This set of MCQ(multiple choice questions) focuses on the **Data Base Management System NPTEL 2022 Week 0 Assignment Solutions**.

Databases form the backbone of all major applications today – tightly or loosely coupled, intranet or internet based, financial, social, administrative, and so on. Structured Database Management Systems (DBMS) based on relational and other models have long formed the basis for such databases. Consequently, Oracle, Microsoft SQL Server, Sybase etc. have emerged as leading commercial systems while MySQL, PostgreSQL etc. lead in open source and free domain.

The course introduces relational data models; entity-relationship modeling, SQL, data normalization, and database design. Further it introduces query coding practices using MySQL (or any other open system) through various assignments. Design of simple multi-tier client / server architectures based and Web-based database applications is also introduced.

### Course layout (Answers link)

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Week 0: Assignment answers

Week 1: *Course Overview. Introduction to RDBMS*

Week 2: *Structured Query Language (SQL) *

Week 3: *Relational Algebra. Entity-Relationship Model *

Week 4: *Relational Database Design*

Week 5: *Application Development. Case Studies. Storage and File Structure*

Week 6: *Indexing and Hashing. Query Processing*

Week 7: *Query Optimization. Transactions (Serializability and Recoverability)*

Week 8: *Concurrency Control. Recovery Systems. Course Summarization.*

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### **Data Base Management System** NPTEL 2022 Week 0 Assignment Solutions

**Q1.** If A={a, b, c}, which of the following represent all possible proper subsets of A?

a) 𝛟, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}

b) 𝛟, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c}

c) {a}, {b}, {c}, {a,b}, {a,c}, {b,c}

d) {a}, {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c}

Answer: a) 𝛟, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}

**Q2.** If X={{a, b}, {c}}, which of the following is the power set of X?

a) { 𝛟,{a},{b,c}}

b) { 𝛟,{a},{b},{c}}

c) { 𝛟,{a, b},{c},{{a, b},{c}}}

d) { 𝛟,{a},{b},{c},{a,b},{b,c},{a,c}}

Answer: c) { 𝛟,{a, b},{c},{{a, b},{c}}}

**Q3.** Let A={4,5,6} and B={6,7,8}. Which of the following pairs is not included in A x B, where x defines cartesian product?

a) (6,6)

b) (5,7)

c) (6,8)

d) (5,5)

Answer: d) (5,5)

**Q4.** Let a given function be f: R -> R given by f(x) = [x] where [x] is the greatest integer less than or equal to x. Which of the following statements is/are true?

a) It is a one-one function but not onto.

b) It is an onto function but not one-one.

c) It is both one-one and onto.

d) It is neither one-one nor onto.

Answer: d) It is neither one-one nor onto.

**Q5.** S=[-2, -1, 0, 1, 2] and f: S -> Z given by f(x) = x^{2} – 2x – 3. What is/are the pre-image(s) of -3?

a) -2

b) {0, 2}

c) 1

d) {1, -2}

Answer: b) {0, 2}

**Q6.** Let the cartesian product of two set X and Y be {(a,2), (a,-6), (a,5), (b,2), (b,-6), (b,5), (s,2), (s,-6), (s,5)}. Considering distinct elements in each set and n(X) = n(Y) = 3, find the two sets X and Y.

a) X = {a, b, s}, Y = {2, -2, 5}

b) X = {a, b, s}, Y = {2, -6, 5}

c) X = {a, b, 2}, Y = {2, -2, 5}

d) X = {a, -2, s}, Y = {2, -2, 5}

Answer: b) X = {a, b, s}, Y = {2, -6, 5}

**Q7.** Consider the predicates

R(x): x is red.

G(x): x is green.

Which of the following quantified statements represent “Either everything is red or everything is green”?

a) ∀(x)(R(x) v G(x))

b) ∀(x)(R(x) v ∀(x)G(x))

c) ∀(x)(R(x)) v ∀(x)(G(x))

d) ∀(x)(**¬**R(x) → G(x))

Answer: b), c)

**Q8.** Look at the following truth table

P | Q | P op Q |

F | F | T |

F | T | F |

T | F | F |

T | T | F |

Which binary operation has been carried out?

a) **¬** P v Q

b) **¬** (P v Q)

c) **¬** (P Λ Q)

d) **¬** P Λ Q

Answer: b) ¬ (P v Q)

**Q9.** Consider the relation:

S={(a,b), (b,c), (a,a), (b,b), (c,c), (b,a), (c,b), (a,c), (c,a)}.

