Given below are three algorithms for the motif finding problem. Identify which figure belongs to which algorithm. ████████ randomly select k-mers Motifs = (Motif_1, ..., Motif_t) in each string from Dna BestMotifs ← Motifs for j ← 1 to N i ← RANDOM(t) Profile ← profile matrix formed from all strings in Motifs except for Motif_i Motif_i ← Profile-randomly generated k-mer in the i-th sequence if SCORE(Motifs) < SCORE(BestMotifs) BestMotifs ← Motifs return BestMotifs (a) Figure I ████████ BestMotifs ← motif matrix formed by first k-mers in each string from Dna for each k-mer Motif in the first string from Dna Motif_1 ← Motif for i = 2 to t form Profile from motifs Motif_1, ..., Motif_{i-1} Motif_i ← Profile-most probable k-mer in the i-th string in Dna Motifs ← (Motif_1, ..., Motif_t) if SCORE(Motifs) < SCORE(BestMotifs) BestMotifs ← Motifs return BestMotifs (b) Figure II ████████ randomly select k-mers Motifs = (Motif_1, ..., Motif_t) in each string from Dna BestMotifs ← Motifs while forever Profile ← PROFILE(Motifs) Motifs ← MOTIFS(Profile, Dna) if SCORE(Motifs) < SCORE(BestMotifs) BestMotifs ← Motifs else return BestMotifs (c) Figure III

(A) Figure I: Gibbs Sampling; Figure II: Randomized Motif Search; Figure III: Greedy Motif Search

(B) Figure I: Gibbs Sampling; Figure II: Greedy Motif Search; Figure III: Randomized Motif Search

(C) Figure I: Greedy Motif Search; Figure II: Randomized Motif Search; Figure III: Gibbs Sampling

(D) Figure I: Randomized Motif Search; Figure II: Gibbs Sampling; Figure III: Greedy Motif Search

In a Gaussian Mixture Model (GMM) with two components, the parameters are as follows: - Component 1: Mean (\mu_1) = 2, Variance (\sigma_1^2) = 1, Mixture Proportion (\pi_1) = 0.6 - Component 2: Mean (\mu_2) = 5, Variance (\sigma_2^2) = 2, Mixture Proportion (\pi_2) = 0.4 Given a data point x = 3, calculate the responsibilities (posterior probabilities) for each component. Hint: \mathcal{N}(x \mid \mu, \sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)

(A) Option figure from the original question paper

(B) Option figure from the original question paper

(C) Option figure from the original question paper

(D) Option figure from the original question paper

Algorithmic Thinking in Bioinformatics Quiz 2: 3 August 2025 (May 2025 term)

Question 1

+5 marksOne correct option

Given below are three algorithms for the motif finding problem. Identify which figure belongs to which algorithm.

text

1████████
2randomly select k-mers Motifs = (Motif_1, ..., Motif_t) in each string from Dna
3BestMotifs ← Motifs
4for j ← 1 to N
5  i ← RANDOM(t)
6  Profile ← profile matrix formed from all strings in Motifs except for Motif_i
7  Motif_i ← Profile-randomly generated k-mer in the i-th sequence
8  if SCORE(Motifs) < SCORE(BestMotifs)
9    BestMotifs ← Motifs
10return BestMotifs

(a) Figure I

text

1████████
2BestMotifs ← motif matrix formed by first k-mers in each string from Dna
3for each k-mer Motif in the first string from Dna
4  Motif_1 ← Motif
5  for i = 2 to t
6    form Profile from motifs Motif_1, ..., Motif_{i-1}
7    Motif_i ← Profile-most probable k-mer in the i-th string in Dna
8  Motifs ← (Motif_1, ..., Motif_t)
9  if SCORE(Motifs) < SCORE(BestMotifs)
10    BestMotifs ← Motifs
11return BestMotifs

(b) Figure II

text

1████████
2randomly select k-mers Motifs = (Motif_1, ..., Motif_t) in each string from Dna
3BestMotifs ← Motifs
4while forever
5  Profile ← PROFILE(Motifs)
6  Motifs ← MOTIFS(Profile, Dna)
7  if SCORE(Motifs) < SCORE(BestMotifs)
8    BestMotifs ← Motifs
9  else
10    return BestMotifs

A
Figure I: Gibbs Sampling; Figure II: Randomized Motif Search; Figure III: Greedy Motif Search
B
Figure I: Gibbs Sampling; Figure II: Greedy Motif Search; Figure III: Randomized Motif Search
C
Figure I: Greedy Motif Search; Figure II: Randomized Motif Search; Figure III: Gibbs Sampling
D
Figure I: Randomized Motif Search; Figure II: Gibbs Sampling; Figure III: Greedy Motif Search

Also asked in Quiz 2 16 Mar 2025

Question 2

+3 marksOne correct option

A dataset is clustered into two groups using soft K-means. The distance of a data point from the two cluster centroids is $d_1 = 7.0$ and $d_2 = 2.0$ , respectively. Using the soft K-means formula with $\beta = 0.3$ , compute the probabilities of the data point belonging to each cluster. The probability formula is:

$P(C_k \mid x) = \frac{e^{-\beta d_k}}{\sum_{j=1}^{K} e^{-\beta d_j}}$

What are the probabilities $P(C_1)$ and $P(C_2)$ ?

Question 3

+3 marksOne correct option

In a Gaussian Mixture Model (GMM) with two components, the parameters are as follows:

Component 1: Mean $(\mu_1) = 2$ , Variance $(\sigma_1^2) = 1$ , Mixture Proportion $(\pi_1) = 0.6$
Component 2: Mean $(\mu_2) = 5$ , Variance $(\sigma_2^2) = 2$ , Mixture Proportion $(\pi_2) = 0.4$

Given a data point $x = 3$ , calculate the responsibilities (posterior probabilities) for each component. Hint:

$\mathcal{N}(x \mid \mu, \sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)$

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More on the Algorithmic Thinking in Bioinformatics Quiz 2 3 Aug 2025 paper

The IIT Madras BS Algorithmic Thinking in Bioinformatics (Algorithmic Thinking in Bioinformatics) Quiz 2 paper sat on 3 Aug 2025, in the May 2025 term: 18 questions for 53 marks in 120 minutes. The first 3 questions are below. Sign in with Google — it is free — to see the whole paper with its answers and explanations, in learning mode or as a timed mock test.

Feature	Algorithmic Thinking in Bioinformatics Quiz 2 3 Aug 2025 at a glance
Term	May 2025 term
Subject	Algorithmic Thinking in Bioinformatics
Course code	BSBT4001
Questions	18
Marks	53
Duration	120 min
MCQ	11
MSQ	1
Numerical	6
Official paper	IIT M IMPROVEMENT AN EXAM QIA2 03 Aug 2025
Negative marking	No negative marking.
Updated	25 Sept 2026

Algorithmic Thinking in Bioinformatics Quiz 2: 3 August 2025 (May 2025 term)

Question 1

Question 2

Question 3

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