SSC CGL Quant – Algebra – Tier II Level · Marathon
← Back
x² + 1/x² = 7, x³ + 1/x³ = 18 → x⁵ + 1/x⁵ = 7 × 18 − 3 = 123.
₹399 →
SSC CGL Quant – Algebra – Tier II Level · Marathon – 12 questions, subject: Quantitative Aptitude. Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.
Get daily current affairs & exam alerts – follow us
YouTube
WhatsApp Channel
Telegram Channel
Facebook Page
Instagram
Share with friends & study groups
Link to this page from your website / blog (HTML code)
1.
How many integers satisfy both 4x − 3 < 3x + 2 and 3x + 5 ≥ 2x + 2?
Correct Answer: C [8]
Explanation:
x < 5 and x ≥ −3 → −3, −2, …, 4: 8 integers.
2.
Diagram-basedThe number line shows the solution set of one of these. Which one?
Correct Answer: A [−3 ≤ 2x − 1 < 7]
Explanation:
Filled dot at −1, open at 4 → −1 ≤ x < 4 ⟺ −2 ≤ 2x < 8 ⟺ −3 ≤ 2x − 1 < 7.
3.
How many integers x satisfy |x − 3| ≤ 5?
Correct Answer: D [11]
Explanation:
−5 ≤ x − 3 ≤ 5 → −2 ≤ x ≤ 8 → 11 integers.
4.
If x + 1/x = √3, what is the value of x¹⁸ + 1/x¹⁸?
Correct Answer: B [−2]
Explanation:
x² + 1/x² = 1 → x³ + 1/x³ = 3√3 − 3√3 = 0 → x⁶ = −1 → x¹⁸ = −1 → −1 + (−1) = −2.
5.
What is the greatest value of 8x − x² − 10?
Correct Answer: D [6]
Explanation:
−(x − 4)² + 6 → greatest 6 at x = 4.
6.
Diagram-basedThe shaded region is x ≥ 0, y ≥ 0, x + y ≤ 6, x + 3y ≤ 12.
What is the greatest value of 2x + 3y on this region?
What is the greatest value of 2x + 3y on this region?
Correct Answer: C [15]
Explanation:
Corners (0, 0), (6, 0), (3, 3), (0, 4) give 0, 12, 15, 12 → 15.
7.
If x = √10 + 3, what is the value of x³ − 1/x³?
Correct Answer: B [234]
Explanation:
1/x = √10 − 3 → x − 1/x = 6 → 216 + 3 × 6 = 234.
8.
Statement-basedWhich of the following is/are always true?
I. If a > b and c < 0, then ac < bc.
II. If a > b (both non-zero), then 1/a < 1/b.
III. If x² > 9, then x > 3.
I. If a > b and c < 0, then ac < bc.
II. If a > b (both non-zero), then 1/a < 1/b.
III. If x² > 9, then x > 3.
Correct Answer: A [I only]
Explanation:
II fails for a = 1, b = −1; III fails for x = −4.
9.
If (x + 2) and (x − 3) are both factors of x³ + ax² + bx − 6, what is a + b?
Correct Answer: B [−7]
Explanation:
p(−2) = 0 → 2a − b = 7; p(3) = 0 → 3a + b = −7 → a = 0, b = −7 → −7.
10.
If x + 1/x = −1, what is the value of x⁹⁹ + 1/x⁹⁹?
Correct Answer: C [2]
Explanation:
x² + x + 1 = 0 → x³ = 1 → x⁹⁹ = (x³)³³ = 1 → 1 + 1 = 2.
11.
If a² + b² + c² − 2a − 4b − 6c + 14 = 0, what is the value of a + b + c?
Correct Answer: D [6]
Explanation:
(a − 1)² + (b − 2)² + (c − 3)² = 0 → a = 1, b = 2, c = 3 → 6.
12.
If x + 1/x = 3, what is the value of x⁵ + 1/x⁵?
Correct Answer: A [123]
Explanation:
x² + 1/x² = 7, x³ + 1/x³ = 18 → x⁵ + 1/x⁵ = 7 × 18 − 3 = 123.
➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Quantitative Aptitude book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-quantitative-aptitude
📘 TNPSC திறனறிவும் மனக்கணக்கு நுண்ணறிவும் (Aptitude & Mental Ability) – முழுமையான பாடநூல்
Here you get the answer with a one-line explanation. TNPSC திறனறிவு & காரணவியல் சிலபஸ் முழுவதும் · 14 அத்தியாயங்கள் + 2 அலகு மாதிரித் தேர்வுகள் · 357 பயிற்சி வினாக்கள் படிப்படியான தீர்வுடன் · மாதிரித் தாள்கள் (50 வினாக்கள்) · 14 மனவரைபடங்கள் · சூத்திரச் சுருக்கம், கணக்கு அட்டவணைகள்
Get the book – ₹199 More quizzes
› SSC CGL Quant – Mock Test M3 – Tier II Mathematical Abilities – Mock M3 · Tier II · Mathematical Abilities
› SSC CGL Quant – Mock Test M2 – Tier I Quantitative Aptitude – Mock M2 · Tier I · Quantitative Aptitude
› SSC CGL Quant – Mock Test M1 – Tier I Quantitative Aptitude – Mock M1 · Tier I · Quantitative Aptitude
› SSC CGL Quant – Speed Rounds – Tier II Level · Speed Round 5 · Marathon
› SSC CGL Quant – Speed Rounds – Tier II Level · Speed Round 4 · Marathon
› SSC CGL Quant – Speed Rounds – Level 3 · Speed Round 3 · Tier I Challenge
Score: 0
Answered: 0 / 0
