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

1

2012 · General Aptitude (GA) · General Aptitude · Algebra

Textile Engineering & Fibre Science (TF) 2012

A beaker contains 50 cc of an aqueous dye solution of concentration c (w/v). 25 cc of this solution is removed and replaced by 25 cc of distilled water. This process is repeated five more times. The final concentration of the solution is

A

\(c\)

B

\(c\left(\frac{1}{2}\right)^5\)

C

\(c\left(\frac{1}{2}\right)^6\)

D

\(c\left(\frac{1}{2}\right)^7\)

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2

2012 · General Aptitude (GA) · General Aptitude · Algebra

Textile Engineering & Fibre Science (TF) 2012

The thermal conductivity of a nonwoven fabric is given by \[ \lambda = 0.03 + 0.00005\rho + \frac{0.15}{\rho} \] where \(\lambda\) is the thermal conductivity of the fabric in W/(m·K), \(\rho\) is the bulk density of the fabric in kg/m³, and \(\rho \in [0,200]\). Thermal conductivity is minimum when the bulk density is approximately

A

10

B

20

C

55

D

200

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3

2012 · General Aptitude (GA) · General Aptitude · Algebra

Textile Engineering & Fibre Science (TF) 2012

Let \(f(x) = x - [x]\), where \(x \geq 0\) and \([x]\) is the greatest integer not larger than x. Then \(f(x)\) is a

A

monotonically increasing function

B

monotonically decreasing function

C

linearly increasing function between two integers

D

linearly decreasing function between two integers

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4

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

Textile Engineering & Fibre Science (TF) 2015

Q.36 – Q.65 carry two marks each.

The maximum value of f(x) = √2(sin x + cos x) for x in [0, π] is __________

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5

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

Textile Engineering & Fibre Science (TF) 2015

The maximum value of \( f(x) = \sqrt{2} (\sin x + \cos x) \) for \( x \) in \( [0, \pi] \) is __________

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6

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

Textile Engineering & Fibre Science (TF) 2016

If \( |9y-6|=3 \), then \( y^2 - 4y/3 \) is ______.

A

0

B

+1/3

C

-1/3

D

undefined

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7

2018 · General Aptitude (GA) · General Aptitude · Algebra

Textile Engineering & Fibre Science (TF) 2018

For \(0 \leq x \leq 2\pi\), \(\sin x\) and \(\cos x\) are both decreasing functions in the interval ______.

A

\(\left(0, \frac{\pi}{2}\right)\)

B

\(\left(\frac{\pi}{2}, \pi\right)\)

C

\(\left(\pi, \frac{3\pi}{2}\right)\)

D

\(\left(\frac{3\pi}{2}, 2\pi\right)\)

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8

2018 · General Aptitude (GA) · General Aptitude · Algebra

Textile Engineering & Fibre Science (TF) 2018

If \(x^2 + x - 1 = 0\) what is the value of \(x^4 + \frac{1}{x^4}\)?

A

1

B

5

C

7

D

9

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9

2019 · General Aptitude (GA) · General Aptitude · Algebra

Textile Engineering & Fibre Science (TF) 2019

The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?

A

6

B

7

C

8

D

9.5

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10

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

Textile Engineering & Fibre Science (TF) 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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11

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

Textile Engineering & Fibre Science (TF) 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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12

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

Textile Engineering & Fibre Science (TF) 2025

If \(Pe^x = Qe^{-x}\) for all real values of \(x\), which one of the following statements is true?

A

\(P = Q = 0\)

B

\(P = Q = 1\)

C

\(P = 1; Q = -1\)

D

\(\frac{P}{Q} = 0\)

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