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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.5a^{2} – 18a + 9 =0

II.3b^{2} + 5b – 2 = 0

2.

I.√a – √6 / √a = 0

II. b^{3} – 6^{3/2} = 0

3.

I.(625)^{1/4}a + √1225 = 155

II.√196b + 13 = 279

4.

I. 3a^{2} – 17a + 24 =0

II. 4b^{2} – 15b + 14 = 0

5.

I. a^{2} – 2a – √5 a + 2√5 = 0

II. b^{2} – √3 b – √2 b + √6 =0

Directions:6-10) **In each of the following questions, two equations (i) and (ii) are given. You have to solve them and find the correct option**.

6.

a)3+1/x-10/x^{2}=0

b)3y^{2}-5y=12

7.

a)3y-4x+5=0

b) 6x-5y=11

8.

a)7x^{2}+21x+14=0

b)6y^{2}-35y-26=0

9.

a)15x^{2}-61x+56=0

b)20y^{2}+51y+28=0

10.

a)4x^{2}-17x+18=0

b)2y^{2}+13y+21=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.5a

^{2}– 18a + 9 =0

II.3b^{2}+ 5b – 2 = 0Ans: 1

5a^{2}– 18a + 9 = 0

=> 5a^{2}– 15a – 3a + 9 =0

=> (5a – 3 )(a-3 )= 0

=> a= 3/ 5 or a= 3

3b^{2}+ 5b – 2 = 0

=> 3b^{2}+ 6b – b -2 = 0

=> (3b-1)(b + 2) = 0

=> b = 1/3 or -2##### 2. Question

I.√a – √6 / √a = 0

II. b^{3}– 6^{3/2}= 0Ans: 5

√a – √6 / √a = 0

a – √6 = 0

a = √6

b^{3}– 6^{(3/2)}= 0

=>b^{3}= (√6)^{3}

=> b = √6There is no relation between a and b##### 3. Question

.(625)

^{1/4}a + √1225 = 155

II.√196b + 13 = 279Ans: 1

5a + 35 = 155

=> 5a = 155 – 35

=> a = 120/ 5 = 24√196 b + 13 = 279

=> 14b = 279 -13

=> b = 266/14 =19From I and II, a>b

##### 4. Question

I. 3a

^{2}– 17a + 24 =0

II. 4b^{2}– 15b + 14 = 0Ans: 1

3a^{2}-17a + 24 =0

=> 3a^{2}– 9a – 8a +24 = 0

=> (3a- 8)(a-3) = 0

=> a= 8/3 or 3

4b^{2}– 15b + 14 = 0

=> 4b^{2}– 8b -7b +14 = 0

=> (4b -7 )(b-2)=0

=> b = 7 /4 or 2From I and II, a>b##### 5. Question

I. a

^{2}– 2a – √5 a + 2√5 = 0

II. b^{2}– √3 b – √2 b + √6 =0Ans: 1

a^{2}– 2a- √5 a + 2√5 = 0

=> a(a-2 ) – √5 (a-2 )= 0

=> (a-2)(a-√5)=0

=> a= 2 or √5

b^{2}– √3 b – √2 b + √6 =0

=> b(b-√3) – √2(b – √3) = 0

=> (b – √2)(b- √3) =0

=> b = √2 or √3From I and II, a>bDirections:6-10)

**In each of the following questions, two equations (i) and (ii) are given. You have to solve them and find the correct option**.##### 6. Question

a)3+1/x-10/x

^{2}=0

b)3y^{2}-5y=12Ans: 5

a)3+1/x-10/x^{2}=03+1/x-10/x^{2}=03x

^{2}+x-10=0(3x-5)(x+2)=0

x=5/3 and -2

b)3y

^{2}-5y=123y

^{2}-5y-12=0(3y+4)(y-3)=0

y= 3 and -4/3

**Hence, relationship cannot be determined**##### 7. Question

a)3y-4x+5=0

b) 6x-5y=11Ans: 1

3y-4x+5=0………………….. (1)6x-5y=11…………………… (2)Multiply equation (i) by3

9y-12x+15=0

And multiply equation (ii) by 2

12x-10y=22

Solving these equations, we get

x=-4 and y=-7

**Hence x>y**##### 8. Question

a)7x

^{2}+21x+14=0

b)6y^{2}-35y-26=0Ans: 2

a)7x^{2}+21x+14=07x^{2}+14x+7x+14=0(x+1)(7x+14)=0

x=-1 and -2

b)6y

^{2}-35y-26=06y

^{2}+4y-39y-26=02y(3y+2)-13(3y+2)=0

(2y-13)(3y+2)=0

y=13 /2 and -2/3

y= 6.5 and -0.6

**Hence x<y**##### 9. Question

a)15x

^{2}-61x+56=0

b)20y^{2}+51y+28=0Ans: 1

a)15x^{2}-61x+56=015x^{2}-40x-21x+56=0(5x-7)(3x-8)=0

x=8/3 and 7/5

b)20y

^{2}+51y+28=020y

^{2}+16y+35y+28=0(4y+7)(5y+4)=0

y=-4/5 and -7/4

**Hence, x>y**##### 10. Question

a)4x

^{2}-17x+18=0

b)2y^{2}+13y+21=0Ans: 1

a)4x^{2}-17x+18=04x^{2}-8x-9x+18=0(4x-9)(x-2)=0

x=9/4 and 2

b)2y

^{2}+13y+21=02y

^{2}+7y+6y+21=0(y+3)(2y+7)=0

y=-3 and -7/2

**Hence x>y**