Question 1

**(I)**

Which one of the above underlined parts of the sentence is NOT appropriate?

__While trying to collect__an envelope (II)__from under the table__,(II)__Mr. X fell down and__(IV)__was losing consciousness.__Which one of the above underlined parts of the sentence is NOT appropriate?

A : I

B : II

C : III

D : IV

.

Correct answer is : D

Question 2

**If she _______________ how to calibrate the instrument, she _______________ done the experiment.**

A : knows, will have

B : knew, had

C : had known, could have

D : should have known, would have

.

Correct answer is : C

Question 3

**Choose the word that is opposite in meaning to the word “coherent”.**

A : sticky

B : well-connected

C : rambling

D : friendly

.

Correct answer is : C

Question 4

**Which number does not belong in the series below?**

2, 5, 10, 17, 26, 37, 50, 64

2, 5, 10, 17, 26, 37, 50, 64

A : 17

B : 37

C : 64

D : 26

.

Correct answer is : C

Question 5

**The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination.**

What is the average of the marks obtained by the class in the examination?

What is the average of the marks obtained by the class in the examination?

A : 1.34

B : 1.74

C : 3.02

D : 3.91

.

Correct answer is : C

Solution :

Total question 44×2=88 =>44×3=132

Total marks obtained= (21×2) + (15×3) + (23×2) =133

Total Number of students=44

Average = 133/44 =3.02

Question 6

**A dance programme is scheduled for 10.00 a.m. Some students are participating in the programme and they need to come an hour earlier than the start of the event. These students should be accompanied by a parent. Other students and parents should come in time for the programme. The instruction you think that is appropriate for this is**

A : Students should come at 9.00 a.m. and parents should come at 10.00 a.m.

B : Participating students should come at 9.00 a.m. accompanied by a parent, and other parents and students should come by 10.00 a.m.

C : Students who are not participating should come by 10.00 a.m. and they should not bring their parents. Participating students should come at 9.00 a.m.

D : Participating students should come before 9.00 a.m. Parents who accompany them should come at 9.00 a.m. All others should come at 10.00 a.m.

.

Correct answer is : B

Question 7

**By the beginning of the 20th century, several hypotheses were being proposed, suggesting a paradigm shift in our understanding of the universe. However, the clinching evidence was provided by experimental measurements of the position of a star which was directly behind our sun.**

Which of the following inference(s) may be drawn from the above passage?

Which of the following inference(s) may be drawn from the above passage?

(i) Our understanding of the universe changes based on the positions of stars (ii) Paradigm shifts usually occur at the beginning of centuries (iii) Stars are important objects in the universe (iv) Experimental evidence was important in confirming this paradigm shift

A : (i), (ii) and (iv)

B : (iii) only

C : (i) and (iv)

D : (iv) only

.

Correct answer is : D

Question 8

**The Gross Domestic Product (GDP) in Rupees grew at 7% during 2012-2013. For international comparison, the GDP is compared in US Dollars (USD) after conversion based on the market exchange rate. During the period 2012-2013 the exchange rate for the USD increased from Rs. 50/ USD to Rs. 60/ USD. India’s GDP in USD during the period 2012- 2013**

A : increased by 5 %

B : decreased by 13%

C : decreased by 20%

D : decreased by 11%

.

Correct answer is : D

Solution :

Per 100 Rs final value 107 Rs

Per 100/50 Dollars final value 107/60

for 100 dollars__________?

= 100*50/100 *107/60 = 89.16

Decreased by 11%

Question 9

**The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students in 2011 and 2012 is equal, what is the ratio of male students in 2012 to male students in 2011?**

A : 1:1

B : 2:1

C : 1.5:1

D : 2.5:1

.

Correct answer is : C

Solution :

Take number of female students in 2011=100

Number of male in 2011=100

No. of female in 2012=100

No. of male in 2012=150

Ratio = 150/100 = 1.5 :1

Question 10

**Consider the equation: (7526)8 - (Y)8 = (4364)8 , where (X)N stands for X to the base N. Find Y.**

A : 1634

B : 1737

C : 3142

D : 3162

.

Correct answer is : C

Solution :

Simple subtraction of octal numbers.

Question 11

**Consider the following statements:**

P: Good mobile phones are not cheap

Q: Cheap mobile phones are not good

L: P implies Q

M: Q implies P

N: P is equivalent to Q

Which one of the following about L, M, and N is CORRECT?

P: Good mobile phones are not cheap

Q: Cheap mobile phones are not good

L: P implies Q

M: Q implies P

N: P is equivalent to Q

Which one of the following about L, M, and N is CORRECT?

A : Only L is TRUE.

B : Only M is TRUE.

C : Only N is TRUE.

D : L, M and N are TRUE.

.

Correct answer is : D

Question 12

**Let X and Y be finite sets and f : X -> Y be a function. Which one of the following statements is TRUE?**

A : For any subsets A and B of X, f (A U B) = |f (A)| + |f (B)|

B : For any subsets A and B of X, f (A ∧ B) =f (A) ∧ f (B)

C : For any subsets A and B of X, f (A ∧ B) =min{ f (A) , f (B) }

D : For any subsets S and T of Y, f

^{-1}(S ∧ T) = f

^{-1}(S) ∧ f

^{-1}(T)

.

Correct answer is : D

Question 13

**Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L ≠ G and that the size of L is at least 4. The size of L is _______.**

.

