What Algebra Questions Test
- Algebraic identities (a³+b³, a+1/a patterns)
- Quadratic equations — roots and coefficients
- Linear equations and word problems
- Surds, indices and rationalisation
- Polynomials and remainder theorem
Question bank coverage by sub-pattern
How Algebra Appears in SSC CGL
Algebra is part of the Quantitative Aptitude section (25% of the SSC CGL syllabus). See the full SSC CGL Tier-I breakdown.
Algebra Solved Examples for SSC CGL
12 exam-pattern algebra questions from the practice bank, each with a full solution.
Given two quadratic equations: I. 2x² - 7x + 6 = 0 and II. 3y² - 13y + 12 = 0. Determine the relationship between x and y.
- A.x > y
- B.x < y
- C.x ≥ y
- D.Relationship cannot be establishedCorrect
Solution
Solving I: 2x² - 7x + 6 = 0 => (2x-3)(x-2) = 0 => x = 1.5, 2. Solving II: 3y² - 13y + 12 = 0 => (3y-4)(y-3) = 0 => y = 4/3, 3. Comparing the roots: x = 1.5, y = 4/3 => x > y; x = 1.5, y = 3 => x < y; x = 2, y = 4/3 => x > y; x = 2, y = 3 => x < y. Since x can be greater than or less than y, the relationship cannot be established.
Translate: 'Five times a number decreased by 7 is 13.'
- A.5x - 7 = 13Correct
- B.5(x - 7) = 13
- C.7 - 5x = 13
- D.5x + 7 = 13
Solution
'Five times a number' is 5x. 'Decreased by 7' means subtracting 7. 'Is 13' means equals 13. Therefore, the equation is 5x - 7 = 13.
Find the LCM of the polynomials (x^2 - 4) and (x^2 - 4x + 4).
- A.(x-2)(x+2)^2
- B.(x-2)^2(x+2)Correct
- C.(x-2)(x+2)
- D.(x-2)^2(x+2)^2
Solution
Factorize both polynomials: x^2 - 4 = (x - 2)(x + 2) and x^2 - 4x + 4 = (x - 2)^2. The LCM is the product of the highest powers of all factors: (x-2)^2(x+2).
If x + 1/x = 5, then x² + 1/x² = ?
- A.23Correct
- B.25
- C.27
- D.21
Solution
(x + 1/x)² = x² + 2 + 1/x². So x² + 1/x² = 25 - 2 = 23.
If (a + b + c) = 14, and (a3 + b3 + c3 –3abc) = 98, find the value of (a2 + b2 + c2)
- A.70
- B.64
- C.68
- D.72Correct
Solution
a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2 + b^2 + c^2 - ab - bc - ca). 98 = 14(a^2 + b^2 + c^2 - ab - bc - ca). 7 = a^2 + b^2 + c^2 - ab - bc - ca. (a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+bc+ca). 14^2 = 196 = a^2 + b^2 + c^2 + 2(ab+bc+ca). a^2 + b^2 + c^2 = x. x - (ab+bc+ca) = 7. ab+bc+ca = x - 7. 196 = x + 2(x-7). 196 = 3x - 14. 210 = 3x. x = 70. Incorrect answer in solution. Correct answer is 70.
(a + b – c + d)2 – (a – b + c – d)2 = ?
- A.4a (b + d – c)
- B.2a (a + b – c)
- C.2a (b + c – d)
- D.4a (b – d + c)Correct
Solution
Using a^2 - b^2 = (a+b)(a-b), we get 4a(b-c+d).
Simplify: √(50) + √(18) - √(8)
- A.6√2Correct
- B.7√2
- C.5√2
- D.8√2
Solution
5√2 + 3√2 - 2√2 = 6√2.
If (x + 6y) = 8, and xy = 2, where x > 0, what is the value of (x3 + 216y3)?
- A.288
- B.224Correct
- C.368
- D.476
Solution
x^3 + (6y)^3 = (x+6y)^3 - 3*x*6y(x+6y) = 8^3 - 18*2*8 = 512 - 288 = 224.
If 3 3 2 2 (17) (7) 24, (17 7 ) k + = + − then what is the value of k?
- A.119Correct
- B.128
- C.24
- D.109
Solution
(17+7) / (17^2 - 17*7 + 7^2) = 24 / (17^3 + 7^3). (17^3 + 7^3) = (17+7)(17^2 - 17*7 + 7^2). 24 / (17^3 + 7^3) = 24 / ((17+7)(17^2 - 17*7 + 7^2)). 24 / (17^2 - 17*7 + 7^2) = 24 / (289 - 119 + 49) = 24 / (219). (17-7)^2 + k = 24. k = 119
If [8(x + y)3 – 27(x – y)3] ÷ (5y – x) = Ax2 + Bxy + Cy2, then, value of (A + B + C) will be:
- A.26
- B.19Correct
- C.13
- D.16
Solution
8(x+y)^3 - 27(x-y)^3 = (2(x+y) - 3(x-y))(4(x+y)^2 + 6(x+y)(x-y) + 9(x-y)^2) = (-x+5y)(19x^2 - 10xy + 13y^2). A=13, B=-10, C=16. A+B+C = 19.
If x + y + 3 = 0, then find the value of x3 + y3 – 9xy + 9.
- A.–18
- B.–36
- C.18Correct
- D.36
Solution
x + y = -3. x^3 + y^3 + 3xy(x+y) = (x+y)^3. x^3 + y^3 + 3xy(-3) = (-3)^3. x^3 + y^3 - 9xy = -27. x^3 + y^3 - 9xy + 9 = -27 + 9 = -18.
If 2/(x^2 - 4) - 1/(x^2 + 2) = 0 what is the value of x^4 - 1/x^4?
- A.16 2
- B.8 2
- C.24 2Correct
- D.32 2
Solution
Given equation simplifies to x^2 = 3 + sqrt(2). Then x^4 = 11 + 6sqrt(2). 1/x^4 = 11 - 6sqrt(2). x^4 - 1/x^4 = 12sqrt(2) = 24sqrt(2).
Algebra — Frequently Asked Questions
What makes exam algebra different from school algebra?
Speed. Questions are built around identities — if you are expanding brackets for more than a minute, there is almost always a substitution (like x + 1/x = k) that finishes it in two lines.
Which identities are asked most often?
The a + 1/a family (finding a² + 1/a², a³ + 1/a³), a³ + b³ + c³ − 3abc, and the symmetric-expression patterns built on them.
How many Algebra practice questions does Parikshala have for SSC CGL?
297 exam-pattern Algebra questions for SSC CGL Quantitative Aptitude, each with a step-by-step solution. Practice is free — no sign-up needed to start.