Q1. Lagrange Multipliers
What condition holds at the optimum?
A. ∇f(x) = 0
B. ∇f(x) = Σ λᵢ∇gᵢ(x)
C. g(x) = 1
D. λᵢ = 0
✅ Answer: B
👉 Gradients align at optimum
Q2. KKT Conditions
Which is TRUE?
A. αᵢ < 0
B. αᵢgᵢ(x*) = 1
C. αᵢ ≥ 0
D. Constraints are ignored
✅ Answer: C
Q3. Hyperplane Definition
A hyperplane satisfies:
A. w·x + b = 0
B. x² + y² = 1
C. ∇x = 0
D. y = mx²
✅ Answer: A
Q4. Role of w in SVM
The vector w determines:
A. Bias
B. Orientation of hyperplane
C. Number of classes
D. Dataset size
✅ Answer: B
Q5. Role of b
The bias term controls:
A. Orientation
B. Distance metric
C. Position of hyperplane
D. Kernel
✅ Answer: C
Q6. Support Vectors
Support vectors are:
A. All training points
B. Points far from boundary
C. Points on margin
D. Random points
✅ Answer: C
Q7. Margin Maximisation
SVM maximises:
A. ||w||
B. 1 / ||w||
C. Number of features
D. Training error
✅ Answer: B
Q8. Constraint for Correct Classification
Which is correct?
A. yᵢ(w·xᵢ + b) ≥ 1
B. w·x = 0
C. yᵢ = 0
D. xᵢ ≥ 1
✅ Answer: A
Q9. Dual Problem Uses
The dual formulation depends on:
A. Distances
B. Inner products
C. Gradients
D. Labels only
✅ Answer: B
Q10. Kernel Trick
What does a kernel do?
A. Reduces data size
B. Computes inner product in feature space
C. Removes noise
D. Normalises data
✅ Answer: B
Q11. Kernel Function
k(x, y) represents:
A. Distance
B. Similarity
C. Label
D. Error
✅ Answer: B
Q12. Soft Margin Parameter C
Large C leads to:
A. Wider margin
B. More misclassification
C. Narrow margin, fewer errors
D. No effect
✅ Answer: C
Q13. Small C Leads To
A small C results in:
A. Narrow margin
B. Wide margin
C. Overfitting
D. No classification
✅ Answer: B
Q14. Slack Variable ξᵢ
If ξᵢ > 1:
A. Correct classification
B. Margin violation only
C. Misclassification
D. No effect
✅ Answer: C
Q15. Inner Product
The dot product is:
A. Σ xᵢ²
B. Σ wᵢxᵢ
C. x + w
D. ||x||
✅ Answer: B
Q16. PCA Property
Principal components are:
A. Parallel
B. Random
C. Orthogonal
D. Identical
✅ Answer: C
Q17. Generalisation
Good generalisation means:
A. Perfect training accuracy
B. Good performance on unseen data
C. Large dataset only
D. High variance
✅ Answer: B
Q18. KNN Curse of Dimensionality
As dimensions increase:
A. Performance improves
B. Distance becomes more meaningful
C. Performance worsens
D. No change
✅ Answer: C
Q19. K-Means Property
Each iteration:
A. Increases error
B. Decreases or keeps SSE same
C. Randomly changes clusters
D. Stops immediately
✅ Answer: B
Q20. Neural Gas
Closest codevector (rank 0):
A. Moves least
B. Moves most
C. Does not move
D. Is removed
✅ Answer: B
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