Question 1

1. Solve the given equations and determine the correct relationship between x and y: I. $x^2 - 43x + 450 = 0$ II. $y^2 - 37y + 342 = 0$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option E

Question 2

2. Solve the given equations and determine the correct relationship between x and y: I. $3x^2 - 22x + 40 = 0$ II. $5y^2 - 21y + 16 = 0$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$

Question 3

3. Solve the given equations and determine the correct relationship between x and y: I. $x^2 - 7\sqrt{3}x + 36 = 0$ II. $y^2 - 11\sqrt{2}y + 60 = 0$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option B

Question 4

4. Solve the given equations and determine the correct relationship between x and y: I. $x^3 = 4913$ II. $y^2 = 289$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option C

Question 5

5. Solve the given equations and determine the correct relationship between x and y: I. $2x^2 + 11x + 14 = 0$ II. $4y^2 + 12y + 9 = 0$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option B

Question 6

6. Solve the given equations and determine the correct relationship between x and y: I. $x^2 - 32x + 255 = 0$ II. $y^2 - 35y + 306 = 0$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option D

Question 7

7. Solve the given equations and determine the correct relationship between x and y: I. $(x+2)^2 = 9x - 2$ II. $(y-2)^2 = 5y - 16$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option B

Question 8

8. Solve the given equations and determine the correct relationship between x and y: I. $\sqrt{x+4} = \sqrt{225} - \sqrt{121}$ II. $y^2 = 324$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option E

Question 9

9. Solve the given equations and determine the correct relationship between x and y: I. $\frac{15}{\sqrt{x}} - \frac{9}{\sqrt{x}} = x^{1/2}$ II. $y^{10} - (36)^5 = 0$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option C

Question 10

10. Solve the given equations and determine the correct relationship between x and y: I. $8x^2 - 26x + 21 = 0$ II. $10y^2 - 43y + 28 = 0$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option E

Question 11

11. Solve the given equations and determine the correct relationship between x and y: I. $x^2 - 14x + 48 = 0$ II. $y^2 - 25y + 154 = 0$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option B

Question 12

12. Solve the given equations and determine the correct relationship between x and y: I. $6x^2 + 19x + 15 = 0$ II. $24y^2 + 11y + 1 = 0$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option B

Question 13

13. Solve the given equations and determine the correct relationship between x and y: I. $x^2 - 1089 = 0$ II. $y - \sqrt{1089} = 0$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option D

Question 14

14. Solve the given equations and determine the correct relationship between x and y: I. $3x^2 - 13x - 10 = 0$ II. $3y^2 + 10y - 8 = 0$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option E

Question 15

15. Solve the given equations and determine the correct relationship between x and y: I. $x^3 = 512$ II. $y^2 = 64$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option C

Question 16

16. Solve the given equations and determine the correct relationship between x and y: I. $x^{3/2} - \frac{81}{\sqrt{x}} = 0$ II. $\sqrt{16} y^2 = \sqrt{81}$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option A

Question 17

17. Solve the given equations and determine the correct relationship between x and y: I. $4x^2 - 15x + 9 = 0$ II. $3y^2 - 11y + 10 = 0$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option E

Question 18

18. Solve the given equations and determine the correct relationship between x and y: I. $x^2 + 14x + 45 = 0$ II. $y^2 + 22y + 121 = 0$

A) x > yB) x < yC) $x \geq y$D) $x \leq y$E) x = y or relationship cannot be established.

Answer

✓ Correct Answer: Option A

Question 19

19. If a + b = 15 and $a^2 + b^2 = 113$, what is the value of $a^3 + b^3$?

A) 750B) 815C) 825D) 855E) 925

Answer

✓ Correct Answer: Option D

Question 20

20. If $x + \frac{1}{x} = 5$, find the value of $x^4 + \frac{1}{x^4}$.

A) 525B) 529C) 527D) 123E) 623

Answer

✓ Correct Answer: Option C

Accepted Answer

✓ Correct Answer: Option A

Hard Algebra Quiz for IBPS & SBI PO

1. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $x^2 - 43x + 450 = 0$<br>II. $y^2 - 37y + 342 = 0$

2. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $3x^2 - 22x + 40 = 0$<br>II. $5y^2 - 21y + 16 = 0$

3. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $x^2 - 7\sqrt{3}x + 36 = 0$<br>II. $y^2 - 11\sqrt{2}y + 60 = 0$

4. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $x^3 = 4913$<br>II. $y^2 = 289$

5. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $2x^2 + 11x + 14 = 0$<br>II. $4y^2 + 12y + 9 = 0$

6. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $x^2 - 32x + 255 = 0$<br>II. $y^2 - 35y + 306 = 0$

7. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $(x+2)^2 = 9x - 2$<br>II. $(y-2)^2 = 5y - 16$

8. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $\sqrt{x+4} = \sqrt{225} - \sqrt{121}$<br>II. $y^2 = 324$

9. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $\frac{15}{\sqrt{x}} - \frac{9}{\sqrt{x}} = x^{1/2}$<br>II. $y^{10} - (36)^5 = 0$

10. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $8x^2 - 26x + 21 = 0$<br>II. $10y^2 - 43y + 28 = 0$

11. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $x^2 - 14x + 48 = 0$<br>II. $y^2 - 25y + 154 = 0$

12. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $6x^2 + 19x + 15 = 0$<br>II. $24y^2 + 11y + 1 = 0$

13. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $x^2 - 1089 = 0$<br>II. $y - \sqrt{1089} = 0$

14. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $3x^2 - 13x - 10 = 0$<br>II. $3y^2 + 10y - 8 = 0$

15. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $x^3 = 512$<br>II. $y^2 = 64$

16. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $x^{3/2} - \frac{81}{\sqrt{x}} = 0$<br>II. $\sqrt{16} y^2 = \sqrt{81}$

17. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $4x^2 - 15x + 9 = 0$<br>II. $3y^2 - 11y + 10 = 0$

18. Solve the given equations and determine the correct relationship between x and y:<br><br>I. $x^2 + 14x + 45 = 0$<br>II. $y^2 + 22y + 121 = 0$

19. If a + b = 15 and $a^2 + b^2 = 113$, what is the value of $a^3 + b^3$?

20. If $x + \frac{1}{x} = 5$, find the value of $x^4 + \frac{1}{x^4}$.