If x + 1/x = 3, what is the value of x³ + 1/x³?
- A36
- 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.
NDA & NA Algebra Questions with Answers & Explanations
20 Algebra questions from the Mathematics section of NDA & NA, 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 = 8, what is the value of x² + 1/x²?
- A61
- B64
- C62
- D16
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Answer: (C) 62
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 8² − 2 = 62.
Solve: 2x + 3y = 27 and 1x − 2y = 3. What is the value of x?
- A10
- B11
- C9
- D12
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Answer: (C) 9
Solving the two equations gives x = 9, y = 3.
If x + 1/x = 4, what is the value of x³ + 1/x³?
- A52
- B76
- C55
- D48
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Answer: (A) 52
x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 4³ − 3 × 4 = 52.
If x + 1/x = 7, what is the value of x² + 1/x²?
- A47
- B51
- C14
- D49
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Answer: (A) 47
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 7² − 2 = 47.
Solve: 4x + 1y = 47 and 1x − 4y = -18. What is the value of x?
- A9
- B11
- C10
- D8
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Answer: (C) 10
Solving the two equations gives x = 10, y = 7.
If x + 1/x = 7, what is the value of x³ + 1/x³?
- A343
- B322
- C364
- 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 = 5, what is the value of x² + 1/x²?
- A23
- B27
- C10
- D25
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Answer: (A) 23
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 5² − 2 = 23.
Solve: 5x + 5y = 80 and 3x − 1y = 0. What is the value of x?
- A6
- B4
- C3
- D7
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Answer: (B) 4
Solving the two equations gives x = 4, y = 12.
If x + 1/x = 6, what is the value of x² + 1/x²?
- A38
- B34
- C33
- D12
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Answer: (B) 34
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 6² − 2 = 34.
Solve: 4x + 3y = 42 and 5x − 1y = 43. What is the value of x?
- A9
- B8
- C7
- D12
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Answer: (A) 9
Solving the two equations gives x = 9, y = 2.
Solve: 2x + 5y = 16 and 2x − 1y = 4. What is the value of x?
- A5
- B6
- C3
- D1
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Answer: (C) 3
Solving the two equations gives x = 3, y = 2.
If x + 1/x = 9, what is the value of x² + 1/x²?
- A79
- B78
- C81
- D83
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Answer: (A) 79
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 9² − 2 = 79.
Solve: 4x + 2y = 16 and 3x − 5y = -1. What is the value of x?
- A3
- B4
- C2
- D1
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Answer: (A) 3
Solving the two equations gives x = 3, y = 2.
If x + 1/x = 5, what is the value of x³ + 1/x³?
- A110
- B113
- C125
- D105
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Answer: (A) 110
x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 5³ − 3 × 5 = 110.
If x + 1/x = 4, what is the value of x² + 1/x²?
- A14
- B8
- C13
- D16
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Answer: (A) 14
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 4² − 2 = 14.
If x + 1/x = 8, what is the value of x² + 1/x²?
- A61
- B62
- C64
- D16
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Answer: (B) 62
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 8² − 2 = 62.
If x + 1/x = 6, what is the value of x³ + 1/x³?
- A198
- B216
- C201
- D234
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Answer: (A) 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 x³ + 1/x³?
- A48
- B52
- C64
- D55
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Answer: (B) 52
x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 4³ − 3 × 4 = 52.
Solve: 1x + 5y = 66 and 1x − 2y = -18. What is the value of x?
- A4
- B9
- C6
- D5
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Answer: (C) 6
Solving the two equations gives x = 6, y = 12.
These are RankerClub practice questions written in the NDA & NA pattern. They are not official SSC/IBPS/RRB papers.
