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- Question 1 of 10
##### 1. Question

Directions:1-5)

**In each of the following questions two equations****Ⅰ****and****Ⅱ****are given. You have to solve both the equations and give answer**- 9P
^{2}– 9P + 2 = 0 - 18Q
^{2}+ 3Q = 1

Correct9P

^{2}– 9P + 2 = 0Or,

^{2}– 6P – 3P + 2 = 0Or, (3P – 1)(3P – 2) = 0

P = (1 / 3), (2 / 3)

Ⅱ. 18Q

^{2}+ 3Q – 1 = 0Or, 18Q

^{2}+ 6Q – 3Q – 1 = 0Or, (6Q – 1)(3Q + 1) = 0

Q = – (1 / 3), (1 / 6)

Hence, P > Q

Incorrect9P

^{2}– 9P + 2 = 0Or,

^{2}– 6P – 3P + 2 = 0Or, (3P – 1)(3P – 2) = 0

P = (1 / 3), (2 / 3)

Ⅱ. 18Q

^{2}+ 3Q – 1 = 0Or, 18Q

^{2}+ 6Q – 3Q – 1 = 0Or, (6Q – 1)(3Q + 1) = 0

Q = – (1 / 3), (1 / 6)

Hence, P > Q

- 9P
- Question 2 of 10
##### 2. Question

- I. P
^{2}+ 13P + 42 = 0 - 2Q
^{2}+ 22Q + 60 = 0

CorrectⅠ

**.**P^{2}+ 13P + 42 = 0Or,

^{2}+ 7P + 6P + 42 = 0Or, (P + 7)(P + 6) = 0

∴ P = -7, -6

Ⅱ. 2Q

^{2}+ 22Q + 60 = 0Or, Q

^{2}+ 11Q + 30 = 0Or, (Q + 5)(Q + 6) = 0

∴ Q = -5, -6

Hence , Q ≥ P

IncorrectⅠ

**.**P^{2}+ 13P + 42 = 0Or,

^{2}+ 7P + 6P + 42 = 0Or, (P + 7)(P + 6) = 0

∴ P = -7, -6

Ⅱ. 2Q

^{2}+ 22Q + 60 = 0Or, Q

^{2}+ 11Q + 30 = 0Or, (Q + 5)(Q + 6) = 0

∴ Q = -5, -6

Hence , Q ≥ P

- I. P
- Question 3 of 10
##### 3. Question

- I. 6P + 7Q = 45
- 2P + 3Q = 17

CorrectP = 4 and Q = 3

Hence P > Q

IncorrectP = 4 and Q = 3

Hence P > Q

- Question 4 of 10
##### 4. Question

- I. 3P
^{2}+ 192 = – 48P - Q
^{2}+ 16Q + 64 = 0

CorrectⅠ

**.**3P^{2}+ 48P + 192 = 0Or,

^{2}+ 16P + 64 = 0Or, (P + 8)

^{2}= 0∴ P = -8

Ⅱ. Q

^{2}+ 16Q + 64 = 0Or, (Q + 8)

^{2}= 0∴ Q = -8

Hence , P = Q

IncorrectⅠ

**.**3P^{2}+ 48P + 192 = 0Or,

^{2}+ 16P + 64 = 0Or, (P + 8)

^{2}= 0∴ P = -8

Ⅱ. Q

^{2}+ 16Q + 64 = 0Or, (Q + 8)

^{2}= 0∴ Q = -8

Hence , P = Q

- I. 3P
- Question 5 of 10
##### 5. Question

I. 15P

^{2}– 8P + 1 = 0II. 45Q

^{2}+ 21Q = 6CorrectⅠ

**.**15P^{2}– 8P + 1 = 0Or,

^{2}– 3P – 5P + 1 = 0Or, (3P – 1)(5P – 1) = 0

∴ P = (1 / 3), (1 / 5)

Ⅱ. 45Q

^{2}+ 21Q – 6 = 015Q

^{2}+ 7Q – 2 = 0Or, 15Q

^{2}+ 10Q – 3Q – 2 = 0Or, (5Q – 1)(3Q + 2) = 0

∴ Q = (1 / 5), – (2 / 3)

Hence, P ≥ Q

IncorrectⅠ

**.**15P^{2}– 8P + 1 = 0Or,

^{2}– 3P – 5P + 1 = 0Or, (3P – 1)(5P – 1) = 0

∴ P = (1 / 3), (1 / 5)

Ⅱ. 45Q

^{2}+ 21Q – 6 = 015Q

^{2}+ 7Q – 2 = 0Or, 15Q

^{2}+ 10Q – 3Q – 2 = 0Or, (5Q – 1)(3Q + 2) = 0

∴ Q = (1 / 5), – (2 / 3)

Hence, P ≥ Q

- Question 6 of 10
##### 6. Question

Directions:6-10)

**In the following questions two equations numbered I and II are given. You have to solve both the equations and**I. X – 8/√X=0

