**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**

**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

**For which of the following equations the value of X is less than or equal to Y (X≤ Y)**

**I.**X^{2}– 4X + 3= 0; Y^{2}– 8Y + 15 = 0

**II**. 3X^{2}– 19X + 28= 0; 4Y^{2}– 29Y + 45 = 0

**III.**x^{2}– (16)^{2}= (23)^{2}– 56; y^{1/3}– 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, x^{2}– (16)^{2}= (23)^{2}– 56

x^{2}= 729

x = ± 27

y^{1/3}– 55 + 376 = (18)^{2}

y = 3^{3}= 27

**For which of the following equations the value of X is greater than or equal to Y (X ≥ Y)**

**I**.X^{2}-3X – 4 = 0; 3Y^{2}– 10Y+8 = 0

**II**.√(x + 6) = √121 – √36; y^{2}+ 112 = 473

**III.**5x^{2}– 7x – 6 = 0; 5y^{2}+ 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

y^{2}+ 112 = 473

y^{2}= 361; y = ± 19

From III, 5x^{2}– 7x – 6 = 0; x = -3/5, 2

5y^{2}+ 23y + 12 = 0; y = -4, -3/5

**For which of the following equations the value of X is greater than Y(X>Y)**

**I.**3X^{2}+23X + 44 = 0; 3Y^{2}+ 20Y +33 = 0

**II.**3X^{2}+29 X +56 = 0; 2Y^{2 }+ 15Y + 25 = 0

**III.**3X^{2}– 16X + 21 = 0; 3Y^{2}– 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

**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

**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

**For which of the following equations the value of X is less than or equal to Y (X≤ Y)**

**I.**[48 / x^{4/7}] – [12 / x^{4/7}] = x^{10/7}; y³ + 783 = 999

**II.**9/√x + 19/√x = √x; y^{5 }– [(28)11/2 /√y] = 0

**III.**6X^{2}– 7X + 2 = 0; 12Y^{2}– 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

**For which of the following equations the value of X is greater than or equal to Y (X ≥ Y)**

**I.**3X^{2}+17X + 10=0; 10Y^{2}+ 9Y+2 = 0

**II.**X^{2}+X – 56 = 0; Y^{2}– 17Y+72 = 0

**III.**X^{2}– 12X + 35= 0; Y^{2}+ 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

**For which of the following equations the value of X is greater than Y(X>Y)**

**I.**2X^{2 }+ 15X + 25= 0; 3Y^{2}+ 29Y + 56 = 0

**II.**3X^{2}– 19X + 28= 0; 4Y^{2}– 29Y + 45 = 0

**III.**X^{2}– 13X + 42= 0; Y^{2 }– 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

**For which of the following equations the value of X=Y or relationship cannot be established.**

**I.**x^{2}– 18x + 72= 0; 3y^{2}+ 7y + 4 = 0

**II.**2x^{2}+ x – 36 = 0; 2y^{2}– 13y + 20 = 0

**III.**4X^{2}– 19X + 12= 0; 3Y^{2}+ 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

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