SSC CGL Algebraic Result Practice Test 2026 — Free Chapter Wise Questions

The x + 1/x ladder from squares to eighth powers, cube rules for sums and differences, quadratics and surds that hide the reciprocal pair, sign and range rules, and power cycles for very high exponents — 25 questions per test, with full solutions and shortcut tricks in English or हिंदी.

2 Difficulty Levels 25 Questions per Test 30 min optional timer English & हिंदी

Algebraic Result Tests — Pick a Level and Start

Tap a level to see every test in it. Start at Level 1 the day you learn the ladder, then move to Level 2 with the timer running to push accuracy under pressure.

Level 1 Basic Checking… View tests

One step on the ladder — find x2 + 1/x2 from x + 1/x, use the cube rule, read the pair off a quadratic, and come back down a level. Attempt these without the clock while the rules are still fresh.

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Level 2 Tier I Standard Checking… View tests

Real SSC CGL Tier I difficulty — two ideas chained in one question: a multiplier in front of the bracket, a quadratic written backwards, a surd given that turns whole when you cross over, a range like 0 < x < 1 that flips the sign, and a power so large that only a cycle reaches it. This is the score that tells you the chapter is exam-ready.

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The x + 1/x family is one of the most predictable sources of marks in the SSC CGL Quantitative Aptitude paper. A shift almost always carries a question from it — a reciprocal sum that must become a cube, a quadratic that hides the pair, a surd value that turns whole the moment you cross over, or a power so large that only a cycle can reach it. None of them needs heavy calculation; each is a walk up or down one short ladder.

These practice tests put twenty-five reciprocal-power questions in front of you in one sitting, which is what turns the ladder from something you can recite into something you climb without thinking. Every question comes with a full solution and the shortcut, in English or Hindi.

How Many Algebraic Result Questions Are Asked in SSC CGL?

The chapter usually gets one to two direct questions, and it is one of the most repeated patterns in the advanced maths block across recent shifts.

ChapterTier I (out of 25)Tier II Paper I (out of 30)
Algebraic Result (x + 1/x)1–22–3
Algebraic Formula1–22–3
Algebraic Expressions11–2
Quadratic Equations11–2
Powers, Indices & Surds1–21–2

Typical spread across recent SSC CGL shifts. SSC does not publish a chapter-wise breakup, so treat these as planning ranges. Tier I maths is always 25 questions in a locked 15-minute section.

What You Will Practice in the Algebraic Result Chapter

Core topics

  • The ladder up: square the bracket and adjust by 2, and why each squaring doubles the power
  • The ladder down: add 2 and take the root, and which 2 to use for a sum or a difference
  • The root level — √x + 1/√x and where it lands
  • Cube rules for sums and differences, and the sixth power as the square of the cube
  • Fifth, seventh and other odd powers by multiplying two levels
  • Quadratic equations that hide the pair, and the constant-term sign rule
  • Single fractions such as (x2+1)/x that split into a reciprocal sum
  • Surd values, and rationalising to find the reciprocal
  • Scaled and shifted terms: 3p with 1/3p, x/5 with 5/x, (x−3) with 1/(x−3)
  • Self-referential definitions such as x = 1/(x − 4)
  • Crossing between sum and difference, and ranges that decide the final sign
  • Values with no real solution, and power cycles for x50 and x99

Every one of these is explained from zero, with a worked example and the common trap, in the Algebraic Result study notes (also in हिंदी).

Solved Examples — SSC CGL Algebraic Result

Q1. If x + 1/x = 3, find x8 + 1/x8.
Square and subtract 2 each time: 9 − 2 = 7, then 49 − 2 = 47, then 2209 − 2. The −2 applies at every step. Answer: 2207
Q2. If x2 − 9x + 1 = 0 and x ≠ 0, find x + 1/x.
The constant is 1, so divide every term by x: x − 9 + 1/x = 0. Answer: 9
Q3. If x + 1/x = √13 and x > 1, find x3 − 1/x3.
Cross over: (x − 1/x)2 = 13 − 4 = 9, so x − 1/x = 3. Then k3 + 3k = 27 + 9. The surd disappears because 13 − 4 is a perfect square. Answer: 36
Q4. If x2 + 1/x2 = 27 and 0 < x < 1, find x − 1/x.
27 − 2 = 25, so the size is 5. But x is small and 1/x is large, so the difference is negative. Answer: −5
Q5. If x2 + x + 1 = 0, find x99 + 1/x99.
Multiplying by (x − 1) gives x3 = 1, so powers repeat every 3. 99 is a multiple of 3, so x99 = 1. Answer: 2

How the Algebraic Result Chapter Tests Work

  • 25 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
  • Optional 30-minute timer — with the clock to build exam speed, without it while you are still learning the rules.
  • Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
  • Solutions, shortcut tricks and concept notes open after you submit, question by question.
  • English and हिंदी, chosen at the start of every test.
  • Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.

