SSC CGL Quant – Algebra – Level 3 · Challenge
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½(a + b + c)[(a − b)² + (b − c)² + (c − a)²] = ½ × 78 × (1 + 1 + 4) = 234.
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SSC CGL Quant – Algebra – Level 3 · Challenge – 10 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.
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1.
What is the minimum value of x² − 6x + 14?
Correct Answer: B [5]
Explanation:
(x − 3)² + 5 → least value 5 at x = 3.
2.
If a + b + c = 9 and ab + bc + ca = 26, what is a³ + b³ + c³ − 3abc?
Correct Answer: D [27]
Explanation:
a² + b² + c² = 81 − 52 = 29 → 9 × (29 − 26) = 27.
3.
If x = 7 + 4√3, what is the value of x + 1/x?
Correct Answer: B [14]
Explanation:
1/x = 7 − 4√3 (product 7² − (4√3)² = 49 − 48 = 1) → sum 14.
4.
Odd one outWhich of these is NOT a factor of x³ − 7x + 6?
Correct Answer: D [(x + 2)]
Explanation:
p(1) = p(2) = p(−3) = 0 but p(−2) = −8 + 14 + 6 = 12 ≠ 0.
5.
Data tablea linear expression ax + b takes these values:
x = 1 → 5 | x = 2 → 8 | x = 3 → 11
What is its value at x = 10?
x = 1 → 5 | x = 2 → 8 | x = 3 → 11
What is its value at x = 10?
Correct Answer: A [32]
Explanation:
Step 3 per unit → 3x + 2 → 32.
6.
The sum of two numbers is 17 and the sum of their squares is 169. What is the positive difference of the numbers?
Correct Answer: C [7]
Explanation:
ab = (289 − 169)/2 = 60; (a − b)² = 169 − 120 = 49 → 7 (the numbers are 12 and 5).
7.
If x² − 7x + 1 = 0, what is x² + 1/x²?
Correct Answer: D [47]
Explanation:
Divide by x: x + 1/x = 7 → 49 − 2 = 47.
8.
If a + b + c = 0 (none of them zero), what is the value of a²/bc + b²/ca + c²/ab?
Correct Answer: B [3]
Explanation:
Common denominator abc: (a³ + b³ + c³)/abc = 3abc/abc = 3.
9.
If x² + y² − 6x + 8y + 25 = 0, what is the value of x + y?
Correct Answer: A [−1]
Explanation:
(x − 3)² + (y + 4)² = 0, so x = 3 and y = −4 → x + y = −1.
10.
What is the value of 25³ + 26³ + 27³ − 3 × 25 × 26 × 27?
Correct Answer: C [234]
Explanation:
½(a + b + c)[(a − b)² + (b − c)² + (c − a)²] = ½ × 78 × (1 + 1 + 4) = 234.
➤ 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
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