Consider the following logical inferences.

I₁: If it rains then the cricket match will not be played.
    The cricket match was played.
     Inference: There was no rain.
I₂: If it rains then the cricket match will not be played.
     It did not rain.
     Inference: The cricket match was played.

Which of the following is TRUE?

•  (A) Both I₁ and I₂ are correct inferences
•  (B) I₁ is correct but I₂ is not a correct inference
•  (C) I₁ is not correct but I₂ is a correct inference
•  (D) Both I₁ and I₂ are not correct inferences

Which of the following is TRUE?

•  (A) Every relation in 3NF is also in BCNF
•  (B) A relation R is in 3NF if every non-prime attribute of R is fully functionally dependent on every key of R
•  (C) Every relation in BCNF is also in 3NF
•  (D) No relation can be in both BCNF and 3NF

What will be the output of the following C program segment?

char inChar = ‘A’ ;
switch ( inChar ) {
case ‘A’ : printf (“Choice A\ n”) ;
case ‘B’ :
case ‘C’ : printf (“Choice B”) ;
case ‘D’ :
case ‘E’ :
default : printf ( “ No Choice” ) ; }

•  (A) No Choice
•  (B) Choice A
•  (C) Choice A
    Choice B No Choice
•  (D) Program gives no output as it is erroneous

Assuming P ≠ NP, which of the following is TRUE?

•  (A) NP-complete = NP
•  (B) NP-complete ∩ P = $\varnothing$
•  (C) NP-hard = NP
•  (D) P = NP-complete

The worst case running time to search for an element in a balanced binary search tree with n2ⁿ elements is

•  (A) Θ (n log n)
•  (B) Θ (n2ⁿ)
•  (C) Θ (n)
•  (D) Θ (log n)

The truth table

represents the Boolean function

•  (A) X
•  (B) X + Y
•  (C) X $\oplus$ Y
•  (D) Y

The decimal value 0.5 in IEEE single precision floating point representation has

•  (A) fraction bits of 000…000 and exponent value of 0
•  (B) fraction bits of 000…000 and exponent value of −1
•  (C) fraction bits of 100…000 and exponent value of 0
•  (D) no exact representation

A process executes the code

     fork();
     fork();
     fork();

The total number of child processes created is

•  (A) 3
•  (B) 4
•  (C) 7
•  (D) 8

Consider the function f(x) = sin(x) in the interval x $\in$$\left[\mathrm{\pi }/4,7\mathrm{\pi }/4\right]$. The number and location(s) of the local minima of this function are

•  (A) One, at $\mathrm{\pi }$/2
•  (B) One, at 3$\mathrm{\pi }$/2
•  (C) Two, at $\mathrm{\pi }$/2 and 3$\mathrm{\pi }$/2
•  (D) Two, at $\mathrm{\pi }$/4 and 3$\mathrm{\pi }$/2

The protocol data unit (PDU) for the application layer in the Internet stack is

•  (A) Segment
•  (B) Datagram
•  (C) Message
•  (D) Frame

Let A be the 2 × 2 matrix with elements a₁₁ = a₁₂ = a₂₁ = +1 and a₂₂ = −1. Then the eigenvalues of the matrix A¹⁹ are

•  (A) 1024 and −1024
•  (B) 1024√2 and −1024√2
•  (C) 4√2 and −4√2
•  (D) 512√2 and −512√2

What is the complement of the language accepted by the NFA shown below? Assume $\Sigma$ = {a} and $\epsilon$ is the empty string.

•  (A) $\varnothing$
•  (B) $\left\{\epsilon \right\}$
•  (C) $a^{*}$
•  (D) $\{a,\epsilon \}$

What is the correct translation of the following statement into mathematical logic?

 “Some real numbers are rational”

•  (A) $\exists x\left(\mathrm{real}\left(x\right)\vee \mathrm{rational}\left(x\right)\right)$
•  (B) $\forall x\left(\mathrm{real}\left(x\right)\to \mathrm{rational}\left(x\right)\right)$
•  (C) $\exists x\left(\mathrm{real}\left(x\right)\wedge \mathrm{rational}\left(x\right)\right)$
•  (D) $\exists x\left(\mathrm{rational}\left(x\right)\to \mathrm{real}\left(x\right)\right)$

Given the basic ER and relational models, which of the following is INCORRECT?

•  (A) An attribute of an entity can have more than one value
•  (B) An attribute of an entity can be composite
•  (C) In a row of a relational table, an attribute can have more than one value
•  (D) In a row of a relational table, an attribute can have exactly one value or a NULL value

Which of the following statements are TRUE about an SQL query?

P : An SQL query can contain a HAVING clause even if it does not have a GROUP BY clause
Q : An SQL query can contain a HAVING clause only if it has a GROUP BY clause
R : All attributes used in the GROUP BY clause must appear in the SELECT clause
S : Not all attributes used in the GROUP BY clause need to appear in the SELECT clause

•  (A) P and R
•  (B) P and S
•  (C) Q and R
•  (D) Q and S

The recurrence relation capturing the optimal execution time of the Towers of Hanoi problem with n discs is

•  (A) T(n) = 2T(n − 2) + 2
•  (B) T(n) = 2T(n − 1) + n
•  (C) T(n) = 2T(n/2) + 1
•  (D) T(n) = 2T(n − 1) + 1

Let G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to

•  (A) 3
•  (B) 4
•  (C) 5
•  (D) 6

Let W(n) and A(n) denote respectively, the worst case and average case running time of an algorithm executed on an input of size n. Which of the following is ALWAYS TRUE?

•  (A) A(n) = Ω (W(n))
•  (B) A(n) = Θ (W(n))
•  (C) A(n) = O (W(n))
•  (D) A(n) = o (W(n))

The amount of ROM needed to implement a 4 bit multiplier is

•  (A) 64 bits
•  (B) 128 bits
•  (C) 128 bits
•  (D) 2 Kbits

Register renaming is done in pipelined processors

•  (A) as an alternative to register allocation at compile time
•  (B) for efficient access to function parameters and local variables
•  (C) to handle certain kinds of hazards
•  (D) as part of address translation