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

1.

I. X2+5 √3x -42 =0
II. Y2 -√2y -24 =0

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

X =-7 √3,, 2√3

Y2 – √2y -24 =0

Y2 – 4 √2y +3 √2y -24 =0

Y = 4 √2, -3 √2

The relationship cannot be determined.

2.

I. 5x – 2.2y = –17
II. 4x + 0.6y = 31

Ans:2
5x – 2.2y = –174x + 0.6y = 31

Simply the above equation, we get x= 10 and y = 15

x < y

3.

I. 30×2+89x+58 =0
II. 27y2 -51y -56 =0

Ans:2
I. 30x2+89x +58 =030x2 +60x + 29x +58 =0

30x(x+2)+29 (x+2) =0

(30x+29) (x+2) =0

X = -29/30, -2

II. 27y2-51y -56 =0

27y2 -72y + 21y -56 =0

9y(3y -8) +7(3y-8) =0

(9y+7)(3y-8) =0

Y = -7/9, 8/3

X < Y

4.

I. X2 -4x +3.91 =0
II. Y2-6y +8.75 =0

Ans:2
X2 -4x +3.91 =0X2-2.3x – 1.7x +3.91 =0

X(x-2.3) – 1.7 (x-3.91) =0

(x-1.7)(x-2.3) =0

X=2.3, 1.7

Y2-6y +8.75 =0

Y2-3.5y-2.5y+8.75 =0

Y (y-3.5) – 2.5 (y-3.5) =0

(y-3.5)(y-2.5)=0

Y=3.5, 2.5

x < y

5.

I. 78x2+199x+65 =0
II. 56y2+127y+72 =0

Ans:5
I. 78x2+199x +65 =078x2 +169x+30x +65 =0

13x (6x+13) +5(6x+13) =0

(13x+5) (6x+13) =0

X= -5/13, -13/6

II. 56y2+127y +72 =0

56y2 +64y+63y +72 =0

8y (7y+8) +9(7y+8) =0

(8y+9)(7y+8) =0

Y= -9/8, -8/7

Relationship cannot be determined.

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.

  1. (x1/4 /20)2 = 196/X3/2
  2. Y1/3*y2/3*143 = 7*y4

Ans:5
(x1/4 /20)2 = 196/X3/2X1/2/202 =196 / X3/2

X2=78400

X = 280 , -280

Y1/3*y2/3*143 = 7*y4

Y*143=7 * y4

14*14*14/7 =y3

Y3= 196*2

Y3 =392

Y = 7.31 =7

The relation cannot be established.

7.

  1. 4/x1/2 +7/x1/2 = x1/2
  2. Y2 – (115/2/y1/2) =0

Ans:5
4/x1/2 +7/ x1/2 = x1/211 =X

Y2 – (115/2/y1/2) =0

Y5/2 =115/2

Y =11

x = y or relation cannot be established.

8.

  1. 5001/2x +4021/2 =0
  2. 3601/2y +2001/2 =0

Ans:2
5001/2x +4021/2 =0X = – (402/500)1/2

X = – 20/22 = -10/11

3601/2y +2001/2 =0

Y = – ( 200/360 )1/2 = – 14/19

x < y

9.

  1. X2-5 √3x -42 =0
  2. 4 √3 y2 -5y -2 √3 =0

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

X =-7 √3 , 2√3

4 √3Y2 -5y -2 √3 =0

Y = +8 /4√3 , -3 / 4 √3

x = y or relation cannot be established.

10.

  1. (x+40)1/2 =2561/2 – 1211/2
  2. Y2+576 =697

Ans:2
(x+40)1/2 =2561/2 – 1211/2X+40 =25

X=-15

Y2+576 =697

Y2 =121

Y =11 ,-11

x < y

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