Algebra Questions for SSC CGL: What This Set Covers
These are 20 original algebra questions in the SSC CGL and CHSL pattern, each solved in one or two lines. They follow the official syllabus wording in the SSC CGL 2026 notice: "Basic algebraic identities of School Algebra & Elementary surds, Graphs of Linear Equations" (Tier 1, para 13.10.3) and "Basic algebraic identities of School Algebra and Elementary surds (simple problems) and Graphs of Linear Equations" (Tier 2, para 13.11.1.3). In practice SSC algebra means five families: x + 1/x, a + b with ab, a + b + c, surds, and linear equations/graphs.
Key takeaway: almost every SSC algebra question is one identity used once. Write the identity first, then substitute; and when options are numbers, try simple values (x = 1, a = b = c) to check your answer in seconds.
SSC CGL Tier 2 is tentatively in December 2026, and SSC CHSL Tier 1 runs 30 November–31 December 2026 (official SSC notices). Identities are listed in our Algebra Formulas for SSC CGL; this page is the practice set.
Identities Used in This Set
| Identity | Form used |
|---|---|
| x² + 1/x² | (x + 1/x)² − 2 or (x − 1/x)² + 2 |
| x³ + 1/x³ | (x + 1/x)³ − 3(x + 1/x) |
| a² + b² | (a + b)² − 2ab |
| a³ + b³ | (a + b)³ − 3ab(a + b) |
| a³ − b³ | (a − b)³ + 3ab(a − b) |
| a² + b² + c² | (a + b + c)² − 2(ab + bc + ca) |
| a³ + b³ + c³ − 3abc | (a + b + c)(a² + b² + c² − ab − bc − ca) |
| If a + b + c = 0 | a³ + b³ + c³ = 3abc |
Set A: x + 1/x Type (Q1–Q6)
Q1. If x + 1/x = 5, find x² + 1/x². (a) 23 (b) 25 (c) 27 (d) 21 Answer: (a) 23. 25 − 2.
Q2. If x − 1/x = 3, find x² + 1/x². (a) 7 (b) 9 (c) 11 (d) 13 Answer: (c) 11. 9 + 2. Trap: with a minus sign you add 2.
Q3. If x + 1/x = 3, find x³ + 1/x³. (a) 9 (b) 18 (c) 24 (d) 27 Answer: (b) 18. 27 − 9.
Q4. If x + 1/x = 2, find x¹⁰⁰ + 1/x¹⁰⁰. (a) 0 (b) 1 (c) 2 (d) 2¹⁰⁰ Answer: (c) 2. x + 1/x = 2 only when x = 1.
Q5. If x⁴ + 1/x⁴ = 119 and x > 1, find x − 1/x. (a) 2 (b) 3 (c) 4 (d) 11 Answer: (b) 3. x² + 1/x² = √(119 + 2) = 11, and (x − 1/x)² = 11 − 2 = 9.
Q6. If x² − 5x + 1 = 0, find x³ + 1/x³. (a) 100 (b) 110 (c) 115 (d) 125 Answer: (b) 110. Divide by x: x + 1/x = 5; then 125 − 15.
Set B: a + b and ab Type (Q7–Q10)
Q7. If a + b = 10 and ab = 21, find a² + b². (a) 58 (b) 79 (c) 100 (d) 42 Answer: (a) 58. 100 − 42. (Check: a, b = 7, 3.)
Q8. If a + b = 7 and ab = 12, find a³ + b³. (a) 91 (b) 97 (c) 127 (d) 343 Answer: (a) 91. 343 − 3 × 12 × 7. (Check: 4³ + 3³ = 91.)
Q9. If a − b = 4 and ab = 5, find a³ − b³. (a) 64 (b) 84 (c) 124 (d) 144 Answer: (c) 124. 64 + 3 × 5 × 4. (Check: a = 5, b = 1.)
Q10. Find (0.7³ + 0.3³)/(0.7² − 0.7 × 0.3 + 0.3²). (a) 0.4 (b) 1 (c) 0.21 (d) 1.21 Answer: (b) 1. (a³ + b³)/(a² − ab + b²) = a + b.
Set C: a + b + c Type (Q11–Q14)
Q11. If a + b + c = 0 and abc = 6, find a³ + b³ + c³. (a) 0 (b) 6 (c) 18 (d) 216 Answer: (c) 18. 3abc.
Q12. If a + b + c = 9 and ab + bc + ca = 26, find a² + b² + c². (a) 29 (b) 55 (c) 81 (d) 107 Answer: (a) 29. 81 − 52.
