(d) if x ≤ y
(e) If x = y or no relation can be established between x and y
Question 11. I.4x²+4x-3=0
II. 4y²-8y+3=0
Question 12. I.11x-13y+48=0
II. 13y+11x=290
Q13. I.2x+3xy=207
II. 15x=945/year
Question 14. I.x²-14x+33=0
II. y2-15y+44=0
Question 15. I. 8x²+22x-21=0
II. 18y²+27y-35=0
Directions (16 – 20): In each of the following questions, two equations (I) and (II) are given, you have to solve both the equations and 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.
Q16. I.x²+9x-22=0
II. 2y² – 7y + 6 = 0
Q17. I. 2y² – 13y – 34 = 0
II. 3x² – 11x – 20 = 0
Question 18. I. x4 = 256
II. y2 – 16y + 64 = 0
Question 19. I. 9x² – 54x + 77 = 0
II. 12y² – 55y + 63 = 0
Q20. I. (x – 1)² = 121
II. y2 – 24y + 144 = 0
Solution
S1. Answer(D)
Sol.
I. 2x² – 17x+ 36 = 0
2x² – 8x – 9x + 36 = 0
2x (x – 4) – 9 (x – 4) = 0
(2x – 9) (x-4) = 0
x=9/2, 4
II. 2y² – 19y + 45 = 0
2y² – 10y – 9y + 45 = 0
2y (y- 5) – 9 (y- 5) = 0
(2y- 9) (y- 5) = 0
y=9/2,5
∴ y ≥ x
S2. Answer(E)
Sol.
I. x² – 25x + 154 = 0
x² – 14x – 11x + 154 = 0
x(x – 14) – 11(x – 14) = 0
(x – 11) (x – 14) = 0
x = 11, 14
II. y2 – 28y + 195 = 0
y² – 13y – 15y + 195 = 0
y (y- 13) – 15 (y -13) =0
(y-13) (y-15) = 0
y = 13, 15
∴ no relation
S3. Answer(A)
Sol.
I. 10/x-24/x² =1
multiplying both sides by x²
10x – 24 = x²
x² – 10x + 24 = 0
x² – 6x -4x+ 24 = 0
x(x – 6) – 4 (x- 6) = 0
(x – 4) (x – 6) = 0
x= 4, 6
II. 5/y-6/y² =1
multiplying both sides by y²
5y – 6 = y²
y² – 5y + 6 = 0
y² – 3y – 2y + 6 = 0
y (y- 3) – 2 (y- 3) = 0
(Y-2) (Y-3) = 0
y = 2, 3
∴ x > y
S4. Answer(D)
Sol.
I. 3x² – 10x – 8 = 0
3x² – 12x + 2x – 8 = 0
3x (x – 4) + 2 (x- 4) = 0
(3x+ 2) (x- 4) = 0
x= -2/3,4
II. 2y²-23y+60=0
2y² – 8y- 15y + 60 = 0
2y (y- 4) -15(y-4) = 0
(y- 4) (2y- 15) = 0
y=4,15/2
∴ y ≥ x
S5. Answer(A)
Sol.
I. 12x – 16y +16 = 0
3x – 4y + 4 = 0 …(i)
II. 17y- 13x = 12…(ii)
By multiplying equation (i) by 13 and equation (ii) by 3
39x – 52y = -52
-39x + 51y = 36
y = 16 and x = 20
∴ x > y
S6. Answer (C)
Sol. I.4x²+4x+1=0
(2x+1)²=0
x=-1/2
II. 9y²+6y+1=0
(3y+1)²=0
y=-1/3
∴
S7. Year
Sol. I.(x-2)²=4
x-2=±2
x=0,4
II. y2−2y+1=0
(y-1)²=0
you=1
∴ No relation can be obtained.
