Hard Algebra Quiz for IBPS & SBI PO | Concept of Maths

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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: A

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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: B

Question 4

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

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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \geq y \)

D) \( x \leq y \)

E) \( x = y \) or relationship cannot be established.

Answer

Correct Answer: A

Question 19

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

A) 750

B) 815

C) 825

D) 855

E) 925

Answer

Correct Answer: D

Question 20

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

A) 525

B) 529

C) 527

D) 123

E) 623

Answer

Correct Answer: C

Accepted Answer

Correct Answer: C

Ultimate Banking Algebra MasterQuiz: Conquer PO & Clerk Exams | Concept of Maths

Ultimate Banking Algebra MasterQuiz: Conquer PO & Clerk Exams | Concept of Maths

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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 \( x^4 + \frac{1}{x^4} \).

Hard Algebra Quiz for IBPS & SBI PO | Concept of Maths

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. \( y^2 = 289 \)

Ultimate Banking Algebra MasterQuiz: Conquer PO & Clerk Exams | Concept of Maths

Ultimate Banking Algebra MasterQuiz: Conquer PO & Clerk Exams | Concept of Maths

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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 \( x^4 + \frac{1}{x^4} \).