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2015 Questions

Q.1 Which one of the following is a closed form expression for the generating function of the
sequence {an}, where an = 2n + 3 for all n = 0, 1, 2,... ?


Q.2 Consider the following C program.
#include<stdio.h>
struct Ournode{
char x,y,z;
};
int main(){
struct Ournode p = {'1', '0', 'a'+2};
struct Ournode *q = &p;
printf ("%c, %c", *((char*)q+1), *((char*)q+2));
return 0;
}
The output of this program is:
 

(A) 0, c (B) 0, a+2 (C) '0', 'a+2' (D) '0', 'c'
 

Q.3 A queue is implemented using a non-circular singly linked list. The queue has a head pointer
and a tail pointer, as shown in the figure. Let n denote the number of nodes in the queue. Let
enqueue be implemented by inserting a new node at the head, and dequeue be
implemented by deletion of a node from the tail.

Which one of the following is the time complexity of the most time-efficient implementation
of enqueue and dequeue, respectively, for this data structure?
(A) θ(1), θ(1) (B) θ(1), θ(n) (C) θ(n), θ(1) (D) θ(n), θ(n)


Q.4 Let ⊕ and ⊙ denote the Exclusive OR and Exclusive NOR operations, respectively.
Which one of the following is NOT CORRECT?
(A) P̅̅̅⊕̅̅̅̅Q̅ = P ⊙ Q
(B) P̅ ⊕ Q = P ⊙ Q
(C) P̅ ⊕ Q̅ = P ⊕ Q
(D) (P ⊕ P̅) ⊕ Q = (P ⊙ P̅) ⊙ Q̅

Q.5 Consider the following processor design characteristics.
I. Register-to-register arithmetic operations only
II. Fixed-length instruction format
III. Hardwired control unit
Which of the characteristics above are used in the design of a RISC processor?
(A) I and II only (B) II and III only (C) I and III only (D) I, II and III
 

Q.6 Let N be an NFA with n states. Let k be the number of states of a minimal DFA which is
equivalent to N. Which one of the following is necessarily true?
(A) k ≥ 2n  (B) k ≥ n  (C) k ≤ n2  (D) k ≤ 2n


Q.7 The set of all recursively enumerable languages is
(A) closed under complementation.
(B) closed under intersection.
(C) a subset of the set of all recursive languages.
(D) an uncountable set.

Q.8 Which one of the following statements is FALSE?
(A) Context-free grammar can be used to specify both lexical and syntax rules.
(B) Type checking is done before parsing.
(C) High-level language programs can be translated to different Intermediate
Representations.
(D) Arguments to a function can be passed using the program stack.


Q.9 The following are some events that occur after a device controller issues an interrupt while
process L is under execution.
(P) The processor pushes the process status of L onto the control stack.
(Q)The processor finishes the execution of the current instruction.
(R) The processor executes the interrupt service routine.
(S) The processor pops the process status of L from the control stack.
(T) The processor loads the new PC value based on the interrupt.
Which one of the following is the correct order in which the events above occur?
(A) QPTRS (B) PTRSQ (C) TRPQS (D) QTPRS
 

Q.10 Consider a process executing on an operating system that uses demand paging. The average
time for a memory access in the system is M units if the corresponding memory page is
available in memory, and D units if the memory access causes a page fault. It has been
experimentally measured that the average time taken for a memory access in the process is
X units.
Which one of the following is the correct expression for the page fault rate experienced by
the process?
(A) (D – M) / (X – M) (B) (X – M) / (D – M)
(C) (D – X) / (D – M) (D) (X – M) / (D – X)

Q.11 In an Entity-Relationship (ER) model, suppose R is a many-to-one relationship from entity
set E1 to entity set E2. Assume that E1 and E2 participate totally in R and that the cardinality
of E1 is greater than the cardinality of E2.
Which one of the following is true about R?
(A) Every entity in E1 is associated with exactly one entity in E2.
(B) Some entity in E1 is associated with more than one entity in E2.
(C) Every entity in E2 is associated with exactly one entity in E1.
(D) Every entity in E2 is associated with at most one entity in E1.


Q.12 Consider the following two tables and four queries in SQL.

Book (isbn, bname), Stock (isbn, copies)
Query 1: SELECT B.isbn, S.copies
FROM Book B INNER JOIN Stock S
ON B.isbn = S.isbn;
Query 2: SELECT B.isbn, S.copies
FROM Book B LEFT OUTER JOIN Stock S
ON B.isbn = S.isbn;
Query 3: SELECT B.isbn, S.copies
FROM Book B RIGHT OUTER JOIN Stock S
ON B.isbn = S.isbn;
Query 4: SELECT B.isbn, S.copies
FROM Book B FULL OUTER JOIN Stock S
ON B.isbn = S.isbn;
Which one of the queries above is certain to have an output that is a superset of the outputs
of the other three queries?
(A) Query 1 (B) Query 2 (C) Query 3 (D) Query 4
Q.13 Match the following:

Field Length in bits
P. UDP Header’s Port Number I. 48
Q. Ethernet MAC Address II. 8
R. IPv6 Next Header III. 32
S. TCP Header’s Sequence Number IV. 16

(A) P-III, Q-IV, R-II, S-I (B) P-II, Q-I, R-IV, S-III
(C) P-IV, Q-I, R-II, S-III (D) P-IV, Q-I, R-III, S-II


Q.14 Consider the following statements regarding the slow start phase of the TCP congestion
control algorithm. Note that cwnd stands for the TCP congestion window and MSS denotes
the Maximum Segment Size.
(i) The cwnd increases by 2 MSS on every successful acknowledgment.
(ii) The cwnd approximately doubles on every successful acknowledgement.
(iii) The cwnd increases by 1 MSS every round trip time.
(iv) The cwnd approximately doubles every round trip time.
Which one of the following is correct?
(A) Only (ii) and (iii) are true (B) Only (i) and (iii) are true
(C) Only (iv) is true (D) Only (i) and (iv) are true
 

Q.15 Two people, P and Q, decide to independently roll two identical dice, each with 6 faces,numbered 1 to 6. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a trial as a throw of the dice by P and Q. Assume that all 6 numbers on each dice are equi-probable and that all trials are independent. The probability (rounded to 3 decimal places) that one of them wins on the third trial is _____.

Q.16 The value of ∫ x cos(x2)dx π/40 correct to three decimal places (assuming that π = 3.14 ) is _____.

Q.17
Consider a matrixT
A uv 
where
1 1
,
2 1
u v
           
 . Note that Tv denotes the transpose of v. The largest eigenvalue of A is _____.

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