**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**

**4/√x + 2/√x = √x**

**8/√y + 6/√y = √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:

4/√x + 2/√x = √x

1/√x (4 + 2) = √x => x = 6

8/√y + 6/√y = √y => y = 14**x² – 300 = 724**

**y – √225 = √289**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**D. X ≤ Y**

Explanation:

x² – 300 = 724

x = ± 32

y – √225 = √289

y = 17 + 15 = 32**x² – 14**^{5/2}/√x = 0

**y² – 11**^{5/2}/√y = 0

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**A. X > Y**

Explanation:

x² – 14^{5/2}/√x = 0

x^{5/2}= 14^{5/2}

x = 14

y² – 11^{5/2}/√y = 0 => y = 11**√(x + 20) = √256 – √169**

**y² + 256 = 377**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**D. X ≤ Y**

Explanation:

√(x + 20) = √256 – √169

x + 20 = 9 => x = -11

y² + 256 = 377

y = ± 11**y² – x² = 96**

**y – x = 8**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**B. X < Y**

Explanation:

y² – x² = 96

y – x = 8

(y + x) (y – x) = 96

(y + x) 8 = 96

y + x = 12

y – x = 8

y = 10 and x = 2**x(10x – 1) = 2**

**4y² + 3y – 27 = 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(10x – 1) = 2

10x^{2}– x – 2 = 0; x = 0.5, -0.4

4y² + 3y – 27 = 0

y = -3, 2.25**x**^{2}=841, y=√841

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**D. X ≤ Y**

Explanation:

x^{2}=841

x = 29, -29

y = √841

y = 29

Put on number line

-29 29 29**√2025x + √8100 = 0, (625)**^{1/4}y + (1331)^{1/3}=0

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**A. X > Y**

Explanation:

√2025x + √8100 = 0

45x + 90 = 0

x = -2

(625)^{1/4}y + (1331)^{1/3}=0

5y + 11 = 0

y = -2.2

Put on number line

-2.2 -2**(16/√x) + (9/√x) = 10√x, (√y/4) + (6√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:

(16/√x) + (9/√x) = 10√x

25/√x = 10√x

x = 25/10 = 2.5

(√y/4) + (6√y/12)= (1/√y)

(9√y/12) = (1/√y)

y = 1.3**9x – 15.45 = 64.55 + 4x, √(y+153) – 6 = 7**

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:

9x – 15.45 = 64.55 + 4x

9x – 4x = 64.55 + 15.45

5x = 80 => x= 16

√(y+155) – 6 = 7

√(y+155) = 13

Squaring on both sides

y + 153 = 169

y = 16

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