S8. Year
Sol. I.3x+2y=5
II. 4x+6y=10
Equivalent to II by applying 2 × I
x = y = 1
∴ x=y
S9. year(d)
Sol. I. x²-4x-21=0
x²-7x+3x-21=0
x(x-7)+3(x-7)=0
(x+3)(x-7)=0
x=-3,7
II. y2-16y+63=0
y²-7y-9y+63=0
y(y-7)-9(y-7)=0
(y-7)(y-9)=0
y=7,9
So, y≥x
S10. Answer (A)
Sol. I.2x=3y-1
II. x+y=7
2×II-I installation
2x+2y-2x=14-3y+1
5y = 15
you=3
and x=4
∴ x>y
S11. year(d)
Sol. I. 4x²+6x-2x-3=0
2x(2x+3)-1(2x+3)=0
(2x-1)(2x+3)=0
So, x=1/2,-3/2
II. 4y²-6y-2y+3=0
2y(2y-3)-1(2y-3)=0
(2y-1)(2y-3)=0
y=1/2,3/2
So, y≥x
S12. year(c)
Sol. I.11x-13y+48=0
II. 13y+11x=290
On joining I and II
22x+48=290
x=242/22
x=11
Put x = 11 in I
121-13y+48=0
13y=169
y=13
So, y > x
S13. year(y)
Sol. I.2x+3xy=207
II. 15x=945/year
from second
xy=63
So, 3xy=189
Put the value of 3xy in I
2x+189=207
x=18/2
x=9
y=7
So, x > y
S14. Year
Sol. I.x²-14x+33=0
x²-11x-3x+33=0
x(x-11)-3(x-11)=0
(x-11)(x-3)=0
x=3,11
II. y2-15y+44=0
y²-11y-4y+44=0
y(y-11)-4(y-11)=0
(y-4)(y-11)=0
y=4,11
Therefore, no relation can be obtained between x and y.
S15. Year
Sol. I. 8x²+28x-6x-21=0
4x(2x+7)-3(2x+7)=0
(4x-3)(2x+7)=0
x=-7/2,3/4
II. 18y²+42y-15y-35=0
6y(3y+7)-5(3y+7)=0
(6y-5)(3y+7)=0
y=-7/3,5/6
Therefore, no relation can be obtained between x and y.
S16. Answer(E)
Sol. I.x²+9x-22=0
⇒ x² + 11x – 2x – 22 = 0
⇒ (x + 11) (x – 2) = 0
⇒ x = – 11, 2
II. 2y² – 7y + 6 = 0
⇒ 2y² – 4y – 3y + 6 = 0
⇒ 2y(y–2)–3(y–2) =0
⇒ (y–2) (2y–3) = 0
⇒ y = 2, 3/2
no relation
S17. Answer(E)
Sol. I. 2y² – 13y – 34 = 0
⇒ 2y² – 17y + 4y – 34 = 0
⇒ y(2y–17) + 2(2y–17) = 0
⇒ (2y–17) (y+2) = 0
⇒ y = 17/2,–2
II. 3x² – 11x – 20 = 0
⇒ 3x² – 15x + 4x – 20 = 0
⇒ 3x (x–5) + 4(x–5) =0
⇒ (x – 5) (3x + 4) = 0
⇒ x = 5, (-4)/3
no relation
S18. Answer (C)
Sol. I. x4 = 256
⇒ x = ± 4
II. y2 – 16y + 64 = 0
⇒ (y – 8) ² = 0
⇒ y = 8
y > x
S19. Answer(B)
Sol. I. 9x² – 54x + 77 = 0
9x² – 21x – 33x + 77 = 0
3x (3x – 7) – 11(3x – 7) = 0
(3x – 7)(3x – 11) = 0
x = 7/3,11/3
II. 12y² – 55y + 63 = 0
12y² – 28y – 27y + 63 = 0
4y (3y – 7) –9 (3y – 7) = 0
(4y – 9) (3y – 7) = 0
y = 9/4,7/3
So, x ≥ y
S20. Answer(D)
Sol. I. (x – 1)² = 121
x – 1 = ± 11
x = 12, – 10
II. y2 –24y + 144 = 0
(y – 12)² = 0
y = 12
So, y ≥ x
