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Aptitude Questions: Quadratic Equations Set 27

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

Follow the link To solve Quadratic Equations with the help of Number Line

  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.2x² -15x + 27 = 0; 5y² – 26y + 33 = 0
    III.25/√x + 9/√x = 17√x; √y/3 + 5√y/6 = 3/√y
    1.Only I
    2.Only II
    3.Only III
    4.Both II and III
    5.None
    Answer – 3.Only III
    Explanation :
    25/√x + 9/√x = 17√x
    34 = 17x
    x = 2
    21√y/18 = 3/√y
    y = 18/7 = 2.57

  2. 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
    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, x2 – (16)2 = (23)2 – 56
    x2 = 729
    x = ± 27
    y1/3 – 55 + 376 = (18)2
    y = 33 = 27

  3. 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
    Answer – 4.Both II and III
    Explanation :
    From II, √(x + 6) = √121 – √36
    x + 6 = 25; x = 19
    y2 + 112 = 473
    y2 = 361; y = ± 19
    From III, 5x2 – 7x – 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.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
    Answer – 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 – 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
    Answer – 1.Only I
    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
    Answer – 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 (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
    Answer – 1.Only I
    Explanation :
    From I, x = ± 6; y = 6

  8. 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
    Answer – 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 – 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
    Answer – 3.Only III
    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.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
    Answer – 2.Only II
    Explanation :
    From II, x = 4 , -9/2; y = 4, 5/2