Algebra - General Aptitude - General Aptitude (GA) Previous Year Questions

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2024 · General Aptitude (GA) · General Aptitude · Algebra

Geomatics Engineering (GE) 2024

The real variables \(x, y, z\), and the real constants \(p, q, r\) satisfy \[\frac{x}{pq - r^2} = \frac{y}{qr - p^2} = \frac{z}{rp - q^2}\] Given that the denominators are non-zero, the value of \(px + qy + rz\) is

A

0

B

1

C

pqr

D

p^2 + q^2 + r^2

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2

2025 · General Aptitude (GA) · General Aptitude · Algebra

Geomatics Engineering (GE) 2025

The 12 musical notes are given as \( C, C^\#, D, D^\#, E, F, F^\#, G, G^\#, A, A^\#, \) and \( B \). Frequency of each note is \( \sqrt[12]{2} \) times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes \( F^\# \) and C is:

A

\(\sqrt[6]{2} \)

B

\(\sqrt{2} \)

C

\(\sqrt[4]{2} \)

D

2

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3

2022 · General Aptitude (GA) · General Aptitude · Algebra

Geomatics Engineering (GE) 2022

Which one of the following is a representation (not to scale and in bold) of all values of \(x\) satisfying the inequality \(2 - 5x \leq -\frac{6x - 5}{3}\) on the real number line?

A

B

C

D

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4

2022 · General Aptitude (GA) · General Aptitude · Algebra

Geomatics Engineering (GE) 2022

If \(f(x) = 2 \ln(\sqrt{e^x})\), what is the area bounded by \(f(x)\) for the interval \([0, 2]\) on the \(x\)-axis?

A

\(\frac{1}{2}\)

B

1

C

2

D

4

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5

2022 · General Aptitude (GA) · General Aptitude · Algebra

Geomatics Engineering (GE) 2022

For the past m days, the average daily production at a company was 100 units per day.
If today's production of 180 units changes the average to 110 units per day, what is the value of m?

A

18

B

10

C

7

D

5

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6

2022 · General Aptitude (GA) · General Aptitude · Algebra

Geomatics Engineering (GE) 2022

Consider the following functions for non-zero positive integers, p and q.
\( f(p,q) = \underbrace{p \times p \times p \times ...... \times p}_{q \text{ terms}} = p^q; \quad f(p,1) = p \)
\( g(p,q) = p^{p^{p^{p^{\dots}}}} \) (up to q terms) ; \( g(p,1) = p \)
Which one of the following options is correct based on the above?

A

\(f(2,2) = g(2,2) \)

B

\(f(g(2,2),2) < f(2,g(2,2)) \)

C

\(g(2,1) \neq f(2,1) \)

D

\(f(3,2) > g(3,2) \)

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7

2023 · General Aptitude (GA) · General Aptitude · Algebra

Geomatics Engineering (GE) 2023

The coefficient of \(x^4\) in the polynomial \((x - 1)^3(x - 2)^3\) is equal to _____.

A

33

B

-3

C

30

D

21

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