II. √Y- √7/√Y=0

CorrectI. X – 8/√X=0

Or, x

^{3/2}= 8Or, X = 4

II. √Y- √7/√Y=0

Or, Y = √7

Y = 2.6

Hence X > Y

IncorrectI. X – 8/√X=0

Or, x

^{3/2}= 8Or, X = 4

II. √Y- √7/√Y=0

Or, Y = √7

Y = 2.6

Hence X > Y

- Question 7 of 10
##### 7. Question

I. 8X

^{2}+78X+169=0II. 5Y

^{2}+ 14Y+8=0CorrectI. 8X

^{2}+78X+169=0Or, 8X

^{2}+52X+26X+169=0Or, 4X(2X+13)+ 13(2X+13)=0

Or, (4X+13)(2X+13)=0

X= (-13)/4,(-13)/2

II.5Y

^{2}+ 14Y+8=0Or, 5Y

^{2}+10Y+4Y+8=0Or, 5Y(Y+2)+4(Y+2)=0

Or, (5Y+4)(Y+2)=0

Y= -2 , (-4)/5

Hence X< Y

IncorrectI. 8X

^{2}+78X+169=0Or, 8X

^{2}+52X+26X+169=0Or, 4X(2X+13)+ 13(2X+13)=0

Or, (4X+13)(2X+13)=0

X= (-13)/4,(-13)/2

II.5Y

^{2}+ 14Y+8=0Or, 5Y

^{2}+10Y+4Y+8=0Or, 5Y(Y+2)+4(Y+2)=0

Or, (5Y+4)(Y+2)=0

Y= -2 , (-4)/5

Hence X< Y

- Question 8 of 10
##### 8. Question

I. 12X

^{2}-5X-25=0II. 12Y

^{2}+17Y-40=0CorrectI. 12X

^{2}-5X-25=0Or, 12X

^{2}+15X-20X-25=0Or, 3X(4X+5)-5(4X+5)=0

Or, (3X-5)(4X+5)=0

X = 5/3,(-5)/4

II. 12Y

^{2}+17Y-40=0Or, 12Y

^{2}-15Y+32Y-40=0Or, 3Y(4Y-5)+8(4Y-5)=0

Or, (3Y+8)(4Y-5)=0

Y = 5/4,(-8)/3

Hence the relationship between x and y cannot be established

IncorrectI. 12X

^{2}-5X-25=0Or, 12X

^{2}+15X-20X-25=0Or, 3X(4X+5)-5(4X+5)=0

Or, (3X-5)(4X+5)=0

X = 5/3,(-5)/4

II. 12Y

^{2}+17Y-40=0Or, 12Y

^{2}-15Y+32Y-40=0Or, 3Y(4Y-5)+8(4Y-5)=0

Or, (3Y+8)(4Y-5)=0

Y = 5/4,(-8)/3

Hence the relationship between x and y cannot be established

- Question 9 of 10
##### 9. Question

I. 15X+13Y=221

II. 4Y+2X=51

Correct15X+13Y=221 … (i) ×4

2X+4Y=51 … (ii) × 13

60X + 52Y = 884 …. iii

26X + 52Y = 663 ….iv

After solving (iii) and (iv), we have

34X = 221

Or, X = 6.5

Putting the value of X in (i), we get

Or, 97.5 + 13Y= 221

Or, 13Y=123.5

Y= 9.5

Hence X< Y

Incorrect15X+13Y=221 … (i) ×4

2X+4Y=51 … (ii) × 13

60X + 52Y = 884 …. iii

26X + 52Y = 663 ….iv

After solving (iii) and (iv), we have

34X = 221

Or, X = 6.5

Putting the value of X in (i), we get

Or, 97.5 + 13Y= 221

Or, 13Y=123.5

Y= 9.5

Hence X< Y

- Question 10 of 10
##### 10. Question

6X

^{2}+34=29X8Y

^{2}+3Y=38Correct. 6X

^{2 }-29X+34=0Or, 6X

^{2}-12X-17X+34=0Or, 6X(X-2)-17(X-2)=0

Or, (6X-17)(X-2)=0

X= 2, 17/6

II. 8Y

^{2}+3Y=38Or, 8Y

^{2}+3Y-38=0Or, 8Y

^{2}-16Y+19Y-38=0Or, 8Y(Y-2)+19(Y-2)=0

Or, (8Y+19)(Y-2)=0

Y= 2, (-19)/8

Hence X ≥ Y

Incorrect. 6X

^{2 }-29X+34=0Or, 6X

^{2}-12X-17X+34=0Or, 6X(X-2)-17(X-2)=0

Or, (6X-17)(X-2)=0

X= 2, 17/6

II. 8Y

^{2}+3Y=38Or, 8Y

^{2}+3Y-38=0Or, 8Y

^{2}-16Y+19Y-38=0Or, 8Y(Y-2)+19(Y-2)=0

Or, (8Y+19)(Y-2)=0

Y= 2, (-19)/8

Hence X ≥ Y