LLM — da5004_2026T2_Q1_NA

Source: da5004_2026T2_Q1_NA.pdf · Academic questions: 16 · Separately counted children: 0
Provenance: Large_Language_Models/da5004_2026T2_Q1_NA.pdf · SHA-256 7ca18a647a21b6dba359c95e4275ab1a3ff1ea251ef5388e72916cbc5e104049

Scope: Section 1: LLM (Degree Level : Large Language Models), physical pages 1 to 10. The in-scope subject starts on physical page 1 with Section Id 640653141358 and terminates on physical page 10 after Question 17.

Questions

Question 2

Question ID: 6406532166233

Type: MSQ · Marks: 4
PDF pages: 2

Which statements are true about traditional attention used in sequence-to-sequence models?

Options

The decoder decides which encoder states are important.

Source option ID: 6406537043567

Attention weights are computed over all decoder hidden states.

Source option ID: 6406537043568

The context vector is a weighted sum of encoder states.

Source option ID: 6406537043569

Encoder hidden states are ignored after encoding.

Source option ID: 6406537043570

Correct answer: A, C

Source evidence: [{"page": 2, "bbox": [23.62, 374.08, 119.02, 390.4], "type": "green source option", "detail": "Option 6406537043567 is marked in green with color 32768"}, {"page": 2, "bbox": [23.62, 415.72, 119.02, 432.04], "type": "green source option", "detail": "Option 6406537043569 is marked in green with color 32768"}]

Shared context 3 to 4

Question ID: 6406532166234

Type: COMPREHENSION
PDF pages: 2, 3

Consider the text "learn easy math", consisting of three tokens: {learn,easy,math}.

The token embeddings are arranged in the input matrix \(X\):

\[X = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \end{bmatrix}\]

The query, key, and value projection matrices are given by:

\[W_Q = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\]

\[W_K = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\]

\[W_V = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\]

\[\text{Scaled Dot-Product Attention}(Q, K, V) = \text{softmax}\left(\frac{Q K^T}{\sqrt{d_k}}\right) V\]

Input matrix X and query projection matrix W_Q for text learn easy math

Figure 1. Input matrix X and query projection matrix W_Q for text learn easy math

Key projection matrix W_K, value projection matrix W_V, and Scaled Dot-Product Attention formulation

Figure 2. Key projection matrix W_K, value projection matrix W_V, and Scaled Dot-Product Attention formulation

Based on the above data, answer the given subquestions.

Question 3

Question ID: 6406532166235

Type: SA · Marks: 3
PDF pages: 3

Shared context: ctx-3-4

Compute the \((Q K^T)\) of the final scaled dot-product attention and submit the sum of the diagonal elements of \((Q K^T)\) matrix.

Question 3 prompt: Compute the (Q K^T) of the final scaled dot-product attention and sum of diagonal elements

Figure 3. Question 3 prompt: Compute the (Q K^T) of the final scaled dot-product attention and sum of diagonal elements

Correct answer: 4

Source evidence: [{"page": 3, "bbox": [22.87, 506.0, 119.02, 530.0], "type": "explicit field", "detail": "Official Possible Answers: 4"}]

Question 4

Question ID: 6406532166236

Type: MCQ · Marks: 3
PDF pages: 3

Shared context: ctx-3-4

Choose the token pair with the least attention score.

Options

{"learn", "easy"}

Source option ID: 6406537043572

{"learn", "math"}

Source option ID: 6406537043573

{"easy", "math"}

Source option ID: 6406537043574

{"learn", "learn"}

Source option ID: 6406537043575

{"easy" , "easy"}

Source option ID: 6406537043576

Correct answer: A

Source evidence: [{"page": 3, "bbox": [23.62, 643.24, 119.02, 659.56], "type": "green source option", "detail": "Option 6406537043572 is marked in green with color 32768"}]

Question 5

Question ID: 6406532166237

Type: SA · Marks: 4
PDF pages: 4

A Transformer model processes a sequence containing 6 tokens using Multi-Head Attention. The model initially uses 4 attention heads. If the number of attention heads is doubled to 8, while the sequence length remains unchanged, how many additional attention scores are computed across all heads?