Q13. If a + b + c = 6, a² + b² + c² = 14 and abc = 6, find a³ + b³ + c³. (a) 18 (b) 27 (c) 36 (d) 48 Answer: (c) 36. ab + bc + ca = (36 − 14)/2 = 11; a³ + b³ + c³ = 3(6) + 6(14 − 11) = 36. (Check: 1, 2, 3.)
Q14. If a² + b² + c² = ab + bc + ca for real a, b, c (c ≠ 0), find (a + b)/c. (a) 0 (b) 1 (c) 2 (d) 3 Answer: (c) 2. The condition forces a = b = c.
Set D: Surds (Q15–Q17)
Q15. If x = 3 + 2√2, find x + 1/x. (a) 4√2 (b) 6 (c) 3 (d) 9 Answer: (b) 6. 1/x = 3 − 2√2 (rationalise), so the √2 terms cancel.
Q16. If x = √3 + √2, find x² + 1/x². (a) 6 (b) 8 (c) 10 (d) 12 Answer: (c) 10. 1/x = √3 − √2, so x + 1/x = 2√3 and x² + 1/x² = 12 − 2.
Q17. If x + 1/x = √3, find x⁶ + 1. (a) 0 (b) 1 (c) 2 (d) 3√3 Answer: (a) 0. x³ + 1/x³ = 3√3 − 3√3 = 0, so x⁶ = −1.
Set E: Linear Equations and Graphs (Q18–Q20)
Q18. If 2x + 3y = 13 and 3x + 2y = 12, find xy. (a) 5 (b) 6 (c) 8 (d) 12 Answer: (b) 6. Add: x + y = 5; subtract: y − x = 1; so x = 2, y = 3.
Q19. Where does the line 2x − 3y = 12 cut the y-axis? (a) (6, 0) (b) (0, 4) (c) (0, −4) (d) (−4, 0) Answer: (c). Put x = 0: −3y = 12.
Q20. Find the area of the triangle formed by 3x + 2y = 12 with the coordinate axes. (a) 6 (b) 12 (c) 24 (d) 36 Answer: (b) 12. Intercepts 4 and 6; ½ × 4 × 6.
Answer Key
| Q | Ans | Q | Ans | Q | Ans | Q | Ans |
|---|---|---|---|---|---|---|---|
| 1 | a | 6 | b | 11 | c | 16 | c |
| 2 | c | 7 | a | 12 | a | 17 | a |
| 3 | b | 8 | a | 13 | c | 18 | b |
| 4 | c | 9 | c | 14 | c | 19 | c |
| 5 | b | 10 | b | 15 | b | 20 | b |
The Value-Putting Trick (Saves Time in the Exam)
When a question gives a symmetric condition, try simple numbers that satisfy it:
| Condition | Try | Example from this set |
|---|---|---|
| x + 1/x = 2 | x = 1 | Q4 |
| a + b + c = 0 | a = 1, b = 1, c = −2 | Q11 type |
| a² + b² + c² = ab + bc + ca | a = b = c = 1 | Q14 |
| a + b = 7, ab = 12 | a = 4, b = 3 | Q8 |
Then compute the expression directly and match the option. Use the identity only when simple values do not exist.
Practise Under Time
- SSC CGL algebra mock test 01, 02, 03
- Graphs and lines: Coordinate geometry questions for SSC CGL, SSC CGL Tier 1 mock: Geometry and Coordinate Geometry
- More practice: Trigonometry questions for SSC CGL
Algebra Questions FAQs
Which algebra topics are in the SSC CGL syllabus?
Basic algebraic identities of school algebra, elementary surds and graphs of linear equations, as per the SSC CGL 2026 notice for both Tier 1 and Tier 2.
What is the fastest way to solve x + 1/x questions?
Remember the ladder: x² + 1/x² = (x + 1/x)² − 2 and x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x). Every higher power is built from these two.
When is a³ + b³ + c³ = 3abc?
When a + b + c = 0 (or when a = b = c).
How do I rationalise a surd like 1/(3 + 2√2)?
Multiply numerator and denominator by 3 − 2√2. The denominator becomes 9 − 8 = 1, so the answer is 3 − 2√2.
How many algebra questions come in SSC CGL?
SSC does not publish topic-wise counts; algebra is part of Quantitative Aptitude (Tier 1) and Mathematical Abilities (Tier 2) in the official syllabus.
Practice Next for SSC Maths
- Formulas: Algebra formulas, Surds and indices, Number system
- Plans: SSC CGL Tier 2 preparation strategy 2026, SSC CHSL preparation strategy 2026
Sources: SSC CGL 2026 notice (syllabus paras 13.10.3 and 13.11.1.3); SSC notice dated 01.10.2026. Questions and solutions are original BookOfExams material. Last checked 7 November 2026.