Aptitude Questions: Quadratic Equations Set 31

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. 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
   
   Answer & Explanation

   B. X < Y
   Explanation:
   4/√x + 2/√x = √x
   1/√x (4 + 2) = √x => x = 6
   8/√y + 6/√y = √y => y = 14
   
   
2. 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
   
   Answer & Explanation

   D. X ≤ Y
   Explanation:
   x² – 300 = 724
   x = ± 32
   y – √225 = √289
   y = 17 + 15 = 32
   
   
3. 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
   
   Answer & Explanation

   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
   
   
4. √(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
   
   Answer & Explanation

   D. X ≤ Y
   Explanation:
   √(x + 20) = √256 – √169
   x + 20 = 9 => x = -11
   y² + 256 = 377
   y = ± 11
   
   
5. 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
   
   Answer & Explanation

   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
   
   
6. 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
   
   Answer & Explanation

   E. X = Y or relation cannot be established
   Explanation:
   x(10x – 1) = 2
   10x² – x – 2 = 0; x = 0.5, -0.4
   4y² + 3y – 27 = 0
   y = -3, 2.25
   
   
7. x² =841, y=√841
   A. X > Y
   B. X < Y
   C. X ≥ Y
   D. X ≤ Y
   E. X = Y or relation cannot be established
   
   Answer & Explanation

   D. X ≤ Y
   Explanation:
   x² =841
   x = 29, -29
   y = √841
   y = 29
   Put on number line
   -29 29 29
   
   
8. √2025x + √8100 = 0, (625)^1/4y + (1331)^1/3=0
   A. X > Y
   B. X < Y
   C. X ≥ Y
   D. X ≤ Y
   E. X = Y or relation cannot be established
   
   Answer & Explanation

   A. X > Y
   Explanation:
   √2025x + √8100 = 0
   45x + 90 = 0
   x = -2
   (625)^1/4y + (1331)^1/3=0
   5y + 11 = 0
   y = -2.2
   Put on number line
   -2.2 -2
   
   
9. (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
   
   Answer & Explanation

   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
   
   
10. 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
    
    Answer & Explanation

    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