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Maths for GenAI · Most repeated questions

21 questions · 85 marks · 4 papers · 10 question types

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Mathematical Foundations of Generative AI

Most repeated questions

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
MSQ: One or more options correct. Select all to score.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

Type 1 · asked 3 times · VAEs & reparameterisation

Count trainable parameters of fully connected generator/encoder layers

Q1NAT3 Marks·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
Your answer:
Q2MCQ4 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
Given d_z=20, if the first decoder layer is a fully connected layer that outputs 3 x 64 x 64 units and includes a bias term, how many trainable parameters does this layer have?
1. A245,760
2. B258,048
3. C122,880
4. D262,144
Q3MCQ2 Marks·Choose one option
Quiz 1 · 26 Oct 2025 (AN)Key ↓
1. A80,402
2. B99,402
3. C242,503
4. D159,3

Type 2 · asked 2 times · VAEs & reparameterisation

Compute the latent z with the reparameterisation trick

Q4NAT2 Marks·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
Your answer:
Q5MCQ4 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
1. A(1.205,−3.210)
2. B(1.205,−1.895)
3. C(0.500,−3.210)
4. D(0.705,−2.000)

Type 3 · asked 2 times · DDPM: forward & reverse process

Compute the noised sample x_t in the DDPM forward process

Q6NAT4 Marks·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
Your answer:
Q7MCQ5 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
1. A1.797
2. B1.910
3. C2.000
4. D1.620

Type 4 · asked 2 times · GAN objective & training

Find the GAN generator gradient when supports are disjoint

Q8MCQ3 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
1. AZero a.e.
2. BNonzero and large
3. CUndefined
4. DEqual to the score of p_g
Q9NAT2 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Your answer:

Type 5 · asked 2 times · GAN objective & training

Compute the output spatial size of (transposed) conv layers

Q10MCQ4 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
1. A31
2. B32
3. C33
4. D34
Q11MCQ4 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
Starting from 4×4 spatial size, apply four ConvTranspose2d blocks each with kernel 4, stride 2, padding 1. Final spatial size is:
1. A16 × 16
2. B32 × 32
3. C64 × 64
4. D128 × 128

Type 6 · asked 2 times · DDPM: forward & reverse process

Pick the PyTorch code for the DDPM mean from predicted noise

Q12MCQ5 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Q13MCQ5 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 7 · asked 2 times · Transformers, attention & decoding

Renormalise token probabilities after top-p/top-k filtering

Q14MCQ5 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
1. ASize = 4, prob ≈ 0.105
2. BSize = 3, prob = 0
3. CSize = 5, prob = 0.1
4. DSize = 4, prob = 0.1
Q15MCQ5 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
1. A0.6
2. B0.5
3. C0.67
4. D0.75

Type 8 · asked 2 times · Transformers, attention & decoding

Count projection matrix parameters in self-attention

Q16MCQ5 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
1. A1,048,576 params
2. B786,432 params
3. C524,288 params
4. D262,144 params
Q17MCQ5 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
1. A768 × 768 = 589,824
2. B768 × 64 = 49,152
3. C64 × 64 = 4,096
4. D12 × 64 = 768

Type 9 · asked 2 times · RL for LMs: policy gradient & PPO

Evaluate the PPO clipped surrogate objective

Q18MCQ5 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
1. A−0.85
2. B−0.80
3. C−0.20
4. D−1.00
Q19MCQ5 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
1. A0.600
2. B0.750
3. C0.500
4. D0.300

Type 10 · asked 2 times · BiGAN, domain adaptation & FID

Identify what the BiGAN discriminator distinguishes/optimises

Q20MCQ4 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
1. A
2. B
3. C
4. D
Q21MSQ4 Marks·Choose all correct options
Quiz 1 · 26 Oct 2025 (AN)Key ↓
1. A
2. B
3. C
4. D

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q18020

Q2B

Q3C

Q4-0.93 to -0.73

Q5A

Q60.5 to 0.7

Q7A

Q8A

Q90

Q10B

Q11C

Q12A

Q13A

Q14A

Q15A

Q16A

Q17A

Q18A

Q19A

Q20B

Q21A, B, D

Questions and answer keys are reproduced from the official IIT Madras BS papers. Topics and repeated question types are BTechi’s own grouping. BTechi is not affiliated with IIT Madras.