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IIT M DIPLOMA AN EXAM QDD4 24 Mar 2024 - 24 Mar 2024

MLF Quiz 214 questions40 marks8 MCQ · 5 MSQ · 1 SADiploma / afternoon / QDD4
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Q1MSQ3 marksselect all that apply
Consider two complex matrices A and B such that both are the Hermitian matrices. Which of the following statements is/are true?
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Comprehension passage - the questions below it refer to this
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Q2MSQ3 marksselect all that apply
Which of the following statements is/are true about A?
  1. A is the Hermitian matrix.
  2. A is the Unitary matrix.
  3. All eigenvalues are real.
  4. Eigenvalues are complex.
Q3MSQ3 marksselect all that apply
Which of the following statements is/are true about A?
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Comprehension passage - the questions below it refer to this
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Q4MSQ3 marksselect all that apply
Which of the following options is/are true?
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Q5MSQ3 marksselect all that apply
Which of the following options is/are true?
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Comprehension passage - the questions below it refer to this
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Q6MCQ2 marks
Which of the following options represents matrix A?
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Q7MCQ3 marks
Which of the following options is/are true?
  1. A is a negative definite matrix.
  2. A is a positive definite matrix.
  3. A is a negative semi-definite matrix.
  4. A is a positive semi-definite matrix.
  5. A is a indefinite matrix.
Comprehension passage - the questions below it refer to this
Based on the above data, answer the given subquestions question figure
Q8MCQ3 marks
Compute the sample covariance matrix C for the given dataset.
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Q9MCQ3 marks
Which is the principal direction that is chosen for performing PCA?
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Q10MCQ3 marks
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Q11MCQ2 marks
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  1. A is positive definite.
  2. A is positive semi-definite.
  3. A is negative definite.
  4. A is negative semi-definite.
Q12MCQ3 marks
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Q13MCQ3 marks
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  1. -1.5, -2.5
  2. 1.5, 2.5
  3. 1.5, -2.5
  4. -1.5, 2.5
Q14SA3 marks
The value of a function at point 5 is 10. The values of the function’s first and second order derivatives at this point are 5 and 2 respectively. What will be the function’s approximate value at the point 5.1? (Enter the answer correct up to two decimal places).

Answer key

  1. Q1 (MSQ, 3 marks): A, B
  2. Q2 (MSQ, 3 marks): A, C
  3. Q3 (MSQ, 3 marks): A, B, C
  4. Q4 (MSQ, 3 marks): C, D
  5. Q5 (MSQ, 3 marks): B, C
  6. Q6 (MCQ, 2 marks): A
  7. Q7 (MCQ, 3 marks): E
  8. Q8 (MCQ, 3 marks): A
  9. Q9 (MCQ, 3 marks): B
  10. Q10 (MCQ, 3 marks): D
  11. Q11 (MCQ, 2 marks): A
  12. Q12 (MCQ, 3 marks): D
  13. Q13 (MCQ, 3 marks): B
  14. Q14 (SA, 3 marks): 10.2 to 10.8