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Maths for GenAI · Quiz 1 · 26 Oct 2025 (Afternoon)

20 questions · 50 marks · 60 min

Answer key Take as mock

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Mathematical Foundations of Generative AI

Quiz 1 · 26 Oct 2025 (Afternoon)

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.

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:

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

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