SSC CGL Quant – Algebra – Level 1 · Warm-up · Tier I Level

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SSC CGL Quant – Algebra – Level 1 · Warm-up · Tier I Level – 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.

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1.  
If a + b = 10 and ab = 21, what is the value of a² + b²?

Correct Answer: D [58]

Explanation:

(a + b)² − 2ab = 100 − 42 = 58.

2.  
If x + 1/x = 4, what is the value of x² + 1/x²?

Correct Answer: C [14]

Explanation:

k² − 2 = 16 − 2 = 14.

3.  
What is the value of 101² − 99²?

Correct Answer: A [400]

Explanation:

(101 + 99)(101 − 99) = 200 × 2 = 400.

4.  
(a + b)² − (a − b)² is equal to:

Correct Answer: B [4ab]

Explanation:

Expand: 2ab − (−2ab) = 4ab.

5.  
If 5x − 9 = 3x + 7, what is x?

Correct Answer: B [8]

Explanation:

5x − 3x = 7 + 9 → 2x = 16 → x = 8.

6.  
If x + y = 12 and x − y = 4, what is xy?

Correct Answer: A [32]

Explanation:

x = 8, y = 4 → xy = 32.

7.  
If a + b + c = 0, then a³ + b³ + c³ equals:

Correct Answer: D [3abc]

Explanation:

a³ + b³ + c³ − 3abc = (a + b + c)(…) = 0.

8.  
Fill in the blankx³ − y³ = (x − y)(___).

Correct Answer: C [x² + xy + y²]

Explanation:

Difference of cubes: (x − y)(x² + xy + y²).

9.  
Statement-basedWhich of the following is/are true for all numbers a and b?
I. (a + b)² = a² + b²
II. a² − b² = (a + b)(a − b)

Correct Answer: A [Only II]

Explanation:

I misses the 2ab term (a = b = 1: 4 ≠ 2).

10.  
If x = 2 is a root of x² + kx − 10 = 0, what is k?

Correct Answer: C [3]

Explanation:

4 + 2k − 10 = 0 → k = 3.

11.  
Where does the line 5x + 2y = 30 cut the x-axis?

Correct Answer: B [(6, 0)]

Explanation:

Put y = 0: 5x = 30 → x = 6.

12.  
Match the followingMatch each expression with its expansion:
P. (a + b)³ Q. a³ + b³ R. a² − b²
1. (a + b)(a² − ab + b²) 2. (a + b)(a − b) 3. a³ + b³ + 3ab(a + b)

Correct Answer: D [P-3, Q-1, R-2]

Explanation:

Cube of a sum has the 3ab(a + b) term; sum of cubes factors with a² − ab + b².

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Quantitative Aptitude book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-quantitative-aptitude

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