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SECTION A WEEKS 1 - 4

MODEL QUESTIONS / ANSWERS ETC

Q: Write R code to create a vector v with elements 3, NA, Inf, and -Inf. Then, explain what happens if you add 5 to v.

A:v <- c(3, NA, Inf, -Inf). Adding 5: v + 5 outputs [1] 8 NA Inf -Inf. NA propagates (remains NA), Inf + finite = Inf, -Inf + finite = -Inf (from specialvalues.html: arithmetic with Inf behaves sensibly, but NA is "not available").

Q: Given vector a <- c(10, 15, NA, 20), write code to count NAs and replace them with the

Brain networks in social media use: Reward - VTA, VMPFC, VS; Mentalizing - TPJ, ATP, IFG, PCC, DMPFC; Self-referential - MPFC

🧠 Neuroimaging & Brain Anatomy

• Structural MRI = anatomy
• Functional MRI (fMRI) = activity (BOLD signal)
• fMRI designs: block, event-related, resting-state
• Models:
  • Subtraction/contrast: A vs B
  • Parametric: activity scales with variable
• Group contrast: compare brain activity between groups
• Limitations: indirect signal, reverse inference risk
• Reverse inference: flawed

1. Constructional Details of a Single-Phase Induction Motor (5 Marks)

A single-phase induction motor is a widely used AC motor in domestic and commercial appliances. It works on the principle of electromagnetic induction and has a simple and rugged construction similar to a three-phase squirrel cage induction motor.

Main Parts:

1. Stator:

   • The stator is a stationary part made of laminated steel to reduce eddy current losses.

   • A single-phase winding is placed in slots distributed around the stator

124. Design recommendation system using collaborative filtering (movie streaming) (10 marks — 10 points)

Input: users, movies, ratings → construct utility matrix.

Step 1: compute similarity between users (user-based) or movies (item-based).

Step 2: nearest neighbors identification using cosine/Pearson similarity.

Step 3: predict ratings for unseen movies via weighted average of neighbors’ ratings.

Step 4: recommend top-N movies with highest predicted ratings.

Handle sparsity with matrix factorization

99. Given documents — compute i) Jaccard, ii) Cosine, iii) Hamming (detailed) (10 marks — 10 points)

Documents (after lowercasing and tokenizing words, remove punctuation):

• D1: “the night is dark and the moon is red”

• D2: “the moon in the night is red”

• D3: “i can see moon is red the night is dark”

Step A — construct word sets / vectors (unified vocabulary):
Vocabulary (unique words across D1–D3):
{the, night, is, dark, and, moon, red, in, i, can, see} (11 words)

i) Jaccard

79. Explain MapReduce algorithm for matrix multiplication.

(10 Marks)

1. Input matrices A and B stored in HDFS.

2. Map Phase: Emits key-value pairs for each element multiplication.

3. Mapper emits (i,j), value = A[i][k]×B[k][j].

4. Shuffle Phase: Groups values by (i,j).

5. Reduce Phase: Sums all values for each key (i,j).

6. Final result = Σ A[i][k]×B[k][j].

7. Each Mapper processes partial multiplication.

8. Reducer aggregates partial results.

9. Data locality optimizes performance.

10. Scalable to huge