To solve Quadratic Equations with the help of Number Line
1. x² + 4x - 221 = 0 y² - 21y - 196 = 0
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
2. x² - 56x + 255 = 0 y² - 34y + 208 = 0
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
3. x² + x - 272 = 0 y² - 30y + 224 = 0
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
4. x² - 27x + 182 = 0 y²+ 41y - 702 = 0
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
5. x² - 27x + 180 = 0 y² + 20y + 91 = 0
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
6. x² + 39x + 324 = 0 6y² - y - 5 = 0
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
7. x² + 23x - 420 = 0 y² - 28y + 195 = 0
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
8. x² - 20x + 525 = 0 y² + 40y + 391 = 0
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
9. 2x² - 3x - 20 = 0 y² - 9y + 20 = 0
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
10.x² - 19x + 90 = 0 y² - 16y + 63 = 0
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
11.For which of the following equations the value of X is less than Y(XY)
I. 3X2+23X + 44 = 0; 3Y2 + 20Y +33 = 0
II. 3X2+29 X +56 = 0; 2Y2 + 15Y + 25 = 0
III. 3X2- 16X + 21 = 0; 3Y2 - 28Y + 65 = 0
1.Only I
2.Only II
3.Both I and III
4.Both II and III
5.None follow
12.For which of the following equations the value of X is less than or equal to Y (X? Y)
I. X2- 4X + 3= 0; Y2 - 8Y + 15 = 0
II. 3X2 - 19X + 28= 0; 4Y2 - 29Y + 45 = 0
III. x2 - (16)2 = (23)2 - 56; y1/3 - 55 + 376 = (18)2
1.Only I
2.Only II
3.Both I and III
4.Both II and III
5.All follow
13.For which of the following equations the value of X is greater than or equal to Y ( X ? Y)
I. X2 -3X - 4 = 0; 3Y2 - 10Y+8 = 0
II. ?(x + 6) = ?121 - ?36; y2 + 112 = 473
III. 5x2- 7x - 6 = 0; 5y2 + 23y + 12 = 0
1.Only I
2.Only II
3.Both I and III
4.Both II and III
5.None follow
14. For which of the following equations the value of X is greater than Y(X>Y)
I. 3X2+23X + 44 = 0; 3Y2 + 20Y +33 = 0
II. 3X2+29 X +56 = 0; 2Y2 + 15Y + 25 = 0
III. 3X2- 16X + 21 = 0; 3Y2 - 28Y + 65 = 0
1.Only I 2.Only II
3.Both I and III
4.Both II and III
5.None follow
15. For which of the following equations the value of X=Y or relationship cannot be established.
I. 1/x + 1/(x-10) = 8/75; 132/y - 132/(y + 11) = 1
II. (3x - 2)/y = (3x + 6)/(y + 16); (x + 2)/(y + 4) = (x + 5)/(y + 10)
III. x² - 4x - 21 = 0; y² - 35y + 306 = 0
1.Only I
2.Only II
3.Both I and III
4.Both II and III
5.All follow
16. For which of the following equations the value of Y is greater than X(Y>X)
I. 7x + 6y + 4z = 122; 4x + 5y + 3z = 88; 9x + 2y + z = 78
II. 7x + 6y = 110; 4x + 3y = 59
III. 2x+5y = 23.5, 5x+ 2y = 22
1.Only I
2.Only II
3.Both I and II
4.Both II and III
5.All follow
17. For which of the following equations the value of X is less than or equal to Y (X? Y)
I. [48 / x4/7] - [12 / x4/7] = x10/7; y³ + 783 = 999
II. 9/?x + 19/?x = ?x; y5 - [(28)11/2 /?y] = 0
III. 6X2 - 7X + 2 = 0; 12Y2 - 7Y+1 = 0
1. Only I
2. Only II
3. Both I and II
4. Both I and III
5. All follow
18. For which of the following equations the value of X is greater than or equal to Y (X ? Y)
I. 3X2 +17X + 10=0; 10Y2 + 9Y+2 = 0
II. X2 +X - 56 = 0; Y2 - 17Y+72 = 0
III. X2- 12X + 35= 0; Y2 + Y - 30 = 0
1. Only I
2. Only II
3. Both I and II
4. Both I and III
5. None of these
19. For which of the following equations the value of X is greater than Y(X>Y)
I. 2X2 + 15X + 25= 0; 3Y2 + 29Y + 56 = 0
II. 3X2 - 19X + 28= 0; 4Y2 - 29Y + 45 = 0
III. X2 - 13X + 42= 0; Y2 - 9Y + 20 = 0
1. Only I
2. Only II
3. Only III
4. Both II and III
5. None of these
20. For which of the following equations the value of X=Y or relationship cannot be established.
I. x2 - 18x + 72= 0; 3y2 + 7y + 4 = 0
II. 2x2 + x - 36 = 0; 2y2 - 13y + 20 = 0
III. 4X2 - 19X + 12= 0; 3Y2 + 8Y + 4 = 0
1. Only I
2.Only II
3. Both I and II
4. Both II and III
5. None of these
21. (x - 3)(x + 2) = 0 y² - 7y + 12 = 0
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
22. 1/x+4 - 1/x-7 = 11/30 1/y-3 + 1/y+5 = 1/3
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
23. x(35 - x) = 124 y(2y + 3) = 90
A. X > Y
B. X < Y C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
24. x(27 - x) = 182 y(55 - y) = 750
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
25. x(x + 1) = 306 y(2y + 1) = 528
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation can not be established
26. (x + 3)(x + 29) = 360 480/y =[480/(y - 8)] - 3
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
27. 360/x = 360/(x +5) + 1 y² - 6y - 216 = 0
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
28. 2x² + x - 300 = 0 y² - 45y + 324 = 0
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
29. (x + 2)(x + 1)=(x -2)(x - 3) (y + 3)(y +2) =(y - 1)(y - 2)
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
30. (x - 2)(x - 3)=(x - 4)(x - 5) (y - 6)(y - 5) =(y - 4)(y - 3)
A. X > Y
B. X < Y
C. X ? Y
D. X ? Y
E. X = Y or relation cannot be established
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