# Aptitude Questions: Quadratic Equations Set 27

Hello Aspirants. Welcome to Online Quantitative Aptitude Section in AffairsCloud.com. Here we are creating sample questions inÂ Quadratic Equations which is common for all the competitive exams. We have included Some questions that are repeatedly asked in bank exams !!!

1. For which of the following equations the value of X is less than Y(X<Y)
I.5x + 2y = 31; 3x + 7y = 36
II.2xÂ² -15x + 27 = 0; 5yÂ² â€“ 26y + 33 = 0
III.25/âˆšx + 9/âˆšx = 17âˆšx; âˆšy/3 + 5âˆšy/6 = 3/âˆšy
1.Only I
2.Only II
3.Only III
4.Both II and III
5.None
Explanation :
25/âˆšx + 9/âˆšx = 17âˆšx
34 = 17x
x = 2
21âˆšy/18 = 3/âˆšy
y = 18/7 = 2.57

2. For which of the following equations the value of X is less than or equal to Y (Xâ‰¤ Y)
I.X2â€“ 4X + 3= 0; Y2 â€“ 8Y + 15 = 0
II. 3X2 â€“ 19X + 28= 0; 4Y2 â€“ 29Y + 45 = 0
III.x2Â â€“ (16)2Â = (23)2Â â€“ 56; y1/3Â â€“ 55 + 376 = (18)2
1.Only I
2.Only II
3.Both I and III
4.Both II and III
5.All follow
Answer – 3.Both I and III
Explanation :
From I, (x-3)(x-1) = 0 X=1,3
(y-5)(y-3) = 0 Y = 5,3
From III, x2Â â€“ (16)2Â = (23)2Â â€“ 56
x2Â = 729
x = Â± 27
y1/3Â â€“ 55 + 376 = (18)2
y = 33Â = 27

3. For which of the following equations the value of X is greater than or equal to Y (X â‰¥ Y)
I.X2 -3X â€“ 4 = 0; 3Y2 â€“ 10Y+8 = 0
II.âˆš(x + 6) = âˆš121 â€“ âˆš36; y2Â + 112 = 473
III.5x2â€“ 7x â€“ 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
Answer – 4.Both II and III
Explanation :
From II, âˆš(x + 6) = âˆš121 â€“ âˆš36
x + 6 = 25; x = 19
y2Â + 112 = 473
y2Â = 361; y = Â± 19
From III, 5x2 â€“ 7x â€“ 6 = 0; x = -3/5, 2
5y2 + 23y + 12 = 0; y = -4, -3/5

4. 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.3X2â€“ 16X + 21 = 0; 3Y2 â€“ 28Y + 65 = 0
1.Only I
2.Only II
3.Both I and III
4.Both II and III
5.None follow
Explanation :
From I, X = -4, -11/3; Y = -3, -11/3
From II, X=-7, -8/3; Y = -5, -5/2
From III,X= 3,7/3; Y = 5,13/3

5. 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 â€“ 132/(y + 11) = 1
II.(3x â€“ 2)/y = (3x + 6)/(y + 16); (x + 2)/(y + 4) = (x + 5)/(y + 10)
III. xÂ² â€“ 4x â€“ 21 = 0; yÂ² â€“ 35y + 306Â = 0
1.Only I
2.Only II
3.Both I and III
4.Both II and III
5.All follow
Explanation :
From I, x = 25, 3.75; y = -44, 33

6. 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
Explanation :
From I, x = 6, y = 8
From II, x = 8; y = 9
From III, x = 3, y = 3.5

7. For which of the following equations the value of X is less than or equal to Y (Xâ‰¤ Y)
I.[48 / x4/7] â€“ [12 / x4/7] = x10/7; yÂ³ + 783 = 999
II.9/âˆšx + 19/âˆšx = âˆšx; y5 â€“ [(28)11/2 /âˆšy] = 0
III.6X2 â€“ 7X + 2 = 0; 12Y2 â€“ 7Y+1 = 0
1.Only I
2.Only II
3.Both I and II
4.Both I and III
5.All follow
Explanation :
From I, x = Â± 6; y = 6

8. For which of the following equations the value of X is greater than or equal to Y (X â‰¥ Y)
I.3X2 +17X + 10=0; 10Y2 + 9Y+2 = 0
II.X2 +X â€“ 56 = 0; Y2 â€“ 17Y+72 = 0
III.X2â€“ 12X + 35= 0; Y2 + Y â€“ 30 = 0
1.Only I
2.Only II
3.Both I and II
4.Both I and III
5.None of these
Explanation :
Only III follows, From III, X = 7,5; Y = 5, -6

9. 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 â€“ 19X + 28= 0; 4Y2 â€“ 29Y + 45 = 0
III.X2 â€“ 13X + 42= 0; Y2 â€“ 9Y + 20 = 0
1.Only I
2.Only II
3.Only III
4.Both II and III
5.None of these
Explanation :
From III, X=7,6; Y =5,4

10. For which of the following equations the value of X=Y or relationship cannot be established.
I.x2Â â€“ 18x + 72= 0; 3y2Â + 7y + 4 = 0
II.2x2Â + x â€“ 36 = 0; 2y2Â â€“ 13y + 20 = 0
III.4X2 â€“ 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