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

1

2012 · General Aptitude (GA) · General Aptitude · Limits

Mechanical Engineering (ME) 2012

Consider the function \(f(x) = |x|\) in the interval \(-1 \leq x \leq 1\). At the point \(x = 0\), \(f(x)\) is

A

continuous and differentiable.

B

non-continuous and differentiable.

C

continuous and non-differentiable.

D

neither continuous nor differentiable.

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2

2012 · General Aptitude (GA) · General Aptitude · Limits

Mechanical Engineering (ME) 2012

\(\lim_{x\to0} \frac{1-\cos x}{x^2}\) is

A

1/4

B

1/2

C

1

D

2

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3

2012 · General Aptitude (GA) · General Aptitude · Limits

Mechanical Engineering (ME) 2012

At x = 0, the function f(x) = x^3 + 1 has

A

a maximum value

B

a minimum value

C

a singularity

D

a point of inflection

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4

2014 · General Aptitude (GA) · General Aptitude · Limits

Mechanical Engineering (ME) 2014 [Session 2]

\(\lim_{x\to 0} \left( \frac{e^{2x}-1}{\sin(4x)} \right)\) is equal to

A

0

B

0.5

C

1

D

2

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5

2015 · General Aptitude (GA) · General Aptitude · Limits

Mechanical Engineering (ME) 2015 [Session 1]

The value of \(\lim_{x \to 0}\frac{1-\cos(x^2)}{2x^4}\) is

A

0

B

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

C

\(\frac{1}{4}\)

D

undefined

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6

2015 · General Aptitude (GA) · General Aptitude · Limits

Mechanical Engineering (ME) 2015 [Session 3]

The value of \(\lim_{x\to 0} \left( \frac{-\sin x}{2\sin x + x\cos x} \right)\) is __________

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