Solve: 4x + 1y = 38 and 5x − 2y = 15. What is the value of x?
- A9
- B6
- C7
- D8
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Answer: (C) 7
Solving the two equations gives x = 7, y = 10.
MAT Algebra Questions with Answers & Explanations
20 Algebra questions from the Mathematical Skills section of MAT, each with the correct answer and a worked explanation. Try each question first, then tap Show answer to check. When you're ready, take the timed chapter-wise test to see your all-India rank.
If x + 1/x = 4, what is the value of x³ + 1/x³?
- A48
- B55
- C76
- D52
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Answer: (D) 52
x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 4³ − 3 × 4 = 52.
If x + 1/x = 6, what is the value of x² + 1/x²?
- A33
- B12
- C34
- D38
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Answer: (C) 34
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 6² − 2 = 34.
If x + 1/x = 6, what is the value of x³ + 1/x³?
- A192
- B201
- C216
- D198
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Answer: (D) 198
x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 6³ − 3 × 6 = 198.
If x + 1/x = 4, what is the value of x² + 1/x²?
- A16
- B14
- C8
- D13
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Answer: (B) 14
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 4² − 2 = 14.
Solve: 2x + 5y = 56 and 5x − 3y = -15. What is the value of x?
- A5
- B1
- C3
- D4
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Answer: (C) 3
Solving the two equations gives x = 3, y = 10.
If x + 1/x = 3, what is the value of x³ + 1/x³?
- A27
- B15
- C18
- D21
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Answer: (C) 18
x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 3³ − 3 × 3 = 18.
Solve: 3x + 1y = 25 and 5x − 4y = 19. What is the value of x?
- A4
- B5
- C8
- D7
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Answer: (D) 7
Solving the two equations gives x = 7, y = 4.
If x + 1/x = 7, what is the value of x² + 1/x²?
- A46
- B47
- C51
- D49
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Answer: (B) 47
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 7² − 2 = 47.
Solve: 1x + 3y = 46 and 5x − 1y = 38. What is the value of x?
- A7
- B10
- C11
- D12
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Answer: (B) 10
Solving the two equations gives x = 10, y = 12.
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If x + 1/x = 7, what is the value of x³ + 1/x³?
- A343
- B322
- C315
- D325
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Answer: (B) 322
x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 7³ − 3 × 7 = 322.
If x + 1/x = 3, what is the value of x² + 1/x²?
- A7
- B11
- C9
- D6
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Answer: (A) 7
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 3² − 2 = 7.
Solve: 1x + 1y = 15 and 3x − 5y = -11. What is the value of x?
- A9
- B8
- C6
- D5
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Answer: (B) 8
Solving the two equations gives x = 8, y = 7.
If x + 1/x = 9, what is the value of x² + 1/x²?
- A79
- B78
- C83
- D81
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Answer: (A) 79
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 9² − 2 = 79.
Solve: 2x + 1y = 26 and 3x − 2y = -3. What is the value of x?
- A4
- B7
- C10
- D8
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Answer: (B) 7
Solving the two equations gives x = 7, y = 12.
Solve: 5x + 1y = 57 and 5x − 2y = 51. What is the value of x?
- A8
- B14
- C11
- D13
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Answer: (C) 11
Solving the two equations gives x = 11, y = 2.
If x + 1/x = 5, what is the value of x³ + 1/x³?
- A140
- B105
- C113
- D110
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Answer: (D) 110
x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 5³ − 3 × 5 = 110.
If x + 1/x = 3, what is the value of x³ + 1/x³?
- A21
- B18
- C36
- D15
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Answer: (B) 18
x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 3³ − 3 × 3 = 18.
Solve: 3x + 3y = 66 and 5x − 1y = 44. What is the value of x?
- A11
- B10
- C12
- D13
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Answer: (A) 11
Solving the two equations gives x = 11, y = 11.
If x + 1/x = 9, what is the value of x² + 1/x²?
- A83
- B79
- C78
- D18
Show answer
Answer: (B) 79
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 9² − 2 = 79.
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