**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**

**5x + 2y = 31**

**3x + 7y = 36**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**A. X > Y**

Explanation:

5x + 2y = 31 —-(1)

3x + 7y = 36 —-(2)

By solving eqn(1) and (2)

x = 5 ; y = 3**x**^{2}– x – √3x + √3= 0

**y**^{2}– 3y + 2 = 0

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**E. X = Y or relation cannot be established**

Explanation:

x^{2}– x – √3x + √3= 0

x (x-1) – √3(x -1) = 0

(x-1) (x-√3) = 0

x = 1, 1.732

y^{2}– 3y + 2 = 0

y^{2}– y – 2y + 2 = 0

y = 1, 2

Put on number line

1, 1, 1.732, 2**[48 / x**^{4/7}] – [12 / x^{4/7}] = x^{10/7}

**y³ + 783 = 999**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**D. X ≤ Y**

Explanation:

(48 – 12) / x^{4/7}= x^{10/7}

36 = x^{(10/7 + 4/7)}

36 = x^{2}

x = ± 6

y^{3}+ 783 = 999

y^{3}= 999 – 783

y^{3}= 216

y = 6

Put on number line

-6, 6, 6**17**^{2}+ 144 ÷ 18 = x

**26**^{2}– 18 * 21 = y

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**B. X < Y**

Explanation:

17^{2}+ 144 ÷ 18 = x

x = 297

26^{2}– 18 * 21 = y

y = 676 – 378 = 29**5/7 – 5/21 = √x/42**

**√y/4 + √y/16 = 250/√y**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**B. X < Y**

Explanation:

5/7 – 5/21 = √x/42

10/21 = √x/42

√x = 20

x = 400

√y/4 + √y/16 = 250/√y

5√y/16 = 250/√y

y = 800**9/√x + 19/√x = √x**

**y5 – [(28)**^{11/2}/√y] = 0

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**E. X = Y or relation cannot be established**

Explanation:

9/√x + 19/√x = √x

x = 28

y5 – [(28)^{11/2}/√y] = 0

y^{11/2}= (28)^{11/2}

y = 28**12/√x – 23/√x = 5√x**

**√y/12 – 5√y/12 = 1/√y**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**A. X > Y**

Explanation:

12/√x – 23/√x = 5√x

-11 = 5x

x = -2.2

√y/12 – 5√y/12 = 1/√y

√y[1/12 – 5/12]= 1/√y

y = -3**7x + 6y + 4z = 122**

**4x + 5y + 3z = 88**

**9x + 2y + z = 78**

A. X < Y = Z

B. X ≤ Y < Z

C. X < Y > Z

D. X = Y > Z

E. X = Y = Z or relation cannot be established

**A. X < Y = Z**

Explanation:

7x + 6y + 4z = 122 —(1)

4x + 5y + 3z = 88 —(2)

9x + 2y + z = 78 —(3)

From (1) and (2) => 5x – 2y =4 —(a)

From (2) and (3) => 23x + y = 146 —(b)

From (a) and (b) => x = 6, y = 8. Put values in eqn (3) => z = 8**(x+y)³ = 1331**

**x – y + z = 0**

**xy = 28**

A. X < Y = Z

B. X ≤ Y < Z

C. X < Y > Z

D. X = Y > Z

E. X = Y = Z or relation cannot be established

**E. X = Y or relation cannot be established**

Explanation:

(x + y)³ = 1331

x + y = 11 —(a)

(x + y)2 = 121

(a + b)2 – (a – b)2 = 4ab

(x – y)2 + 4xy = 121

x – y = 3 —(b)

From eqn (a) and (b)

x = 7; y = 4 Put values in eqn (2) => z = -3

**7x + 6y = 110**

**4x + 3y = 59**

**x + z = 15**

A. X < Y = Z

B. X ≤ Y < Z

C. X < Y > Z

D. X = Y > Z

E. X = Y = Z or relation cannot be established

**C. X < Y > Z**

Explanation:

7x + 6y = 110 —(1)

4x + 3y = 59 —(2)

x + z = 15 —(3)

From eqn(1) and (2)

x = 8; y = 9 Put values in eqn (3) => z = 7

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