Question 1

1. In the following question, two equations I and II are given. You have to solve both the equations and determine the relationship between x and y. I. $x^2 - 7x + 12 = 0$ II. $y^2 - 11y + 30 = 0$

A) x > yB) x < yC) $x \ge y$D) $x \le y$E) x = y or No relation can be established

Answer

✓ Correct Answer: Option B

Question 2

2. In the following question, two equations I and II are given. Determine the relationship between x and y. I. $x^2 + 5x + 6 = 0$ II. $y^2 + 7y + 12 = 0$

A) x > yB) x < yC) $x \ge y$

Question 3

3. In the following question, two equations I and II are given. Determine the relationship between x and y. I. $2x^2 - 7x + 6 = 0$ II. $3y^2 - 14y + 15 = 0$

A) x > yB) x < yC) $x \ge y$D) $x \le y$E) x = y or No relation can be established

Answer

✓ Correct Answer: Option E

Question 4

4. In the following question, two equations I and II are given. Determine the relationship between x and y. I. $x^2 = 81$ II. $y = \sqrt{81}$

A) x > yB) x < yC) $x \ge y$D) $x \le y$E) x = y or No relation can be established

Answer

✓ Correct Answer: Option D

Question 5

5. In the following question, two equations I and II are given. Determine the relationship between x and y. I. $x^2 - 12x + 32 = 0$ II. $y^2 - 17y + 72 = 0$

A) x > yB) x < yC) $x \ge y$D) $x \le y$E) x = y or No relation can be established

Answer

✓ Correct Answer: Option D

Question 6

6. In the following question, two linear equations I and II are given. Determine the relationship between x and y. I. 3x + 2y = 12 II. 4x + 3y = 17

A) x > yB) x < yC) $x \ge y$D) $x \le y$E) x = y or No relation can be established

Answer

✓ Correct Answer: Option B

Question 7

7. In the following question, two equations I and II are given. Determine the relationship between x and y. I. $x^2 - 18x + 77 = 0$ II. $y^2 - 20y + 96 = 0$

A) x > yB) x < yC) $x \ge y$D) $x \le y$E) x = y or No relation can be established

Answer

✓ Correct Answer: Option E

Question 8

8. In the following question, two equations I and II are given. Determine the relationship between x and y. I. $4x^2 - 13x + 9 = 0$ II. $3y^2 - 14y + 16 = 0$

A) x > yB) x < yC) $x \ge y$D) $x \le y$E) x = y or No relation can be established

Answer

✓ Correct Answer: Option E

Question 9

9. In the following question, two equations I and II are given. Determine the relationship between x and y. I. $x^2 + x - 20 = 0$ II. $y^2 - y - 30 = 0$

A) x > yB) x < yC) $x \ge y$D) $x \le y$E) x = y or No relation can be established

Answer

✓ Correct Answer: Option E

Question 10

10. In the following question, two equations I and II are given. Determine the relationship between x and y. I. $x^2 - 19x + 84 = 0$ II. $y^2 - 25y + 156 = 0$

A) x > yB) x < yC) $x \ge y$D) $x \le y$E) x = y or No relation can be established

Answer

✓ Correct Answer: Option D

Question 11

11. If $x + \frac{1}{x} = 5$, find the value of $x^2 + \frac{1}{x^2}$.

A) 23B) 25C) 27D) 21

Answer

✓ Correct Answer: Option A

Question 12

12. If $x - \frac{1}{x} = 4$, find the value of $x^3 - \frac{1}{x^3}$.

A) 64B) 76C) 52D) 68

Answer

✓ Correct Answer: Option B

Question 13

13. The sum of two numbers is 24 and their product is 143. Find the positive difference between the numbers.

A) 2B) 4C) 5D) 3

Answer

✓ Correct Answer: Option A

Question 14

14. If the roots of the quadratic equation $x^2 - px + 24 = 0$ are in the ratio 3:2, find the positive value of p.

A) 8B) 12C) 10D) 14

Answer

✓ Correct Answer: Option C

Question 15

15. If $2^{x+y} = 32$ and $2^{x-y} = 4$, find the value of $x \times y$.

A) 4.5B) 6.25C) 5.25D) 7.5

Answer

✓ Correct Answer: Option C

Question 16

16. Solve for x: $\sqrt{x} + \sqrt{x-5} = 5$

A) 4B) 9C) 16D) 25

Answer

✓ Correct Answer: Option B

Question 17

17. If $5^{x-1} + 5^{x+1} = 130$, find the value of x.

A) 2B) 3C) 1D) 4

Answer

✓ Correct Answer: Option A

Question 18

18. Ten years ago, A's age was half of B's age. If the ratio of their present ages is 3:4, what is the total of their present ages?

