Algebra Quiz for Bank PO, SBI, IBPS & LIC Exams | Concept of Maths

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) \( x > y \)

B) \( x < y \)

C) \( x \ge y \)

D) \( x \le y \)

E) \( x = y \) or No relation can be established

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \ge y \)

D) \( x \le y \)

E) \( x = y \) or No relation can be established

Answer

Correct Answer: C

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) \( x > y \)

B) \( x < y \)

C) \( x \ge y \)

D) \( x \le y \)

E) \( x = y \) or No relation can be established

Answer

Correct Answer: 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. \( y = \sqrt{81} \)

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) \( x > y \)

B) \( x < y \)

C) \( x \ge y \)

D) \( x \le y \)

E) \( x = y \) or No relation can be established

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \ge y \)

D) \( x \le y \)

E) \( x = y \) or No relation can be established

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \ge y \)

D) \( x \le y \)

E) \( x = y \) or No relation can be established

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \ge y \)

D) \( x \le y \)

E) \( x = y \) or No relation can be established

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \ge y \)

D) \( x \le y \)

E) \( x = y \) or No relation can be established

Answer

Correct Answer: 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) \( x > y \)

B) \( x < y \)

C) \( x \ge y \)

D) \( x \le y \)

E) \( x = y \) or No relation can be established

Answer

Correct Answer: D

Question 11

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

A) 23

B) 25

C) 27

D) 21

Answer

Correct Answer: A

Question 12

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

A) 64

B) 76

C) 52

D) 68

Answer

Correct Answer: B

Question 13

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

A) 2

B) 4

C) 5

D) 3

Answer

Correct Answer: 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) 8

B) 12

C) 10

D) 14

Answer

Correct Answer: C

Question 15

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

A) 4.5

B) 6.25

C) 5.25

D) 7.5

Answer

Correct Answer: C

Question 16

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

A) 4

B) 9

C) 16

D) 25

Answer

Correct Answer: B

Question 17

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

A) 2

B) 3

C) 1

D) 4

Answer

Correct Answer: 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) 25

B) 30

C) 40

D) 35

Answer

Correct Answer: D

Question 19

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

A) 134

B) 184

C) 200

D) 210

Answer

Correct Answer: C

Question 20

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

A) 9

B) -9

C) 5

D) -5

Answer

Correct Answer: B

Accepted Answer

Correct Answer: D

Mastering Algebra: Bank PO & Clerk Quantitative Aptitude Quiz | Concept of Maths

Mastering Algebra: Bank PO & Clerk Quantitative Aptitude Quiz | Concept of Maths

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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 \( x - 2 \).

Algebra Quiz for Bank PO, SBI, IBPS & LIC Exams | Concept of Maths

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. \( y = \sqrt{81} \)

Mastering Algebra: Bank PO & Clerk Quantitative Aptitude Quiz | Concept of Maths

Mastering Algebra: Bank PO & Clerk Quantitative Aptitude Quiz | Concept of Maths

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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 \( x - 2 \).