**Directions (Q. 1-10): in each question two equations numbered I and II are given. You have to solve both the equations and mark the answer.**

a) If x> y

b) If x ≥ y

c) If x< y

d) If x ≤ y

e) If x = y or no relation can be established between x and y.

**1).**

**I. x**

^{2}– 16 = 0**II. y**

^{4}– {[(8×2)^{9/4}] / √y } = 0

**2).**

**I. x**

^{2}– 2√3x – 72 = 0**II. y**

^{2}+ 9√3x + 60 = 0

**3).**

**I. x**

^{6}– [(√(54×6))^{6.5}/ √x] = 0**II. y – (36 × 81)**

^{1/2}= 0

**4).**

**I. x**

^{2}– 17x – 234 = 0**II. 4y**

^{2}+ 32y – 192 = 0

**5).**

**I. x**

^{2}= 784**II. y**

^{2}– 11y – 102 = 0

**Directions (Q. 6-10): What will come in place of question mark (?) in the following questions?**

**6). 3/8 of 4/9 of 1575 + (√?) – 32% of 786 = 66.98**

a) √56

b) 56

c) (56)2

d) 36

e) (36)2

**7).**

^{3}√97336 +^{2}√6889 ÷ 2^{?}– 3/4 of 65 + 5^{2}= 43a) 4

b) 16

c) 8

d) 2

e) 2.5

**8). (2**

^{3})^{3}× (2^{2})^{2}× (8^{2})^{3/2}/ (2^{2})^{6}= (4)^{?}a) 8

b) 10

c) 2.5

d) 6

e) 5

**9). (4 × 18)**

^{3.35}× (8)^{5.2}× (64)^{7.3}× (27 × 3)^{9.9}= (72)^{?}a) 23.15

b) 24.15

c) 3.35

d) 7.3

e) 20.75

**10). 4 51/13 × 8 3/37 × 1 7/12 × [(16)**

^{2}+ 3 ] = 23 × ?a) 1141.584

b) 1151.584

c) 11415.84

d) 11515.84

e) None of these

__Explanation With Answer Key:__**1). D)**

I. x

^{2}– 16 = 0x

^{2}= 16x = ±4

II. y

^{4}– {[(8×2)^{9/4}] / √y } = 0y

^{4}√y – [(4^{2})^{9/4}] = 0y

^{(4+1/2)}– (4)^{9/2}= 0y

^{9/2}– 4^{9/2}= 0y = 4

Hence x ≤ y

**2). B)**

I. x

^{2}– 2√3x – 72 = 0x

^{2}– 6√3x + 4√3x – 72 = 0x (x – 6√3) + 4√3 (x – 6√3) = 0

x = -4√3, 6√3

II. y

^{2}+ 9√3y + 60 = 0y

^{2}+ 4√3y + 5√3y + 60 = 0y(y + 4√3) + 5√3 (y + 4√3) = 0

y = -4√3, -5√3

Hence x ≥ y

**3). C)**

I. x

^{6}– [(√(54×6))^{6.5}/ √x] = 0x

^{6+(1/2)}– (18)^{6.5}= 0x

^{6.5}= 18^{6.5}x = 18

II. y – (36 × 81)

^{1/2}= 0y – (6 × 9) = 0

y – 54 = 0

y = 54

Hence x< y

**4). E)**

I. x

^{2}– 17x – 234 = 0x

^{2}– 26x + 9x – 234 = 0x(x – 26) + 9 (x – 26) = 0

(x + 9) (x – 26) = 0

x = -9, 26

II. 4y

^{2}+ 32y – 192 = 0y

^{2}+ 32y – 768 = 0y

^{2}+ 48y – 16y – 768 = 0y (y + 48) -16 (y + 48)

y = -48, 16

Hence relation cannot be determined

**5). E)**

I. x

^{2}= 784x = ±28

II. y

^{2}– 11y – 102 = 0y2 – 17y + 6y – 102 = 0

y (y – 17) +6 (y – 17) = 0

y = 17, -6

Hence Relation cannot be determined

**6). C)**

3/8 × 4/9 × 1575 + (√?) – 32% of 786 = 66.98

1/2 × 525 + (√?) – (32/100) × 786 = 66.98

262.5 (100) + (√?) (100) – 25152 = 66.98(100)

26250 – 25152 + (√?) (100) = 6698

(√?) (100) = 5600

? = (56)

^{2}

**7). D)**

^{3}√97336 +

^{2}√6889 ÷ 2

^{?}– 3/4 of 65 + 5

^{2}= 43

46 + 83/2

^{?}– 48.75 + 25 = 4383/20.75 = 2

^{?}4 = 2

^{?}? = 2

**8). E)**

(2

^{3})^{3}× (2^{2})^{2}× (8^{2})^{3/2}/ (2^{2})^{6}= (4)^{?}(4)

^{?}= 2^{9}× 2^{4}× 8^{3}/ 2^{12}(4)

^{?}= 2^{13 – 12}×8^{3}(4)? = (4)

^{5}? = 5

**9). A)**

(72)

^{?}= (4 × 18)^{3.35}× (8)^{5.2}× (64)^{7.3}× (27 × 3)^{9.9}(72)

^{?}= (4 × 2 × 9)^{3.35}× (8)^{5.2}× (8 ×8)^{7.3}× (9 ×9)^{9.9}(72)

^{?}= (8)^{3.35+5.2+7.3+7.3}× (9)^{3.35+9.9+9.9}(72)

^{?}= (72)^{23.15}**10). A)**

23 x = 103/ 13 x 299/ 37 x 19/12 x 259

x=1141.584