Directions:1-5) In the following question, two equations I and II are given. Solve both the equations carefully & answer the questions given below:

1.
X2 -6 √3 X -48 =0
Y2 – √2y -24 =0

Ans:3
X2 -6 √3 X -48 =0X(x -8 √3) +2 √3 (x -8 √3) =0

(X -8 √3) (x + 2 √3) =0

X =8 √3, – 2 √3

Y2 – √2y -24 =0

Y2 – 4 √2y +3 √2y -24 =0

Y = 4 √2, – 3 √2

Relationship cannot be determined.

2.
X2+5 √3 X -42 =0
Y2 – 8 √2 y +30 = 0

Ans:2
X2+5 √3 X -42 =0(X +7 √3) (X – 2√3) =0

X = -7 √3, 2 √3

Y2 – 8 √2y +30 = 0

Y = 5 √2 , 3 √2

x < y

3.
X2 +4 √10 x+40 =0
4 √3 Y2 -5y -2 √3 =0

Ans:2
X2 +4 √10 x + 40=0(X +2 √10) (X +2 √10) =0

X= – 2 √10, – 2 √10

4 √3 Y2 -5y -2 √3 =0

Y = +8 /4 √3, -3 / 4 √3

x < y

4.
X2– √2 x -24 =0
Y2 – 8  √3 y +48 =0

Ans:2
X2 – √2X -24 =0X2 – 4 √2X +3 √2X -24 =0

X = 4 √2 ,  -3 √2

Y2 – 8 √ 3 y +48 =0

(Y -4 √3 ) (Y -4 √3 ) =0

Y =4 √3   , 4 √3

x < y

5.
2X2 – (4+√13) x +2 √13 =0
10y2 – (18+5 √13) y +9 √13 =0

Ans:3
2X2 – (4+√13)x +2 √13 =0X = 4 /2, √13/2

X=2, 1.8

10y2 – (18+5 √13)y +9 √13 =0

Y = 18/10, 5 √13 /10

Y =1.8, 1.8

x ≥ y

Directions:6-10) In the following question, two equations I and II are given. Solve both the equations carefully & answer the questions given below:

6.
3x+5y =69
9x+4y =108

Ans:2
9x+4y =108 ——– (1)3x+5y =69 ——— (2­)

à(2)*3

9x+15y = 207

9x+4y =108

11y =99

Y=9

9x +36 =108

9x=72

X=8

x < y

7.
63x -194x1/2+143 =0
99y-255y1/2+150=0

Ans:5

  1. 63x -194 x1/2+143 = 0

Or 63x -117 x ½ -77 x ½ +143 = 0

Or (7 x1/2 -13) (9 x1/2 -11) = 0

x =169/ 49,121/81

        2. 99y – 255 y ½ +150 = 0

or 99y – 165 y 1/2 – 90 y 1/2 +150 = 0

or (11y1/2 – 10)(9y1/2 -15) = 0

y = 100/121, 225/81

8.
12x2 + 11 x + 12 = 10x2+22x
13y2 – 18y + 3 = 9y2 – 10y

Ans:3
12x2 + 11 x + 12 = 10x2+22x2x2 -11x +12 =0

X =8/2, 3/2 = 4, 1.5

13y2 – 18y + 3 = 9y2 – 10y

4y2 -8y +3 =0

Y = 6/4, 2/4 =1.5, 0.5

X≥ y

9.
16x2 – 40x – 39 = 0
12y2 – 113y + 255 = 0

Ans:2
16x2 – 40x – 39 = 0or 16x2 – 52x + 12x – 39 = 0

or (4x- 13) (4x + 3)

x= 13/4, – ¾

12y2 – 113y + 255 = 0

or 12y2 – 45y – 68y + 255 = 0

or (4y – 15) (3y – 17) = 0

y =15/4, 17/3

x < y

10.
(X1/4 )2/625 =169/X3/2
Y4/3* Y2/3*2786 =7*Y3

Ans:2
X1/2 /625 =169/X3/2X2 = 625*169

X=  ± (25*13) = ±325

Y6/3*2786 =7*y3

Y =2786/7 =398

X<Y

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