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Maths for GenAI · All 2025 papers

81 questions · 300 marks · 4 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Mathematical Foundations of Generative AI

All 2025 papers

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.

Quiz 1 · 26 Oct 2025 (AN)Quiz 1

Q1MCQ2 Marks·Choose one option
Key ↓
Suppose you replace the log-loss in the original GAN with a general f-divergence minimization framework. Which of the following cannot be directly represented as an f-divergence?
1. AKL divergence
2. BReverse KL divergence
3. CTotal Variation distance
4. DWasserstein distance
Q2MCQ2 Marks·Choose one option
Key ↓
1. A−log 2
2. B0
3. C−log(0.3)
4. Dlog 2
Q3MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q4MCQ2 Marks·Choose one option
Key ↓
1. A−0.8008
2. B−0.6432
3. C−1.1412
4. D−0.4794
Q5MCQ2 Marks·Choose one option
Asked 3 times Key ↓
1. A80,402
2. B99,402
3. C242,503
4. D159,3
Q6MCQ2 Marks·Choose one option
Key ↓
1. A0.22
2. B0.28
3. C0.34
4. D0.41
Q7MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q8MCQ2 Marks·Choose one option
Key ↓
1. AThe first term measures bias shift; the second term measures covariance mismatch.
2. BBoth terms measure covariance only.
3. CBoth terms are dominated by the generator’s variance.
4. DThe first term measures variance difference; the second measures mean shift.
Q9MCQ2 Marks·Choose one option
Key ↓
FID compares real and generated image distributions by assuming they follow multivariate Gaussian distributions in a feature space extracted from a pretrained neural network. Which layer’s activations are typically used to compute this feature space in practice?
1. AThe output logits of the generator
2. BRaw RGB pixel values
3. CThe first convolution layer of the discriminator
4. DThe penultimate layer of an Inception-v3 network
Q10MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q11MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q12MCQ3 Marks·Choose one option
Key ↓
1. A0.20
2. B0.35
3. C0.55
4. D0.75
Q13MCQ3 Marks·Choose one option
Key ↓
1. A0.57
2. B0.24
3. C0.32
4. D0.137
Q14MCQ3 Marks·Choose one option
Key ↓
1. A[−2.1, 0.4]
2. B[−2.2, −4.3]
3. C[0.2, 0.1]
4. D[0, 0]
Q15MSQ3 Marks·Choose all correct options
Key ↓
Which of the following are valid reasons why GAN training based on JSD minimization is unstable?
1. AJSD saturates when the supports of p_(data) and p_g do not overlap.
2. BGradients for the generator can vanish when the discriminator becomes too strong.
3. CJSD is not continuous w.r.t. the parameters of the generator distribution.
4. DJSD always provides unbiased gradients in high dimensions.
Q16MSQ4 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q17NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q18NAT3 Marks·Write the number
Key ↓
Your answer:
Q19NAT3 Marks·Write the number
Key ↓
Your answer:
Q20NAT3 Marks·Write the number
Key ↓
Your answer:

End Term · 31 Aug 2025 (FN)End Term

Q21MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q22MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q23MCQ4 Marks·Choose one option
Asked 2 times 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
Q24MCQ4 Marks·Choose one option
Key ↓
1. AIncrease capacity and reduce bias
2. BReduce capacity, causing underfitting and gradient pathology
3. CEnforce exact 1-Lipschitzness without bias
4. DMake T convex
Q25MCQ4 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q26MCQ4 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q27MCQ4 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q28MCQ5 Marks·Choose one option
Key ↓
In the Sampling pipeline in VAE, Unconditional generation uses
1. A
2. B
3. C
4. D
Q29MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q30MCQ5 Marks·Choose one option
Asked 2 times Key ↓
1. A1.797
2. B1.910
3. C2.000
4. D1.620
Q31MCQ5 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q32MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q33MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q34MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q35MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q36MCQ5 Marks·Choose one option
Asked 2 times Key ↓
1. A0.6
2. B0.5
3. C0.67
4. D0.75
Q37MCQ5 Marks·Choose one option
Key ↓
1. A≈ 1.670
2. B1.500
3. C2.000
4. D≈ 1.333
Q38MCQ5 Marks·Choose one option
Asked 2 times Key ↓
1. A768 × 768 = 589,824
2. B768 × 64 = 49,152
3. C64 × 64 = 4,096
4. D12 × 64 = 768
Q39MCQ5 Marks·Choose one option
Key ↓
1. A(3,−1)
2. B(2, 0)
3. C(1,−1)
4. D(0, 0)
Q40MCQ5 Marks·Choose one option
Key ↓
1. A2.62
2. B2.00
3. C2.81
4. D1.90
Q41MCQ5 Marks·Choose one option
Key ↓
An AR-LM can be viewed as an MDP by
1. AState = token prefix, action = next token
2. BState = next token, action = prefix
3. CState = vocabulary, action = logits
4. DImpossible
Q42MCQ5 Marks·Choose one option
Asked 2 times Key ↓
1. A0.600
2. B0.750
3. C0.500
4. D0.300

