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Also Read: Data Science for engineers week 1 Assignment

NPTEL Data Science for Engineers Week 0 Assignment July 2023

Note : 

This assignment is only for practice purpose and it will not be counted towards the Final score

Q1. Which of the following statements are TRUE in accordance with De Morgan’s laws for 2 given events A and B?

A.P ( A ∩ B )' = P( A' ) ∩ P ( B' ) 

B. P ( A U B )' = P ( A' ∩ B' ) 

C. P ( A ∩ B )' = P ( A' U B' ) 

D. P ( A U B ) = P ( A ) + P ( B ) - P ( A ∩ B )

Answer: [ B ] , [ C ] 

P ( A U B )' = P ( A' ∩ B' ) 

P ( A ∩ B )' = P ( A' U B' ) 

Q2. Determine the total number of outcomes in the sample space if 2 letters are chosen from the letters a, e, i, o, u with repetition

 

A. 10

B. 32

C. 25

D. 20

Answer: [ C ] 25

                In the above given letters are a,e,i,o,u. Here 2 letters are chosen random with repetition. Hence we can choose the same letter twice. The total no of combinations including the selection of same letter twice will become 5*5=25.

Q3. Given a matrix A and a scalar k, (kA)−1 equals

A. kA−1

B. |kA−1|.A

C. (A−1)k

D. A−1/k

Answer: [ D ]  A−1/k

Q4. Given [x1,x2,x3,...,xn] are the possible values of a random variable X, and p1,p2,p3,...,pn

 be the corresponding probabilities to each value of the random variable. The mean is computed by the  formula

A. ∑ni=1pixin

B. ∑i=1npi

C. ∑i=1npixi

D. None of these

Answer:  [ C ] ∑i=1npixi

Q5. State TRUE or FALSE

      Not all mutually exclusive events are exhaustive.

 

A. True

B. False

Answer: [ A ]True

Q6. A manufacturing company is set up in two different locations. If the number of employees in one location are 663, and the average monthly salary for their employees is $13454, and the number of employees in the other location are 504, and the average monthly salary for their employees is $17591. Find the combined arithmetic mean of the monthly salary?

A. $15240.67

B. $15804.33

C. $15522.5

D. None of these

Answer: [ A ]  $15240.67

Q7. Given below is tabular data on a test conducted recently to detect a new mutant of the coronavirus.

Header                       Tested Positive                Tested Negative

Infected                              54                                      138

Non-Infected                    173                                      111

Find the number of people who have not actually contracted the virus yet have been tested positive?

A. 284

B. 173

C. 138

D. 227

Answer: [ B ] 173

 No of People = (Non-Infected People) &  (Tested Positive) = 173

Q8. Given a pie chart that indicates the expenditure of a manufacturing organization towards various activities, what is the ratio of expenditure for the R & D department to the Marketing department?

A.  1 : 1.54

B.  1 : 0.65

C.  1 : 0.44

D. None of these

Answer: [ C ] 1 : 0.44

Q9. 3 natural numbers are chosen at random. What is the probability that their product yields an odd number?

A.  2 / 3

B.  1 / 6

C.  1 / 2

D. 1 / 8

Answer:  [ D ] 1 / 8

Q10. The mean of the first n natural numbers is

A.  n!

B. (n / 2) + 1

C. (n + 1) / 2

D.  n2

Answer:  [ C ] (n + 1) / 2

Conclusion: 

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