Correct answer: 144

Source evidence: [{"page": 4, "bbox": [22.87, 240.0, 119.02, 260.0], "type": "explicit field", "detail": "Official Possible Answers: 144"}]

Question 6

Question ID: 6406532166238

Type: SA · Marks: 4
PDF pages: 4

A batch of 8 sentences is passed through a Transformer Encoder consisting of 6 encoder layers and 8 attention heads. After padding, each sentence has a maximum length of 32 tokens. The model uses an embedding dimension of \(d_{model} = 128\). What is the total number of elements (volume) in the output tensor produced by the final encoder layer for the entire batch?

Question 6 prompt: Transformer encoder output tensor volume calculation with embedding dimension d_model = 128

Figure 4. Question 6 prompt: Transformer encoder output tensor volume calculation with embedding dimension d_model = 128

Correct answer: 32768

Source evidence: [{"page": 4, "bbox": [22.87, 560.0, 119.02, 580.0], "type": "explicit field", "detail": "Official Possible Answers: 32768"}]

Question 7

Question ID: 6406532166239

Type: SA · Marks: 4
PDF pages: 4, 5

Consider a masked multi-head attention layer in a transformer decoder. The source vocabulary is of size \(V_s = 1000\), \(d_{model} = 64\) and context length \(T = 128\). To enforce autoregressive generation, a causal mask is applied to the raw attention score before applying softmax. How many entries in the causal mask are set to \(-\infty\) ?

Question 7 prompt: Causal mask entries set to -infinity with vocabulary size V_s = 1000, d_model = 64, and context length T = 128

Figure 5. Question 7 prompt: Causal mask entries set to -infinity with vocabulary size V_s = 1000, d_model = 64, and context length T = 128

Correct answer: 8128

Source evidence: [{"page": 5, "bbox": [22.87, 95.0, 119.02, 115.0], "type": "explicit field", "detail": "Official Possible Answers: 8128"}]

Question 8

Question ID: 6406532166240

Type: SA · Marks: 4
PDF pages: 5

Consider a Transformer model with a hidden state dimension \(d_{model} = 512\). The positional encoding for a given position, \(pos\) and dimension \(i\) is defined by:

\[\text{PE}_{(pos, 2i)} = \sin\left(\frac{pos}{10000^{2i/d_{model}}}\right)\]

\[\text{PE}_{(pos, 2i+1)} = \cos\left(\frac{pos}{10000^{2i/d_{model}}}\right)\]

Compute the squared euclidean norm for the vector corresponding to \(pos = 3\) and enter the value.

Question 8 prompt: Sinusoidal positional encoding formulation for hidden state dimension d_model = 512 and squared Euclidean norm computation

Figure 6. Question 8 prompt: Sinusoidal positional encoding formulation for hidden state dimension d_model = 512 and squared Euclidean norm computation

Correct answer: 256

Source evidence: [{"page": 5, "bbox": [22.87, 530.0, 119.02, 550.0], "type": "explicit field", "detail": "Official Possible Answers: 256"}]

Question 9

Question ID: 6406532166241

Type: MCQ · Marks: 4
PDF pages: 5, 6

Consider the following statements regarding the use of Teacher Forcing while training
autoregressive sequence-to-sequence models and select the appropriate option:

Statement 1: Teacher Forcing involves passing the input token to a larger Teacher model whose
output is then input as the next token

Statement 2: Teacher Forcing helps to prevent compounding of early incorrect predictions that
can destabilize training

Options

Statement 1 is True but Statement 2 is False

Source option ID: 6406537043581

Statement 1 is False but Statement 2 is True

Source option ID: 6406537043582

Both the statements are True

Source option ID: 6406537043583

Both the statements are False

Source option ID: 6406537043584

Correct answer: B

Source evidence: [{"page": 6, "bbox": [23.62, 93.28, 119.02, 109.6], "type": "green source option", "detail": "Option 6406537043582 is marked in green with color 32768"}]

Shared context 10 to 12

Question ID: 6406532166242

Type: COMPREHENSION
PDF pages: 6

Consider the following language model that generates a sentence of three word tokens after the special token. The language model is trained on a larger vocabulary. The probability tree below shows only the probabilities of the relevant tokens required for this question.

Probability tree of three-token sentences following START token for bigram/trigram language model

Figure 7. Probability tree of three-token sentences following START token for bigram/trigram language model

Based on the above data, answer the given subquestions.

