SSC CGL Algebra Questions
15 questions on Algebra for SSC CGL, including questions from 2024 and 2023 papers. Each comes with the correct answer and a worked explanation.
- Questions
- 15
- Moderate
- 15
Algebra questions with solutions
If x − 1/x = 11, what is the value of x² + 1/x²?
- (A)121
- (B)123
- (C)22
- (D)119
Show answer and explanation
Correct answer: (B) 123
Squaring both sides: (x − 1/x)² = x² + 1/x² − 2 = 121. Therefore x² + 1/x² = 121 + 2 = 123.
Shortcut: x² + 1/x² = k² + 2 when x − 1/x = k.
If x + 1/x = 11, what is the value of x² + 1/x²?
- (A)22
- (B)123
- (C)119
- (D)125
Show answer and explanation
Correct answer: (C) 119
Squaring both sides: (x + 1/x)² = x² + 1/x² + 2 = 121. Therefore x² + 1/x² = 121 − 2 = 119.
Shortcut: x² + 1/x² = k² − 2 when x + 1/x = k.
If x + 1/x = 6, what is the value of x² + 1/x²?
- (A)34
- (B)36
- (C)12
- (D)38
Show answer and explanation
Correct answer: (A) 34
Squaring both sides: (x + 1/x)² = x² + 1/x² + 2 = 36. Therefore x² + 1/x² = 36 − 2 = 34.
Shortcut: x² + 1/x² = k² − 2 when x + 1/x = k.
If x − 1/x = 8, what is the value of x² + 1/x²?
- (A)16
- (B)68
- (C)64
- (D)66
Show answer and explanation
Correct answer: (D) 66
Squaring both sides: (x − 1/x)² = x² + 1/x² − 2 = 64. Therefore x² + 1/x² = 64 + 2 = 66.
Shortcut: x² + 1/x² = k² + 2 when x − 1/x = k.
If x − 1/x = 7, what is the value of x² + 1/x²?
- (A)51
- (B)47
- (C)49
- (D)53
Show answer and explanation
Correct answer: (A) 51
Squaring both sides: (x − 1/x)² = x² + 1/x² − 2 = 49. Therefore x² + 1/x² = 49 + 2 = 51.
Shortcut: x² + 1/x² = k² + 2 when x − 1/x = k.
If x − 1/x = 3, what is the value of x² + 1/x²?
- (A)9
- (B)6
- (C)11
- (D)7
Show answer and explanation
Correct answer: (C) 11
Squaring both sides: (x − 1/x)² = x² + 1/x² − 2 = 9. Therefore x² + 1/x² = 9 + 2 = 11.
Shortcut: x² + 1/x² = k² + 2 when x − 1/x = k.
If x + 1/x = 6, what is the value of x² + 1/x²?
- (A)40
- (B)38
- (C)12
- (D)34
Show answer and explanation
Correct answer: (D) 34
Squaring both sides: (x + 1/x)² = x² + 1/x² + 2 = 36. Therefore x² + 1/x² = 36 − 2 = 34.
Shortcut: x² + 1/x² = k² − 2 when x + 1/x = k.
If x + 1/x = 11, what is the value of x² + 1/x²?
- (A)125
- (B)119
- (C)22
- (D)121
Show answer and explanation
Correct answer: (B) 119
Squaring both sides: (x + 1/x)² = x² + 1/x² + 2 = 121. Therefore x² + 1/x² = 121 − 2 = 119.
Shortcut: x² + 1/x² = k² − 2 when x + 1/x = k.
If x + 1/x = 11, what is the value of x² + 1/x²?
- (A)121
- (B)123
- (C)119
- (D)125
Show answer and explanation
Correct answer: (C) 119
Squaring both sides: (x + 1/x)² = x² + 1/x² + 2 = 121. Therefore x² + 1/x² = 121 − 2 = 119.
Shortcut: x² + 1/x² = k² − 2 when x + 1/x = k.
If x + 1/x = 9, what is the value of x² + 1/x²?
- (A)79
- (B)18
- (C)83
- (D)85
Show answer and explanation
Correct answer: (A) 79
Squaring both sides: (x + 1/x)² = x² + 1/x² + 2 = 81. Therefore x² + 1/x² = 81 − 2 = 79.
Shortcut: x² + 1/x² = k² − 2 when x + 1/x = k.
If x − 1/x = 6, what is the value of x² + 1/x²?
- (A)38
- (B)40
- (C)34
- (D)36
Show answer and explanation
Correct answer: (A) 38
Squaring both sides: (x − 1/x)² = x² + 1/x² − 2 = 36. Therefore x² + 1/x² = 36 + 2 = 38.
Shortcut: x² + 1/x² = k² + 2 when x − 1/x = k.
If x − 1/x = 6, what is the value of x² + 1/x²?
- (A)38
- (B)36
- (C)40
- (D)12
Show answer and explanation
Correct answer: (A) 38
Squaring both sides: (x − 1/x)² = x² + 1/x² − 2 = 36. Therefore x² + 1/x² = 36 + 2 = 38.
Shortcut: x² + 1/x² = k² + 2 when x − 1/x = k.
If x − 1/x = 7, what is the value of x² + 1/x²?
- (A)51
- (B)49
- (C)47
- (D)14
Show answer and explanation
Correct answer: (A) 51
Squaring both sides: (x − 1/x)² = x² + 1/x² − 2 = 49. Therefore x² + 1/x² = 49 + 2 = 51.
Shortcut: x² + 1/x² = k² + 2 when x − 1/x = k.
If x + 1/x = 9, what is the value of x² + 1/x²?
- (A)81
- (B)85
- (C)79
- (D)83
Show answer and explanation
Correct answer: (C) 79
Squaring both sides: (x + 1/x)² = x² + 1/x² + 2 = 81. Therefore x² + 1/x² = 81 − 2 = 79.
Shortcut: x² + 1/x² = k² − 2 when x + 1/x = k.
If x + 1/x = 10, what is the value of x² + 1/x²?
- (A)100
- (B)98
- (C)102
- (D)104
Show answer and explanation
Correct answer: (B) 98
Squaring both sides: (x + 1/x)² = x² + 1/x² + 2 = 100. Therefore x² + 1/x² = 100 − 2 = 98.
Shortcut: x² + 1/x² = k² − 2 when x + 1/x = k.
Frequently asked questions
How many SSC CGL Algebra questions can I practise here?
15 questions — 15 moderate. 15 are shown on this page with answers and explanations, and the practice set draws from all of them.
How should I practise Algebra for SSC CGL?
Read through a few solved questions first to see the method, then take a timed practice set. Afterwards, check which questions you got wrong or spent longest on and redo those before moving on.