How to Prepare Algebraic Result for SSC CGL

  1. Learn the ladder before anything else. Square and subtract 2 going up, add 2 and take the root coming down — that one pair of moves solves most of the chapter.
  2. Fix the sum-and-difference rule. Sums subtract the adjustment, differences add it, for both squares and cubes. Almost every wrong option in this chapter comes from swapping them.
  3. Read the constant term of a quadratic first. A +1 constant gives a reciprocal sum, a −1 constant gives a difference, and a common factor must be cleared before either works.
  4. Remember that odd powers are not on the ladder. Multiply two levels and subtract the leftover level: level 2 times level 3 gives level 5 plus level 1.
  5. Check the range before the final square root. With 0 < x < 1 the difference is negative, and the right-sized wrong-signed option is always offered.
  6. Do Level 1 untimed, the same day you learn the ladder. The aim is correct recall, not speed.
  7. Move to Level 2 with the 30-minute clock on. A climb that takes more than twenty seconds means you are still deriving the rule instead of applying it.
  8. Study it right after algebraic formula. The cube rule carries straight over from algebraic formula, and the chapter notes are best read beside the tests.
  9. Verify against a real paper. Once Level 2 is consistent, attempt a previous year paper and then a full mock test under locked sectional timing.

SSC CGL बीजीय परिणाम (Algebraic Result) चैप्टर टेस्ट — हिंदी में

x + 1/x वाला अध्याय SSC CGL गणित में अंकों का सबसे अनुमानित स्रोत है। लगभग हर शिफ्ट में इसका 1–2 प्रश्न आता है — जैसे व्युत्क्रम योग से घन निकालना, ऐसा द्विघात जो जोड़ी को छिपाए हो, कोई करणी मान जो पार जाते ही पूर्णांक बन जाए, या इतनी बड़ी घात कि केवल कोई चक्र ही वहाँ पहुँचे।

TrickySSC पर इस अध्याय के सभी टेस्ट हिंदी में उपलब्ध हैं — प्रश्न, विकल्प, विस्तृत हल और शॉर्टकट ट्रिक सब हिंदी में। दो स्तर हैं: लेवल 1 (आधारभूत) और लेवल 2 (टियर I स्तर)। प्रत्येक टेस्ट में 25 प्रश्न, वैकल्पिक 30 मिनट का टाइमर और +2 / −0.5 की वही मार्किंग जो असली परीक्षा में होती है।

याद रखने योग्य नियम: x2 + 1/x2 = (x + 1/x)2 − 2, और अंतर दिया हो तो 2 जोड़िए; x3 + 1/x3 = k3 − 3k, जबकि x3 − 1/x3 = k3 + 3k; और 0 < x < 1 होने पर x − 1/x ऋणात्मक होता है। पूरे नोट्स यहाँ हिंदी में पढ़ें।

SSC CGL Algebraic Result — Frequently Asked Questions

How do I find x2 + 1/x2 from x + 1/x?
Square the given value and subtract 2. If the given is a difference instead, square it and add 2. The adjustment is always exactly 2 because x × 1/x = 1.
What is the formula for x3 + 1/x3?
It is k3 − 3k, where k = x + 1/x. For the difference it is k3 + 3k with k = x − 1/x. Sums subtract the correction and differences add it.
How do I get x + 1/x from a quadratic equation?
If the constant term is 1, divide every term by x. So x2 − 9x + 1 = 0 becomes x − 9 + 1/x = 0, giving x + 1/x = 9. A constant of −1 gives a difference instead, and a common factor must be cleared first.
When is x − 1/x negative?
When 0 < x < 1, because then 1/x is the larger term. It is also negative when x < −1. A sum such as x2 + 1/x2 is always positive, so only the final step to a difference depends on the range.
How do I handle very high powers such as x99?
Look for a cycle. If x2 + x + 1 = 0 then x3 = 1 and powers repeat every 3. If x2 − x + 1 = 0 then x3 = −1 and x6 = 1, so they repeat every 6. Reduce the exponent by the cycle and evaluate the level that is left.
How many questions are in each algebraic result practice test?
Twenty-five questions per test, with an optional 30-minute timer and the real exam marking scheme of +2 for a correct answer, −0.5 for a wrong one and 0 for an unattempted question.
Are the algebraic result tests available in Hindi and are they free?
Yes to both. Questions, options, detailed solutions and shortcut tricks are available in हिंदी, and you pick English or Hindi before the test starts. Every test is free — you only need a free TrickySSC account, and the sign-in box opens on the page itself when you start a test.

More Free SSC CGL Practice