Data Base Management System - Week 0 Quiz Solutions

Question 1

Look at the following truth table: A B A op B FFT FTT TFT TTF Which binary operation has been carried out?

A.¬ A ∨ B

B.¬ ( A ∨ B )

C.¬ ( A ∧ B )

D.¬ A ∧ B

Correct Answer: ¬ ( A ∧ B )

Question 2

Consider the following array of seven integers: 30, 15, 10, 40, 25, 20, 12 What will be the contents of this array after the 2nd pass of bubble sort (sorting from smallest to largest)?

A.15, 10, 30, 25, 20, 12, 40

B.10, 12, 15, 25, 20, 30, 40

C.10, 15, 25, 20, 12, 30, 40

D.10, 12, 15, 20, 25, 30, 40

Correct Answer: 10, 15, 25, 20, 12, 30, 40

Question 3

Identify the correct representation of the prefix expression of the tree given below.

A.∗2+4∗6+8 9

B.2+4∗6∗8+9

C.2 4+6 8 9+∗∗

D.∗+2 4∗6+8 9

Correct Answer: ∗+2 4∗6+8 9

Question 4

Consider a set X = { {a, c}, {b, d} }. What is the number of elements in the power set of X?

A.4

B.8

C.12

D.16

Correct Answer: 4

Question 5

When an EVEN decimal number is converted into a binary number, what will be the Least Signaficant Bit(LSB)?

A.0

B.1

C.either 0 or 1

D.only 11

Correct Answer: 0

Question 6

Consider the following arrays of numbers. Which one represents a min-heap?

A.20 5 15 10 6 8 9

B.20 10 15 5 6 8 9

C.9 6 10 8 5 15 20

D.5 6 10 8 9 15 20

Correct Answer: 5 6 10 8 9 15 20

Question 7

Consider two sets A and B. Which of the following statement is true?

A.A − B = A ∩ B

B.A − B = A − ( A ∩ B )

C.A − B = A − ¬ B

D.A − B = A ∩ ( A ∩ B )

Correct Answer: A − B = A − ( A ∩ B )

Question 8

Let a given function be f:I→I given by f(x)=x2 where I stands for the set of all integers. 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

Correct Answer: It is neither one-one nor onto

Question 9

Consider the following: CSE(x): The girl x is in CSE department. DBMS(x): The girl x studies DBMS. Consider the statement : Which of the following formula represents “Not all CSE students study DBMS.”

A.∀ x ( C S E ( x ) → ¬ D B M S ( x ) )

B.∀ x ( ¬ C S E ( x ) → D B M S ( x ) )

C.∃ x ( ¬ C S E ( x ) ∗ D B M S ( x ) )

D.¬ ∀ x ( C S E ( x ) → D B M S ( x ) )

Correct Answer: ¬ ∀ x ( C S E ( x ) → D B M S ( x ) )

Q10

Question 10

Consider the binary relation S1 = {(1, 1), (2, 2), (1, 2), (2, 1)} on the set {1, 2}. Identify the correct statement.

A.S 1 is reflexive

B.S 1 is symmetric

C.S 1 is not transitive

D.S 1 is antisymmetric

Correct Answers: S 1 is reflexive, S 1 is symmetric

Q11

Question 11

What is the domain of the following function if the range is a subset of real numbers? 5x2−9

A.( − ∞ , − 3 ) ∪ ( − 3 , ∞ )

B.( − ∞ , 3 ) ∪ ( 3 , ∞ )

C.( 3 , ∞ ) ∪ ( − ∞ , − 3 )

D.( − 3 , 3 )

Correct Answer: ( 3 , ∞ ) ∪ ( − ∞ , − 3 )

Q12

Question 12

How many functions are there from the set {1, 2, 3} to the set {a, b}?

A.9

B.8

C.6

D.5

Correct Answer: 8

Q13

Question 13

If U is the set of integers excluding zero, V is the set of even integers, and D is the set of odd integers, which of the following statement(s) is (are) true. Note: Here E __ denotes complement over the expression E . U is the Universal set

A.V ∪ D = U

B.U − V = D

C.V __ = D

D.V − D = { 0 }

Correct Answers: U − V = D, V __ = D

Q14

Question 14

Suppose that A and B are two sets. Which of the following is always equivalent to A∪B

A.( A − B ) ∪ ( B − A ) ∪ ( A ∩ B )

B.( A − B ) ∪ ( B − A )

C.A ∪ ( B − A )

D.A __ ∩ B __

Correct Answers: ( A − B ) ∪ ( B − A ) ∪ ( A ∩ B ), A ∪ ( B − A )

Q15

Question 15

Consider the following function from {a,b,c,d} to {1,2,3,4,5}. {(a,2), (b,1), (c,3), (d,4)} Which of the following is true about the function?

A.The function is bijective

B.The function is injective, but not surjective

C.The function is surjective, but not injective

D.The function is neither injective nor surjective

Correct Answer: The function is injective, but not surjective

Q16

Question 16

Numbers 1, 2, 3, 4 are pushed into a stack in that order but these four PUSH operations are intermixed with POP operations as well. Whenever a number is popped, it is printed. Which of the following permutation can be printed by such PUSH and POP operations?

A.3, 4, 1, 2

B.1, 4, 2, 3

C.4, 2, 3, 1

D.3, 2, 4, 1

Correct Answers: 3, 2, 4, 1

Q17

Question 17

Which one of the following is the most appropriate logical formula to represent the statement? "Red and Yellow cars are beautiful". The following notations are used: R(x): x is a Red car Y(x): x is a Yellow car B(x): x is beautiful Note: ∀x denotes for all x. ∃x denotes for some x (atleast 1). → denotes implication. ∨ and ∧ denotes OR and AND operation respectively.

A.∃ x ( R ( x ) ∨ Y ( x ) ) → B ( x )

B.∃ x ( R ( x ) ∧ Y ( x ) ) → B ( x )

C.∀ x ( ( R ( x ) ∨ Y ( x ) ) → B ( x ) )

D.∀ x ( ( R ( x ) ∧ Y ( x ) ) → B ( x ) )

Correct Answer: ∀ x ( ( R ( x ) ∨ Y ( x ) ) → B ( x ) )

Q18

Question 18

Consider a B+-tree of order 5. What is the minimum number of children a root node can have, considering it is not the only node in the tree?

A.5

B.6

C.2

D.1

Correct Answer: 2

Q19

Question 19

A hash table with length of 10 elements use open addressing with hash function h(k)=k mod 10, and linear probing. the table shows the state after insertion of 6 values. Identify a possible order in which the key values could have been inserted in the table. 0 1 222 343 414 562 696 7103 8 9

A.96, 22, 14, 62, 43, 103

B.14, 22, 43, 62, 103, 96

C.22, 96, 43, 103, 14, 62

D.96, 14, 22, 43, 62, 103

Correct Answer: 96, 14, 22, 43, 62, 103

Q20

Question 20

How many comparisons does it take to find the element 10 in the sorted array A = {10,15,17,19,20} using binary search?

A.2

B.3

C.5

D.6

Correct Answer: 2

Practice: Week 0 : Assignment 0