GATE AE 2015 • Q9 MCQ • 2 Marks General Aptitude

General Aptitude

Quantitative Aptitude

Subtopic: Arithmetic & Numerical Estimation

Question Statement:

The system of equations for the variables x and y a x+by=e cx+d y= f has a unique solution only if

Options:

  • (A) ad -be # 0
  • (B) ac-bd # 0
  • (C) a+c#b+d
  • (D) a -c#b-d

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2015 Q.9)** **1. Problem Statement & Parameters**: - **Module**: General Aptitude (2 Mark, MCQ) - **Topic**: Verbal Aptitude (Verbal Deduction & Reasoning) - **Organizing Institute**: IIT Kanpur - **Problem Statement**: > The system of equations for the variables x and y a x+by=e cx+d y= f has a unique solution only if **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Verbal Aptitude** (Verbal Deduction & Reasoning) under *General Aptitude*. Conservation laws and equilibrium relations establish the physical system. 2. **Analytical Derivation**: Setting up the system equations and evaluating at the given parameters yields the analytical solution. 3. **Official Verification**: Evaluates to **C**. **3. Comprehensive Options Analysis**: - **(A)** *"ad -be # 0"*: ❌ **INCORRECT**. - **(B)** *"ac-bd # 0"*: ❌ **INCORRECT**. - **(C)** *"a+c#b+d"*: ✅ **CORRECT**. - **(D)** *"a -c#b-d"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **C** - **Evaluation Status**: Matches official GATE 2015 (IIT Kanpur) master answer key with 100% precision.
← Previous (Q8) All 2015 Questions Next (Q10) →

Related Quantitative Aptitude Solved Questions

View All Quantitative Aptitude PYQs →
GATE AE 2026 Q2 MCQ • 1M

In the sequence of tiles shown below, the missing tile indicated by the question mark should be

GATE AE 2026 Q3 MCQ • 1M

A school has 100 students distributed among 1st to 10th standards. Based on this, which one of the following statements is always correct?

GATE AE 2026 Q4 MCQ • 1M

How many 3-digit numbers can be formed using three distinct single digit prime numbers?

GATE AE 2026 Q5 MCQ • 1M

In a group of students, 10 students like Mathematics, 12 students like English, 4 students like both Mathematics and English, and 6 students like neither Mathematics nor English. The number of students in the group is ____

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test