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

Directions: 1-5)

**In the following questions, two equations I and II are given. You have to solve both the equations.****Give Answer**- p
^{2}– 18p + 72= 0 - 5q
^{2}– 18q + 9 = 0

Correctp

^{2}– 18p + 72= 0

(p-12)(p-6) = 0

Gives p = 6, 12

5q^{2}– 18q + 9 = 0

5q^{2}– 15q – 3q + 9 = 05q (q-3) – 3(q-3) =0

(5q-3) (q-3) =0

Gives q = 3/5, 3

Put on number line

3/5 3 6 12P > q

Incorrectp

^{2}– 18p + 72= 0

(p-12)(p-6) = 0

Gives p = 6, 12

5q^{2}– 18q + 9 = 0

5q^{2}– 15q – 3q + 9 = 05q (q-3) – 3(q-3) =0

(5q-3) (q-3) =0

Gives q = 3/5, 3

Put on number line

3/5 3 6 12P > q

- p
- Question 2 of 10
##### 2. Question

- p
^{2}= 4 - 3q
^{2}– 4q – 4 = 0

Correctp

^{2}= 4

Gives p = 2 , -2

3q^{2}– 4q – 4 = 0

3q^{2}– 6q + 2q – 4 = 0

Gives q = -2/3, 2

Put on number line

-2 -2/3 2

So no relationIncorrectp

^{2}= 4

Gives p = 2 , -2

3q^{2}– 4q – 4 = 0

3q^{2}– 6q + 2q – 4 = 0

Gives q = -2/3, 2

Put on number line

-2 -2/3 2

So no relation - p
- Question 3 of 10
##### 3. Question

- 6p
^{2}– 5p – 6 = 0 - 2q
^{2}– 13q + 20 = 0

Correct6p

^{2}– 5p – 6 = 0

6p^{2}– 9p + 4p – 6 = 0

Gives p = -2/3, 3/2

2q^{2}– 13q + 20 = 0

2q^{2}– 8q – 5q +20 = 0

Gives q = 4, 5/2

Put on number line

-2/3 3/2 5/2 4P < q

Incorrect6p

^{2}– 5p – 6 = 0

6p^{2}– 9p + 4p – 6 = 0

Gives p = -2/3, 3/2

2q^{2}– 13q + 20 = 0

2q^{2}– 8q – 5q +20 = 0

Gives q = 4, 5/2

Put on number line

-2/3 3/2 5/2 4P < q

- 6p
- Question 4 of 10
##### 4. Question

- 2p
^{2}– 5p = 0 - 3q
^{2}– 7q – 6 = 0

Correct2p

^{2}– 5p = 0

p(2p-5) = 0

Gives p = 0, 5/2

3q^{2}– 7q – 6 = 0

3q^{2}– 9q + 2q – 6 = 0

Gives q = -2/3, 3

Put on number line

-2/3 0 5/2 3There is no relation

Incorrect2p

^{2}– 5p = 0

p(2p-5) = 0

Gives p = 0, 5/2

3q^{2}– 7q – 6 = 0

3q^{2}– 9q + 2q – 6 = 0

Gives q = -2/3, 3

Put on number line

-2/3 0 5/2 3There is no relation

- 2p
- Question 5 of 10
##### 5. Question

- 2p
^{2}+ 5p + 2= 0 - 2q
^{2}+ 19q + 45 = 0

Correct2p

^{2}+ 5p + 2= 0

2p^{2}+ 4p + p + 2= 0

Gives p = -1/2, -2

2q^{2}+ 19q + 45 = 0

2q^{2}+ 10q + 9q + 45 = 0

Gives q= -10/2, -9/2

Put on number line

-10/2 -9/2 -2 -1/2P > q

Incorrect2p

^{2}+ 5p + 2= 0

2p^{2}+ 4p + p + 2= 0

Gives p = -1/2, -2

2q^{2}+ 19q + 45 = 0

2q^{2}+ 10q + 9q + 45 = 0

Gives q= -10/2, -9/2

Put on number line

-10/2 -9/2 -2 -1/2P > q

- 2p
- Question 6 of 10
##### 6. Question

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**.i) 3x

^{2}-23x+44=0ii) y

^{2}-23y+132=0Correcti) 3x

^{2}-23x+44=03x

^{2}-12x-11x+44=0(x-4)(3x-11)=0

x= 4 or 11/3

ii) y

^{2}-23y+132=0(y-12)(y-11)=0

y= 12 or 11

Thus

**x<y**Incorrecti) 3x

^{2}-23x+44=03x

^{2}-12x-11x+44=0(x-4)(3x-11)=0

x= 4 or 11/3

ii) y

^{2}-23y+132=0(y-12)(y-11)=0

y= 12 or 11

Thus

**x<y** - Question 7 of 10
##### 7. Question

i) x

^{2}-6√3x-480=0ii) y

^{2}-11√2y-420=0Correcti) x

^{2}-6√3x-480=0x

^{2}-6x-160=0(x-16)(x+10)=0

x= 16 or -10

ii) y

^{2}-11√2y-420=0y

^{2}– 11y- 210=0(y-21)(y+10)=0

y=21 or -10

Hence

**The relationship cannot be determined.**Incorrecti) x

^{2}-6√3x-480=0x

^{2}-6x-160=0(x-16)(x+10)=0

x= 16 or -10

ii) y

^{2}-11√2y-420=0y

^{2}– 11y- 210=0(y-21)(y+10)=0

y=21 or -10

Hence

**The relationship cannot be determined.** - Question 8 of 10
##### 8. Question

i) 7x-5y-74=0

ii) 3x+2y-301=0

Correct7x-5y-74=0 ………… (1)

3x+2y-301=0 …………….. (2)

After solving (1) and (2), we have

x= 57 and y= 65

**x < y**Incorrect7x-5y-74=0 ………… (1)

3x+2y-301=0 …………….. (2)

After solving (1) and (2), we have

x= 57 and y= 65

**x < y** - Question 9 of 10
##### 9. Question

i) x

^{(4/3)}/289=25/x^{(2/3)}ii) y

^{(4/5)}/4913=125/y^{(11/5)}Correcti) x

^{(4/3)}/289=25/x^{(2/3)}x

^{(4/3)}*x^{(2/3)}=7225x

^{2}= 7225x=85 and -85

ii) y

^{(4/5)}/4913=125/y^{(11/5)}y

^{(15/5)}=125*4913y= 85

Thus

**x ≤ y**Incorrecti) x

^{(4/3)}/289=25/x^{(2/3)}x

^{(4/3)}*x^{(2/3)}=7225x

^{2}= 7225x=85 and -85

ii) y

^{(4/5)}/4913=125/y^{(11/5)}y

^{(15/5)}=125*4913y= 85

Thus

**x ≤ y** - Question 10 of 10
##### 10. Question

i) 2x

^{2}+8x-42=0ii) 6y

^{2}-101y+33=0Correcti) 2x

^{2}+8x-42=0x

^{2}+4x-21=0(x-3)(x+7)=0

x=3 or -7

ii) 6y

^{2}-101y+33=06y

^{2}-2y-99y+33=0(3y-1)(2y-33)=0

y=1/3 or 33/2

Hence the relationship cannot be determined.

Incorrecti) 2x

^{2}+8x-42=0x

^{2}+4x-21=0(x-3)(x+7)=0

x=3 or -7

ii) 6y

^{2}-101y+33=06y

^{2}-2y-99y+33=0(3y-1)(2y-33)=0

y=1/3 or 33/2

Hence the relationship cannot be determined.