SSC CGL Quant – Graphs of Linear Equations & Coordinate Basics – Level 2 · Exam Level · Tier I Sprint

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SSC CGL Quant – Graphs of Linear Equations & Coordinate Basics – Level 2 · Exam Level · Tier I Sprint – 15 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 area enclosed by the line 5x + 3y = 30 and the coordinate axes is:

Correct Answer: D [30 sq units]

Explanation:

Intercepts 6 and 10 → ½ × 6 × 10 = 30 (or 900/(2 × 15)).

2.  
Graph readingThe lines 2x + y = 11 and x − y = 1 are drawn below. Their point of intersection is:

Correct Answer: A [(4, 3)]

Explanation:

Add the equations: 3x = 12 → x = 4, y = 3.

3.  
For what value of k do the equations 3x − y = 5 and 6x + ky = 10 have infinitely many solutions?

Correct Answer: C [−2]

Explanation:

3/6 = −1/k = 5/10 → k = −2.

4.  
For what value of k do kx + 2y = 3 and 3x + 6y = 10 have NO solution?

Correct Answer: B [1]

Explanation:

k/3 = 2/6 → k = 1, and 3/10 ≠ 1/3, so the lines are parallel.

5.  
The lines 2x + y = 8 and x − y = 1 and the x-axis form a triangle. Its area is:

Correct Answer: D [3 sq units]

Explanation:

Meet at (3, 2); x-intercepts 4 and 1 → base 3 → ½ × 3 × 2 = 3.

6.  
The distance between (−3, 4) and (5, −2) is:

Correct Answer: B [10]

Explanation:

√(8² + 6²) = 10.

7.  
The slope of a line perpendicular to a line of slope 2/3 is:

Correct Answer: C [−3/2]

Explanation:

m₁ × m₂ = −1 → −3/2.

8.  
Diagram-basedWhich equation represents the line shown?

Correct Answer: A [2x − y + 6 = 0]

Explanation:

Intercepts −3 and 6: x/(−3) + y/6 = 1 → −2x + y = 6 → 2x − y + 6 = 0.

9.  
Two-quantity comparison
Quantity I: Area enclosed by 3x + 4y = 24 and the axes
Quantity II: Area enclosed by 2x + y = 10 and the axes

Correct Answer: B [Quantity I < Quantity II]

Explanation:

QI = ½ × 8 × 6 = 24; QII = ½ × 5 × 10 = 25 → QI < QII.

10.  
Trick SpotterThe fastest correct way to find the area between 6x + 5y = 60 and the axes is:

Correct Answer: B [c²/(2ab) = 3600/60 = 60]

Explanation:

Intercepts 10 and 12 give ½ × 10 × 12 = 60; c²/(2ab) gives it in one step.

11.  
Spot My Mistake“For 3x − 4y = −12, put y = 0: x = 4. So the x-intercept is 4.” The correct x-intercept is:

Correct Answer: A [−4]

Explanation:

3x = −12 → x = −4; the sign of c was dropped.

12.  
The reflection of the point (−5, 2) in the y-axis is:

Correct Answer: C [(5, 2)]

Explanation:

Mirror in the y-axis: change the sign of x only.

13.  
Which point lies in the fourth quadrant AND on the line x − y = 7?

Correct Answer: D [(3, −4)]

Explanation:

(3, −4): 3 + 4 = 7 and x > 0, y < 0.

14.  
The slope of the line through (1, 2) and (4, 11) is:

Correct Answer: B [3]

Explanation:

(11 − 2)/(4 − 1) = 9/3 = 3.

15.  
Reverse questionThe line ax + 3y = 12 has x-intercept 6. Find a.

Correct Answer: D [2]

Explanation:

x-intercept = 12/a = 6 → a = 2.

➤ 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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