A) 25B) 30C) 40D) 35

Answer

✓ Correct Answer: Option D

Question 19

19. Simplify $\frac{x^2 - y^2}{x-y}$ when x = 117 and y = 83.

A) 134B) 184C) 200D) 210

Answer

✓ Correct Answer: Option C

Question 20

20. Find the remainder when the polynomial $P(x) = x^3 - 4x^2 + 2x - 5$ is divided by x - 2.

A) 9B) -9C) 5D) -5

Answer

✓ Correct Answer: Option B

Accepted Answer

✓ Correct Answer: Option C

Algebra Quiz for Bank PO, SBI, IBPS & LIC Exams

1. In the following question, two equations I and II are given. You have to solve both the equations and determine the relationship between x and y.<br><br>I. $x^2 - 7x + 12 = 0$<br>II. $y^2 - 11y + 30 = 0$

2. In the following question, two equations I and II are given. Determine the relationship between x and y.<br><br>I. $x^2 + 5x + 6 = 0$<br>II. $y^2 + 7y + 12 = 0$

3. In the following question, two equations I and II are given. Determine the relationship between x and y.<br><br>I. $2x^2 - 7x + 6 = 0$<br>II. $3y^2 - 14y + 15 = 0$

4. In the following question, two equations I and II are given. Determine the relationship between x and y.<br><br>I. $x^2 = 81$<br>II. $y = \sqrt{81}$

5. In the following question, two equations I and II are given. Determine the relationship between x and y.<br><br>I. $x^2 - 12x + 32 = 0$<br>II. $y^2 - 17y + 72 = 0$

6. In the following question, two linear equations I and II are given. Determine the relationship between x and y.<br><br>I. 3x + 2y = 12<br>II. 4x + 3y = 17

7. In the following question, two equations I and II are given. Determine the relationship between x and y.<br><br>I. $x^2 - 18x + 77 = 0$<br>II. $y^2 - 20y + 96 = 0$

8. In the following question, two equations I and II are given. Determine the relationship between x and y.<br><br>I. $4x^2 - 13x + 9 = 0$<br>II. $3y^2 - 14y + 16 = 0$

9. In the following question, two equations I and II are given. Determine the relationship between x and y.<br><br>I. $x^2 + x - 20 = 0$<br>II. $y^2 - y - 30 = 0$

10. In the following question, two equations I and II are given. Determine the relationship between x and y.<br><br>I. $x^2 - 19x + 84 = 0$<br>II. $y^2 - 25y + 156 = 0$

11. If $x + \frac{1}{x} = 5$, find the value of $x^2 + \frac{1}{x^2}$.

12. If $x - \frac{1}{x} = 4$, find the value of $x^3 - \frac{1}{x^3}$.

13. The sum of two numbers is 24 and their product is 143. Find the positive difference between the numbers.

14. If the roots of the quadratic equation $x^2 - px + 24 = 0$ are in the ratio 3:2, find the positive value of p.

15. If $2^{x+y} = 32$ and $2^{x-y} = 4$, find the value of $x \times y$.

16. Solve for x: $\sqrt{x} + \sqrt{x-5} = 5$

17. If $5^{x-1} + 5^{x+1} = 130$, find the value of x.

18. Ten years ago, A's age was half of B's age. If the ratio of their present ages is 3:4, what is the total of their present ages?

19. Simplify $\frac{x^2 - y^2}{x-y}$ when x = 117 and y = 83.

20. Find the remainder when the polynomial $P(x) = x^3 - 4x^2 + 2x - 5$ is divided by x - 2.