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

1

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

Computer Science & Information Technology (CS) 2012

Q.9 Consider the function f(x) = sin(x) in the interval x ∈ [π/4, 7π/4]. The number and location(s) of the local minima of this function are

A

One, at π/2

B

One, at 3π/2

C

Two, at π/2 and 3π/2

D

Two, at π/4 and 3π/2

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2

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

Computer Science & Information Technology (CS) 2015 [Session 2]

Consider a function \(f(x) = 1 - |x|\) on \(-1 \leq x \leq 1\). The value of \(x\) at which the function attains a maximum, and the maximum value of the function are:

A

0, -1

B

-1, 0

C

0, 1

D

-1, 2

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3

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

Computer Science & Information Technology (CS) 2015 [Session 2]

Let \(f(x) = x^{-(1/3)}\) and \(A\) denote the area of the region bounded by \(f(x)\) and the X-axis, when \(x\) varies from \(-1\) to \(1\). Which of the following statements is/are TRUE?
I) \(f\) is continuous in \([-1, 1]\)
II) \(f\) is not bounded in \([-1, 1]\)
III) \(A\) is nonzero and finite

A

II only

B

III only

C

II and III only

D

I, II and III

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4

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

Computer Science & Information Technology (CS) 2015 [Session 3]

The value of \(\lim_{x \to \infty} (1 + x^2)e^{-x}\) is

A

0

B

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

C

1

D

\(\infty\)

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5

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

Computer Science & Information Technology (CS) 2015 [Session 3]

If for non-zero \( x \), \( af(x) + bf\left(\frac{1}{x}\right) = \frac{1}{x} - 25 \) where \( a \neq b \) then \( \int\limits_1^2 f(x)dx \) is

A

\(\frac{1}{a^2 - b^2} \left[ a(\ln 2 - 25) + \frac{47b}{2} \right] \)

B

\(\frac{1}{a^2 - b^2} \left[ a(2\ln 2 - 25) - \frac{47b}{2} \right] \)

C

\(\frac{1}{a^2 - b^2} \left[ a(2\ln 2 - 25) + \frac{47b}{2} \right] \)

D

\(\frac{1}{a^2 - b^2} \left[ a(\ln 2 - 25) - \frac{47b}{2} \right] \)

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6

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

Computer Science & Information Technology (CS) 2015 [Session 3]

Let \(f(n) = n\) and \(g(n) = n^{(1+\sin n)}\), where \(n\) is a positive integer. Which of the following statements is/are correct?
I. \(f(n) = O(g(n))\)
II. \(f(n) = \Omega(g(n))\)
(A) Only I
(B) Only II
(C) Both I and II
(D) Neither I nor II

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II

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