GATE CS 2015 Set 2 Q.22 (CS Q.12): Combinatorics, Counting, Recurrence Relations and Generating Functions

Consider the basic COCOMO model where $E$ is the effort applied in person-months, $D$ is the development time in chronological months, KLOC is the estimated number of delivered lines of code (in thousands) and $a_b, b_b, c_b, d_b$ have their usual meanings. The basic COCOMO equations are of the form

$E = a_b(\text{KLOC})^{b_b},\; D = c_b(E)^{d_b}$

$D = a_b(\text{KLOC})^{b_b},\; E = c_b(D)^{d_b}$

$E = a_b(b_b),\; D = c_b(\text{KLOC})^{d_b}$

$E = a_b(d_b),\; D = c_b(\text{KLOC})^{b_b}$

Official answer and solution

Official answer: A
From: Official GATE 2015 answer key

Solution

Recall the standard empirical equations of Boehm's Basic COCOMO model.

In Barry Boehm's Basic COCOMO (Constructive Cost Model):

Effort ( $E$ ) in person-months is given by a power law in the estimated size (KLOC):

E = a_b (\text{KLOC})^{b_b}

where $a_b$ and $b_b$ are coefficients determined by the software project mode (organic, semidetached, embedded).

Development Time ( $D$ ) in chronological months is given by a power law in the effort $E$ :

D = c_b (E)^{d_b}

where $c_b$ and $d_b$ are mode-specific coefficients.

Thus, the basic COCOMO equations match option A.

Final answer

Common trap

Confusing the independent variable of development time $D$ , which depends on effort $E$ , not directly on KLOC.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2015 Computer Science and Information Technology (CS) Session 2
Question: 22 of 65, printed as CS Q.12
Section: Computer Science and Information Technology

This question is from a part of the syllabus that is no longer in GATE CS. It is kept because it was in the paper.

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