Maths · Chapter 23
Algebra PYQs
A small set of identities, read the right way, turns most SSC algebra questions into two-line work.
Algebraic expressions: operations, expansion and substitution 5 PYQs
- In which of the following, the two expressions are like terms?SSC Selection Post 2026 · 18 Sep 2026
- Which of the following represents (x + y)2?SSC Selection Post 2026 · 23 Sep 2026
- Factorise: x2 − 10x + 25SSC Selection Post 2026 · 23 Sep 2026
- If p = q² + 4 and q = 2, what is the value of p³ ?UP Police SI 2026 · 15 Mar 2026
- If a # b = a² + 9ab + 7b², then find the value of 3 # 4.UP Police SI 2026 · 14 Mar 2026
Square identities with two variables: sum, difference and product 5 PYQs
- Let x − y = 49, and xy = 64, then find the value of x² + y².UP Police SI 2026 · 15 Mar 2026
- The sum of two positive numbers is 32 and their product is 220. The positive difference between them is:RRB NTPC 2026 · 18 Jun 2026
- The sum of two positive numbers is 51 and their product is 230. The positive difference between them is:RRB NTPC 2026 · 13 Jun 2026
- The sum of two positive numbers is 44 and their product is 228. The positive difference between them is:RRB NTPC 2026 · 16 Jun 2026
- The sum of two positive numbers is 67 and their product is 1012. The positive difference between them is:RRB NTPC 2026 · 15 Jun 2026
Difference of squares: a² − b² = (a + b)(a − b) 4 PYQs
- Officer checks (50 + 1)(50 − 1) = ?Delhi Police 2026 · 16 Jan 2026
- Two twins, Alpha and Beta, were asked to calculate the squares of numbers placed symmetrically around a mysterious number x. According to the given…SSC Selection Post 2026 · 24 Sep 2026
- Find the value of (5x + 2)2 − (5x − 2)2.SSC Selection Post 2026 · 25 Sep 2026
- x and y are positive integers such that x4 + y4 + x2y2 = 473 and xy = 16, then what is the value of x2 + xy + y2?SSC Selection Post 2026 · 19 Sep 2026
Cube identities: (a ± b)³ and a³ ± b³ 3 PYQs
- If a + b = 3 and ab = 2, find a3 + b3.SSC Selection Post 2026 · 19 Sep 2026
- If 8x3 − 27y3 = (2x − 3y)(Mx2 + Ny2 + Oxy), find M2 + N2 + O2.SSC Selection Post 2026 · 17 Sep 2026
- If x = ∛(31 + 14√3) and y = ∛(31 − 14√3), then the value of x³ + y³ + 3x³y³ is:RRB NTPC 2026 · 19 Mar 2026
The x + 1/x family I: squares, fourth powers and x − 1/x 5 PYQs
- If √x + f1√x = √7, what is the value of x + 1/x?SSC Selection Post 2026 · 23 Sep 2026
- If x2 + 1/x2 = 14, find the value of (x + 1/x)2.SSC Selection Post 2026 · 23 Sep 2026
- If fK36 + 1K18 = 11, then find the value of fK72 + 1K36.SSC Selection Post 2026 · 18 Sep 2026
- If x2 − 6x + 1 = 0, find the value of x4 + 1/x4.SSC Selection Post 2026 · 18 Sep 2026
- If x = √7 + √3, then find the exact value of x2 + 16/x2.SSC Selection Post 2026 · 25 Sep 2026