of these

- (0.125)3÷ (0.25)2× (0.5)2=(0.5)?–3

(1) 12 (2) 18 (3) 14 (4) 10 (5) None of these

- 160% of 250 + ? = 120% of 400

(1) 160 (2) 40 (3) 80 (4) 120 (5) None of these

Direction (66-70) : In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer.

**If**

(1) x > y

(2) x y

(3) x < y

(4) x y

(5) x = y or the relationship cannot be established

- I. 5x2 – 87x + 378 = 0
- 3y2 – 49y + 200 = 0

- I. 14x2 – 37x + 24 = 0
- 28y2 – 53y + 24 = 0

- I. 2x2 – 3x – 35 = 0
- y2 – 7y + 6 = 0

- I. 6x2 – 29x + 35 = 0
- 2y2 – 19y + 35 = 0

- I. 12x2 – 47x + 40 = 0
- 4y2 + 3y – 10 = 0

- (1)

624 ÷ 26 × 3 + 110 = ?

24 × 3 + 110

72 + 110

182

- (5)

456 – 5 59 = ? –213 + 1118

? = 456 – 559 + 213 – 1118

? = (4 + 2 – 5) + (56 – 13– 59) – 1118

? = 1 + (15+ 6 – 1018) – 1118

? = 1 + (1118 – 1118)

? = 1 + 2218 = 1 + 119

? = 229

- (2)

567 – 4824 ÷ 134 = ? × 9

567 – 36 = ? × 9

531 = ? × 9

? = 5319 = 59

- (4)

(0.125)3 ÷ (0.25)2 × (0.5)2 = (0.5)? – 3

(0.5)9 ÷ (0.5)4 × (0.5)2 = (0.5)? – 3

? – 3 = 9 – 4 + 2

? – 3 = 7

? = 7 + 3 = 10

- (3)

160% of 250 + ? = 120% of 400

250 × 160100 + ? = 400 × 120100

400 + ? = 480

? = 480 – 400 = 80

- (1)
- 5x2 – 87x + 378 = 0

5x2 – 45x – 42x + 378 = 0

5x (x – 9) – 42(x – 9) = 0

(5x – 42) (x – 9) = 0

x = 425 , 9

- 3y2 – 49y + 200 = 0

3y2 – 24y – 25y + 200 = 0

3y(y – 8) – 25(y – 8) = 0

(3y – 25) (y – 8) = 0

y = 253 , 8

Cleary, x > y

- (2)
- 14x2 – 37x + 24 = 0

14x2 – 21x – 16x + 24 = 0

7x (2x – 3) – 8(2x – 3) = 0

(7x – 8) (2x – 3) = 0

x = 87 , 32

- 28y2 – 53y + 24 = 0

28y2 – 21y – 32y + 24 = 0

7y (4y – 3) – 8(4y – 3) = 0

(7y – 8) (4y – 3) = 0

y = 87 , 34

clearly, x > y

- (5)
- 2x2 – 3x – 35 = 0

2x2 – 10x + 7x – 35 = 0

2x(x – 5) +7(x – 5) = 0

(2x + 7) (x – 5) = 0

x = – 7 2 , 5

- y2 – 7y + 6 = 0

y2 – 6y – y + 6 = 0

y(y – 6) – 1(y – 6) = 0

(y – 1) (y – 6) = 0

y = 1, 6

- (4)
- 6x2 – 29x + 35 = 0

6x2 – 15x – 14x + 35 = 0

3x(2x – 5) – 7(2x – 5) = 0

(3x – 7) (2x – 5) = 0

x = 73 , 52

- 2y2 –19y + 35 = 0

2y2 – 14y – 5y + 35 = 0

2y (y – 7) – 5(y – 7) = 0

(2y – 5) (y – 7) = 0

y = 52 , 7

Clearly, x < y

- (2)
- 12x2 – 47x + 40 = 0

2x2 – 15x – 32x + 40 = 0

3x (4x – 5) – 8(4x – 5) = 0

(3x – 8) (4x – 5) = 0

x = 83 , 54

- 4y2 + 3y – 10 = 0

4y2 + 8y – 5y – 10 = 0

4y (y + 2) – 5(y + 2) = 0

(4y – 5) (y + 2) = 0

y = 54 , –2

Clearly, x y