Question 10

Question ID: 6406532166243

Type: SA · Marks: 3
PDF pages: 6, 7

Shared context: ctx-10-12

Compute the joint probability of the sentence : "You eat apples"

(Provide answer correct upto 2 digits after the decimal)

Question 10 prompt: Joint probability computation for the sentence You eat apples

Figure 8. Question 10 prompt: Joint probability computation for the sentence You eat apples

Correct answer: 0.17 to 0.19

Source evidence: [{"page": 7, "bbox": [22.87, 130.0, 119.02, 150.0], "type": "explicit field", "detail": "Official Possible Answers: 0.17 to 0.19"}]

Question 11

Question ID: 6406532166244

Type: MCQ · Marks: 3
PDF pages: 7

Shared context: ctx-10-12

Choose the option corresponding to the sentence with the highest joint probability under the given language model.

Options

"i eat apples"

Source option ID: 6406537043586

"apples like You"

Source option ID: 6406537043587

"i eat bananas"

Source option ID: 6406537043588

"you like bananas

Source option ID: 6406537043589

"you like apples

Source option ID: 6406537043590

Correct answer: C

Source evidence: [{"page": 7, "bbox": [23.62, 364.3, 119.02, 380.62], "type": "green source option", "detail": "Option 6406537043588 is marked in green with color 32768"}]

Question 12

Question ID: 6406532166245

Type: SA · Marks: 2
PDF pages: 7

Shared context: ctx-10-12

Using the given probability tree calculate the conditional probability of predicting "apples" given "like" [i.e P(apples | like)]. (Submit -1 if the provided information is insufficient)

Correct answer: -1

Source evidence: [{"page": 7, "bbox": [22.87, 595.0, 119.02, 615.0], "type": "explicit field", "detail": "Official Possible Answers: -1"}]

Question 13

Question ID: 6406532166246

Type: MSQ · Marks: 3
PDF pages: 7, 8

Which of the following are components found within a GPT decoder layer?

Options

Causal (Masked) Multi-Head Self-Attention

Source option ID: 6406537043592

Position-wise Feed-Forward Network

Source option ID: 6406537043593

Multi Head (Cross) Attention

Source option ID: 6406537043594

Recurrent Neural Network (RNN) Layer

Source option ID: 6406537043595

Add & Norm Layer

Source option ID: 6406537043596

Correct answer: A, B, E

Source evidence: [{"page": 8, "bbox": [23.62, 75.46, 119.02, 91.78], "type": "green source option", "detail": "Option 6406537043592 is marked in green with color 32768"}, {"page": 8, "bbox": [23.62, 96.28, 119.02, 112.6], "type": "green source option", "detail": "Option 6406537043593 is marked in green with color 32768"}, {"page": 8, "bbox": [23.62, 158.74, 119.02, 175.06], "type": "green source option", "detail": "Option 6406537043596 is marked in green with color 32768"}]

Shared context 14 to 17

Question ID: 6406532166247

Type: COMPREHENSION
PDF pages: 8

The table below represents the conditional probability distribution over the vocabulary. Each column corresponds to a decoding timestep and the values represent the conditional probability of selecting a token at the timestep given the previously generated tokens

Token	\(t = 1\)	\(t = 2\)	\(t = 3\)	\(t = 4\)	\(t = 5\)	\(t = 6\)
abandoned	0.12	0.05	0.05	0.30	0.10	0.40
but	0.05	0.05	0.10	0.07	0.45	0.20
castle	0.05	0.40	0.10	0.02	0.05	0.05
historic	0.38	0.30	0.10	0.20	0.15	0.15
majestic	0.05	0.05	0.10	0.35	0.10	0.10
the	0.30	0.05	0.05	0.03	0.05	0.05
was	0.05	0.10	0.50	0.03	0.10	0.05

Table representing conditional probability distribution over 7 vocabulary tokens across timesteps t=1 to t=6

Figure 9. Table representing conditional probability distribution over 7 vocabulary tokens across timesteps t=1 to t=6

For all calculations, consider only the tokens mentioned in the first column as the Vocabulary

Based on the above data, answer the given subquestions.

