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Directions: In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer.
» Explain it
A
I. 8x2 – 23x + 15 = 0

8x2 – 8x – 15x + 15 = 0

8x (x – 1) – 15 (x – 1) = 0

(8x – 15) (x – 1) = 0

x =  15 , 1
8
 
II. 3y2 + 11y + 8 = 0

3y2 + 3y + 8y + 8 = 0

3y (y + 1) + 8 (y + 1) = 0

(3y + 8) (y + 1) = 0

y = –  8 , – 1
3

Hence, x > y

Hence, option A is correct.
» Explain it
A
I. 2x2 – 19x + 42 = 0

2x2 – 12x – 7x + 42 = 0

2x (x – 6) – 7 (x – 6) = 0

(2x – 7) (x – 6) = 0

x =  7 , 6
2
 
II. 20y2 – 89y + 99 = 0

20y2 – 45y – 44y + 99 = 0

5y (4y – 9) – 11 (4y – 9) = 0

(5y – 11) (4y – 9) = 0

y =   11 ,  2.25
5

Hence, x > y

Hence, option A is correct.
» Explain it
A
I. (144)1/2 x + √7396 = 194

12x + 86 = 194

x =  194 – 86  =  108  = 9
12 12
 
II. (729)1/2 y2 – 545 = √16900

27y2 – 545 = √16900

y2 130 + 545  =  675  = 25
27 27

y = ± 5

Hence, x > y

Hence, option A is correct.
» Explain it
E
I. 2x2 – 23x + 56 = 0

2x2 – 16x – 7x + 56 = 0

2x (x – 8) – 7 (x – 8) = 0

(2x – 7) (x – 8) = 0

x =  7 , 8
2
 
II. 4y2 – 19y + 12 = 0

4y2 – 16y – 3y + 12 = 0

4y (y – 4) – 3 (y – 4) = 0

(4y – 3) (y – 4) = 0

y =   3 , 4
4

Hence, no relationship can be established.

Hence, option E is correct.
» Explain it
A
I. 5x + 9y = 109 .........(i)

II. 3x + 4y = 62 ...........(ii)

Eqn. (i) × 3 – (ii) × 5, we get

15x + 27y = 327
15x + 20y = 310
–     –        –       
           7y = 17

y =  17  = 2  3
7 7

Putting the value of y in eqn. (i) or (ii), we get

x =  122  = 17  3
7 7

Hence, x > y

Hence, option A is correct.