End Term · 31 Aug 2025 (AN)End Term

Q43MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q44MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. AZero a.e.
2. BNonzero and large
3. CUndefined
4. DEqual to the score of p_g
Q45MCQ4 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q46MCQ4 Marks·Choose one option
Asked 2 times Key ↓
1. A31
2. B32
3. C33
4. D34
Q47MCQ4 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q48MCQ4 Marks·Choose one option
Asked 2 times 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)
Q49MCQ4 Marks·Choose one option
Asked 3 times 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
Q50MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q51MCQ5 Marks·Choose one option
Key ↓
1. A1
2. B2
3. C3
4. D4
Q52MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q53MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q54MCQ5 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q55MCQ5 Marks·Choose one option
Key ↓
1. A0.28
2. B0.32
3. C0.20
4. D0.18
Q56MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q57MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q58MCQ5 Marks·Choose one option
Asked 2 times Key ↓
1. ASize = 4, prob ≈ 0.105
2. BSize = 3, prob = 0
3. CSize = 5, prob = 0.1
4. DSize = 4, prob = 0.1
Q59MCQ5 Marks·Choose one option
Asked 2 times Key ↓
1. A1,048,576 params
2. B786,432 params
3. C524,288 params
4. D262,144 params
Q60MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q61MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q62MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q63MCQ5 Marks·Choose one option
Asked 2 times Key ↓
1. A−0.85
2. B−0.80
3. C−0.20
4. D−1.00
Q64MCQ5 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Q65NAT2 Marks·Write the number
Key ↓
Your answer:
Q66NAT2 Marks·Write the number
Key ↓
Your answer:
Q67NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q68NAT3 Marks·Write the number
Key ↓
Your answer:
Q69NAT3 Marks·Write the number
Key ↓
Your answer:
Q70NAT3 Marks·Write the number
Key ↓
Your answer:
Q71NAT3 Marks·Write the number
Key ↓
Your answer:
Q72NAT3 Marks·Write the number
Key ↓
Your answer:
Q73NAT3 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q74NAT4 Marks·Write the number
Key ↓
Your answer:
Q75NAT4 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q76MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q77MCQ3 Marks·Choose one option
Key ↓
1. AAt t = 0, we assume perfect reconstruction
2. BAt t = 0, adding noise will corrupt the final output
3. CAt t = 0, the posterior is deterministic
4. DAll of these
Q78MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q79MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q80MCQ3 Marks·Choose one option
Key ↓
In a U-Net for DDPMs, the time embedding is usually added to the feature maps after a convolutional layer. If a feature map has shape ‘[B, C, H, W]’ and the time embedding has shape ‘[B, C]’, how is the embedding typically broadcasted and combined?
1. AIt is reshaped to ‘[B, C, 1, 1]’ and then added.
2. BIt is tiled to ‘[B, C, H, W]’ and then multiplied.
3. CIt is passed through a separate linear layer for each spatial location.
4. DIt is concatenated along the channel dimension.
Q81MCQ3 Marks·Choose one option
Key ↓
1. A[1]
2. B[1, 1]
3. C[1, 64]
4. D[64, 64]

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1D

Q2B

Q3D

Q4A

Q5C

Q6C

Q7C

Q8A

Q9D

Q10B

Q11B

Q12B

Q13D

Q14C

Q15A, B, C

Q16A, B, D

Q170

Q180.72 to 0.76

Q191.1 to 1.16

Q200.3

Q21B

Q22B

Q23C

Q24B

Q25B

Q26A

Q27A

Q28B

Q29A

Q30A

Q31A

Q32A

Q33A

Q34A

Q35A

Q36A

Q37A

Q38A

Q39A

Q40A

Q41A

Q42A

Q43A

Q44A

Q45B

Q46B

Q47A

Q48A

Q49B

Q50A

Q51C

Q52A

Q53A

Q54A

Q55A

Q56A

Q57A

Q58A

Q59A

Q60A

Q61A

Q62A

Q63A

Q64A

Q650.5 to 0.6

Q6612.8 to 14.8

Q67-0.93 to -0.73

Q68-3.4 to -3.2

Q6928.2 to 30.2

Q702048

Q710.05 to 0.09

Q720.02 to 0.06

Q738020

Q740.6 to 0.7

Q750.5 to 0.7

Q76C

Q77D

Q78B

Q79C

Q80A

Q81A

Questions and answer keys are reproduced from the official IIT Madras BS papers. BTechi is not affiliated with IIT Madras.