SSC CGL Quant – Graphs of Linear Equations & Coordinate Basics – Tier II Level · Marathon

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SSC CGL Quant – Graphs of Linear Equations & Coordinate Basics – Tier II Level · Marathon – 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.  
The lines 2x + 3y = 12, x − y = 1 and the y-axis form a triangle. Its area is:

Correct Answer: C [7.5 sq units]

Explanation:

Meet at (3, 2); y-intercepts 4 and −1 → base 5 on the y-axis; height = x-coordinate 3 → ½ × 5 × 3 = 7.5.

2.  
The equations kx − 2y = 3 and 3x + y = 5 have a unique solution when:

Correct Answer: B [k ≠ −6]

Explanation:

Unique when k/3 ≠ −2/1 → k ≠ −6.

3.  
The point on the x-axis that is equidistant from (2, 3) and (6, 5) is:

Correct Answer: B [(6, 0)]

Explanation:

(x − 2)² + 9 = (x − 6)² + 25 → 8x = 48 → x = 6.

4.  
A line meets the x-axis at A and the y-axis at B. The midpoint of AB is (3, −2). The equation of the line is:

Correct Answer: D [2x − 3y = 12]

Explanation:

A(6, 0), B(0, −4) → x/6 + y/(−4) = 1 → 2x − 3y = 12.

5.  
The area enclosed between the graph of y = |x| and the line y = 5 is:

Correct Answer: A [25 sq units]

Explanation:

Vertices (0, 0), (5, 5), (−5, 5) → ½ × 10 × 5 = 25.

6.  
The line through (2, 3) that makes equal intercepts on the two axes (not through the origin) is:

Correct Answer: C [x + y = 5]

Explanation:

x/a + y/a = 1 → x + y = a; put (2, 3): a = 5.

7.  
In what ratio does the x-axis divide the segment joining (2, −3) and (5, 6)?

Correct Answer: D [1 : 2]

Explanation:

Ratio = 3 : 6 = 1 : 2 (the y-values are −3 and 6).

8.  
Two-quantity comparison
Quantity I: Slope of the line joining (2, 5) and (6, 13)
Quantity II: Slope of the line 4x − 2y = 7

Correct Answer: C [Quantity I = Quantity II]

Explanation:

QI = 8/4 = 2; QII = −4/(−2) = 2 → equal (the lines are parallel).

9.  
The points (a, 2) and (4, b) both lie on 3x − 2y = 8. Find a + b.

Correct Answer: B [6]

Explanation:

3a − 4 = 8 → a = 4; 12 − 2b = 8 → b = 2; a + b = 6.

10.  
The lines x + y = 6, x = 2 and y = 1 form a triangle. Its area is:

Correct Answer: A [4.5 sq units]

Explanation:

Vertices (2, 1), (5, 1), (2, 4): legs 3 and 3 → ½ × 3 × 3 = 4.5.

➤ 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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