Which of the following is TRUE?

a) S is reflexive only

b) S is transitive only

c) S is symmetric only

d) S is an equivalence relation

Answer: d) S is an equivalence relation

**Q10.** Consider the following:

a: Pandemic causes global crisis.

b: Cyclone causes global crisis.

c: Rescue teams are sent.

Consider the statement:

“If pandemic causes global crisis or cyclone causes global crisis, then rescue teams are sent.”

Which of the following is equivalent to the inverse of the statement?

a) **¬**a Λ **¬**b → **¬**c

b) **¬**c → **¬**a v **¬**b

c) b v c → **¬**a

d) **¬**a → b v c

Answer: a) ¬a Λ ¬b → ¬c

**Q11.** Why is not binary search suitable for a sorted linked list of numbers?

a) Worst case time complexity of binary search on a linked list is O(n).

b) Both halves of the list (to the left and the right of the middle element) may have to be explored to search for an element.

c) The middle element in a sorted linked list cannot be found out in O(1) time.

d) Size of a node in a linked list is more.

Answer: a), c)

**Q12.** Consider a max-heap of some numbers. Which of the following is not true about a max-heap of numbers?

a) The second largest element is the number stored at the left or right child of the root node of the max-heap.

b) The smallest element is found only at the leaf nodes of the max-heap.

c) The number of swap operations to initialize a max-heap is O(nlogn).

d) The number of swap operations to find out the least number in a max-heap is O(logn).

Answer: d) The number of swap operations to find out the least number in a max-heap is O(logn).

**Q13.** A single array A[n] (index range is from 0 to n-1) is used to implement two stacks. The two stacks grow from opposite ends of the array. Variables top1 and top2 (top1 < top2) point to the topmost element in each stack. The space is to be used efficiently.

Which of the following statements is wrong?

a) top1 is initialized to -1 and top2 in initialized to n.

b) Stack full condition for any stack is top1 = top2 – 1.

c) In each push operation in the second stack, top2 is decremented by 1.

d) Size of each stack must not be more than n/2.

Answer: d) Size of each stack must not be more than n/2.

**Q14.** Numbers 1, 2, 3 are pushed into a stack in that order but these three PUSH operations are intermixed with POP operations as well. Whenever a number is popped, it is printed. Which of the following permutation cannot be printed by such PUSH and POP operations?

a) 1, 2, 3

b) 3, 1, 2

c) 2, 1, 3

d) 1, 3, 2

Answer: b) 3, 1, 2

**Q15.** Consider the set X={1, 2, 3, 4, 5} and R be a set such that R={(a,b): a^{2}+b^{2} <= 13}. What is n(R)?

a) 5

b) 8

c) 4

d) 10

Answer: b) 8

**Q16.** Let P={2, 3, 5}, Q={3, 4, 7, 8}, R={2, 1}. Find (P – Q) x (P **∩** R).

a) {(2, 2), (3, 2), (5, 2)}

b) {(4, 2), (7, 2), (8, 2)}

c) {(2, 2), (5, 2)}

d) {(2, 2), (3, 5), (5, 2), (4, 2), (7, 2), (8, 2)}

Answer: c) {(2, 2), (5, 2)}

**Q17.** Let U be the universal set. n(U) = 500. If A, B are subsets of U such that n(A) = 100, n(B) = 200 and n(A** ∩** B) = 75, what is the value of n( **¬**A** ∩** **¬**B)?

a) 100

b) 225

c) 275

d) 0

Answer: c) 275

**Q18.** Let a relation R in the set R of real numbers be defined as (p,q) **∈** R if and if only if 1+pq > 0 for all p, q **∈** R.

Which of the following is TRUE about the relation R?

a) reflexive only

b) reflexive and symmetric

c) transitive

d) Equivalence relation

Answer: b) reflexive and symmetric

**Q19.** Consider two sets X and Y. Which of the following statement is false?

a) X – Y = X **∩** **¬**Y

b) X – Y = X – (X **∩** Y)

c) X – Y = X – **¬**Y

d) X – Y = (X U Y) – Y

Answer: c) X – Y = X – ¬Y

**Q20.** Let P = {1, 2, 3} and Q = {2, 3, 4}. How many relations are possible from P to Q?

a) 8

b) 64

c) 256

d) 512

Answer: d) 512

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