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

1

2015 · General Aptitude (GA) · General Aptitude · Algebra

Production & Industrial Engineering (PI) 2015

The function \( f(x) = x^2 = x + x + x + \dots x \) times, is defined

A

at all real values of \(x \)

B

only at positive integer values of \(x \)

C

only at negative integer values of \(x \)

D

only at rational values of \(x \)

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2

2015 · General Aptitude (GA) · General Aptitude · Algebra

Production & Industrial Engineering (PI) 2015

The value of (X₁, X₂) for an optimal solution for
Minimize Z = 6X₁ – 8X₂
subject to: 5X₁ + 10X₂ ≤ 30
4X₁ + 4X₂ ≤ 20
X₁ ≥ 0, X₂ ≥ 0
is

A

(0, 0)

B

(1, 6)

C

(0, 3)

D

(3, 7)

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3

2016 · General Aptitude (GA) · General Aptitude · Algebra

Production & Industrial Engineering (PI) 2016

The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number.

A

39

B

57

C

66

D

93

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4

2021 · General Aptitude (GA) · General Aptitude · Algebra

Production & Industrial Engineering (PI) 2021

\(p\) and \(q\) are positive integers and \(\frac{p}{q} + \frac{q}{p} = 3\), then, \(\frac{p^2}{q^2} + \frac{q^2}{p^2} =\)

A

3

B

7

C

9

D

11

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5

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

Production & Industrial Engineering (PI) 2022

Consider the following inequalities.
(i)    \(3p - q < 4\)
(ii)    \(3q - p < 12\)
Which one of the following expressions below satisfies the above two inequalities?

A

\(p + q < 8\)

B

\(p + q = 8\)

C

\(8 \leq p + q < 16\)

D

\(p + q \geq 16\)

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6

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

Production & Industrial Engineering (PI) 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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7

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

Production & Industrial Engineering (PI) 2024

The sum of the following infinite series is
\[ 2 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{8} + \frac{1}{9} + \frac{1}{16} + \frac{1}{27} + \cdots \]

A

11/3

B

7/2

C

13/4

D

9/2

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8

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

Production & Industrial Engineering (PI) 2025

Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppose this function is identical for two brothers, and it monotonically increases till the age of 50 years and then it monotonically decreases. Let \(a_1\) and \(a_2\) (in years) denote the ages of the brothers and \(a_1 < a_2\).
Which one of the following statements is correct about their age on the day when they attain the same weight?

A

\(a_1 < a_2 < 50\)

B

\(a_1 < 50 < a_2\)

C

\(50 < a_1 < a_2\)

D

Either \(a_1 = 50\) or \(a_2 = 50\)

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9

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

Production & Industrial Engineering (PI) 2025

If a real variable \(x\) satisfies \(3^{x^2} = 27 \times 9^x\), then the value of \(\frac{2^{x^2}}{(2^x)^2}\) is:

A

\(2^{-1}\)

B

\(2^0\)

C

\(2^3\)

D

\(2^{15}\)

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10

2026 · General Aptitude (GA) · General Aptitude · Algebra

Production and Industrial Engineering (PI) 2026

At how many points will the curves \(y = x^2\) and \(y = -x^2 - 2x - 1\) intersect in the real \((x, y)\) plane?

A

0

B

1

C

2

D

3

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11

2026 · General Aptitude (GA) · General Aptitude · Algebra

Production and Industrial Engineering (PI) 2026

P and Q are two positive integers such that \( P^2 = Q^2 + 13 \).
The product of the numbers P and Q is__________

A

13

B

26

C

39

D

42

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