Question 14

Question ID: 6406532166248

Type: SA · Marks: 2
PDF pages: 8, 9

Shared context: ctx-14-17

Use greedy decoding to determine the most likely sequence of 6 tokens and compute the probability of generating that sequence. Enter the value rounded off to 3 decimal places

Correct answer: 0.004 to 0.0055

Source evidence: [{"page": 9, "bbox": [22.87, 160.0, 119.02, 180.0], "type": "explicit field", "detail": "Official Possible Answers: 0.004 to 0.0055"}]

Question 15

Question ID: 6406532166249

Type: SA · Marks: 2
PDF pages: 9

Shared context: ctx-14-17

Use exhaustive search strategy to identify the most probable sequence consisting of 4 tokens. How many decoder runs are required in total to identify the most probable sequence containing 4 tokens?

Correct answer: 400

Source evidence: [{"page": 9, "bbox": [22.87, 420.0, 119.02, 440.0], "type": "explicit field", "detail": "Official Possible Answers: 400"}]

Question 16

Question ID: 6406532166250

Type: SA · Marks: 3
PDF pages: 9

Shared context: ctx-14-17

Use Top-k sampling at timestep t = 4 and k = 3. Compute the renormalized probability of the most probable token from the candidate tokens and enter the value rounded off to three decimal places

Correct answer: 0.410 to 0.414

Source evidence: [{"page": 9, "bbox": [22.87, 680.0, 119.02, 700.0], "type": "explicit field", "detail": "Official Possible Answers: 0.410 to 0.414"}]

Question 17

Question ID: 6406532166251

Type: SA · Marks: 2
PDF pages: 9, 10

Shared context: ctx-14-17

Consider the sequence "the castle was abandoned". What is the minimum beam width required to guarantee that this sequence is retained during beam search at timestep t = 4 ?

Correct answer: 5

Source evidence: [{"page": 10, "bbox": [22.87, 160.0, 119.02, 180.0], "type": "explicit field", "detail": "Official Possible Answers: 5"}]

Answer key

Source question	Source identity	Correct answer	PDF pages
2	6406532166233	A, C	2
3	6406532166235	4	3
4	6406532166236	A	3
5	6406532166237	144	4
6	6406532166238	32768	4
7	6406532166239	8128	4, 5
8	6406532166240	256	5
9	6406532166241	B	5, 6
10	6406532166243	0.17 to 0.19	6, 7
11	6406532166244	C	7
12	6406532166245	-1	7
13	6406532166246	A, B, E	7, 8
14	6406532166248	0.004 to 0.0055	8, 9
15	6406532166249	400	9
16	6406532166250	0.410 to 0.414	9
17	6406532166251	5	9, 10

Extraction notes

Status: verified
Count reconciliation: Section 1 (LLM) declares 11 questions and 50 marks. The 11 portal containers comprise 1 administrative subject-confirmation entry (Question 1, 0 marks, excluded), 7 standalone academic questions (Question 2: 4 marks, Question 5: 4 marks, Question 6: 4 marks, Question 7: 4 marks, Question 8: 4 marks, Question 9: 4 marks, Question 13: 3 marks; total standalone = 27 marks), and 3 comprehension portal containers (Comprehension 6406532166234 covering Q3: 3 marks, Q4: 3 marks; Comprehension 6406532166242 covering Q10: 3 marks, Q11: 3 marks, Q12: 2 marks; Comprehension 6406532166247 covering Q14: 2 marks, Q15: 2 marks, Q16: 3 marks, Q17: 2 marks; total comprehension = 6 + 8 + 9 = 23 marks). The total academic questions reconcile to exactly 16 (7 standalone + 9 comprehension subquestions). The marks sum to 27 + 23 = 50 marks, exactly reconciling the declared Section Marks of 50. The 11 declared questions correspond exactly to the 11 portal containers (1 confirmation + 7 standalone + 3 comprehension blocks).

Exam section 1 LLM runs from physical page 1 to page 10.
Comprehension passages ctx-3-4, ctx-10-12, and ctx-14-17 provide shared context for subquestions (3 to 4), (10 to 12), and (14 to 17) respectively.
All formulas, projection matrices, probability tree diagrams, and vocabulary decoding tables were verified against source rasters with high-resolution crops at 288 DPI.

Excluded source entries:

{"classification": "subject-confirmation", "page": 1, "bbox": [22.87, 750.0, 580.0, 841.9], "reason": "Administrative subject confirmation asking candidate to confirm subject and cross check hall ticket", "identity": "1"}