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# Quant Quiz On Quadratic Equation Questions Day 5 Bag

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**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**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**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**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**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**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**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**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**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**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

**5/√x + 7/√x = √x**

**4/√y + 6/√y = √y**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established**x² – 300 = 325**

**y – √144 = √169**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established**x² – 11**^{5/2}/√x = 0

**y² – 13**^{5/2}/√y = 0

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established**√(x + 20) = √256 – √121**

**y² + 576 = 697**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established**y² – x² = 32**

**y – x = 4**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established**x² + 12x + 32 = 0**

**y² + 19y + 90 = 0**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established**x² – 15x + 56 = 0**

**y² + 17y + 72 = 0**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established**x² – 23x + 132 = 0**

**y² + 13y + 42 = 0**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established**x² – 32x + 255 = 0**

**y² – 35y + 306 = 0**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established**x² – 21x + 108 = 0**

**y² – 17y + 72 = 0**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

Here I am giving you some examples of quadratic equations.

**Ex 1:** x^{2} + 3x – 10 = 0 and y^{2} – 7y + 12 = 0

By solving we get x = -5, 2 and y = 3, 4

Put these values as on a number line as:

-5(x) 2(x) 3(y) 4(y)

By this, it is clear that x is always less than y. So, we will say x < y.

**Ex 2:** x^{2} – 8x + 12 = 0 and y^{2} + 3y – 10 = 0

By solving we get x = 2, 6 and y = -5, 2

Put these values as on a number line as:

-5(y) 2(y,x) 6(x)

When x = 2, x = y=2 and x > y = -5, so x ≥ y.

When x = 6, x > y = 2 and x > y = -5.

By this, it is clear that either x is greater than y always or is equal to y at value 2. So, we will say x ≥ y.

**Ex 3:** x^{2} + 3x – 4 = 0 and y^{2} – y – 6 = 0

By solving we get x = -4, 1 and y = -2, 3

Put these values as on a number line as:

-4(x) -2(y) 1(x) 3(y)

When there are values in between, one cannot find the relationship. So, we will say that no relationship exists between x and y.

**Ex 4:** x^{2} – 5x + 6 = 0 and y^{2} – 7y + 10 = 0

By solving we get x = 2, 3 and y = 2, 5

Put these values as on a number line as:

2(x,y) 3(x) 5(y)

When x = 2, x = y=2 and x < y = 5, so x ≤ y.

When x = 3, x > y = 2 and x < y = 5.

By these values, one cannot find the exact relationship. So, we will say that no relationship exists between x and y.

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