Correct answer is : 5

Solution :

Order of subgroup divides order of group (Lagrange’s theorem).

3, 5 and 15 can be the order of subgroup. As subgroup has atleast 4 elements and it is not equal to the given group, order of subgroup can’t be 3 and 15. Hence it is 5.

Question 14

**Which one of the following statements is TRUE about every n × n matrix with only real eigenvalues?**

A : If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative.

B : If the trace of the matrix is positive, all its eigenvalues are positive.

C : If the determinant of the matrix is positive, all its eigenvalues are positive.

D : If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.

.

Correct answer is : A

Solution :

If the trace of the matrix is positive and the determinant of the matrix is negative then atleast one of its eigen values is negative.

Since determinant = product of eigen values.

Question 15

**If V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of V1 ∧ v2 is _______.**

.

Correct answer is : 2

Solution :

Let the basis of 6-dimensional vector space be {e1, e2, e3,e4, e5, e6}. In order for V1 ∧ V2 to have smallest possible dimension V1 and V2 could be, say, {e1, e2, e3,e4} and {e3, e4, e5, e6} respectively. The basis of V1 ∧ V2 would then be {e3, e4}. => Smallest possible dimension = 2.

Question 16

**Find the value of k**

.

Correct answer is : 4

Question 17

**Consider the following minterm expression for F. F(P,Q,R,S) =∑ 0, 2, 5, 7, 8, 10, 13, 15**

The minterms 2, 7, 8 and 13 are ‘do not care terms. The minimal sum of-products form for F is

The minterms 2, 7, 8 and 13 are ‘do not care terms. The minimal sum of-products form for F is

A : QS` +Q`S

B : Q`S` +QS

C : Q` R` S` +Q` R `S +QR`S +QRS

D : P`Q`S` + P`QS + PQS + PQ`S`

.

Correct answer is : B

Solution :

The K-map for the function F is as follows

P1 = Q`S` and P2 = QS

F(P,Q,R,S) = P1 + p2

= Q`S` + QS

Question 18

**Consider the following combinational function block involving four Boolean variables x, y, a, b where x, a, b are inputs and y is the output.**

f (x, y, a, b)

{

if (x is 1) y = a;

else y = b;

}

Which one of the following digital logic blocks is the most suitable for implementing this function?

f (x, y, a, b)

{

if (x is 1) y = a;

else y = b;

}

Which one of the following digital logic blocks is the most suitable for implementing this function?

A : Full adder

B : Priority encoder

C : Multiplexor

D : Flip-Flop

.

Correct answer is : C

Solution :

y = x`b + xa

‘x’ is working as selection line, where the two input lines are ‘a’ and ‘b’, so the function F(x, y,a,b) can be implemented using (2× 1) multiplexer as follows:

Question 19

**Consider the following processors (ns stands for nanoseconds). Assume that the pipeline registers have zero latency.**

P1: Four-stage pipeline with stage latencies 1 ns, 2 ns, 2 ns, 1 ns.

P2: Four-stage pipeline with stage latencies 1 ns, 1.5 ns, 1.5 ns, 1.5 ns.

P3: Five-stage pipeline with stage latencies 0.5 ns, 1 ns, 1 ns, 0.6 ns, 1 ns.

P4: Five-stage pipeline with stage latencies 0.5 ns, 0.5 ns, 1 ns, 1 ns, 1.1 ns.

Which processor has the highest peak clock frequency?

P1: Four-stage pipeline with stage latencies 1 ns, 2 ns, 2 ns, 1 ns.

P2: Four-stage pipeline with stage latencies 1 ns, 1.5 ns, 1.5 ns, 1.5 ns.

P3: Five-stage pipeline with stage latencies 0.5 ns, 1 ns, 1 ns, 0.6 ns, 1 ns.

P4: Five-stage pipeline with stage latencies 0.5 ns, 0.5 ns, 1 ns, 1 ns, 1.1 ns.

Which processor has the highest peak clock frequency?

A : P1

B : P2

C : P3

D : P4

.

Correct answer is : C

Solution :

Peak clock frequency = 1 / Maximum latency. Max Lat is min in P3 so Peak clock frequency will be maximum.

Question 20

**Let A be a square matrix size n × n. Consider the following pseudocode. What is the expected output?**

C = 100;

for i = 1 to n do

for j = 1 to n do

{

Temp = A[ i ] [ j ] + C ;

A [ i ] [ j ] = A [ j ] [ i ] ;

A [ j ] [ i ] = Temp – C ;

}

for i = 1 to n do

for j = 1 to n do

output (A[ i ] [ j ]);

C = 100;

for i = 1 to n do

for j = 1 to n do

{

Temp = A[ i ] [ j ] + C ;

A [ i ] [ j ] = A [ j ] [ i ] ;

A [ j ] [ i ] = Temp – C ;

}

for i = 1 to n do

for j = 1 to n do

output (A[ i ] [ j ]);

A : The matrix A itself

B : Transpose of the matrix A

C : Adding 100 to the upper diagonal elements and subtracting 100 from lower diagonal elements of A

D : None of these

.

Correct answer is : A

Solution :

In the computation of given pseudo code for each row and column of Matrix A, each upper triangular element will be interchanged by its mirror image in the lower triangular and after that the same lower triangular element will be again re-interchanged by its mirror image in the upper triangular, resulting the final computed Matrix A same as input Matrix A.

Question 21

**The minimum number of arithmetic operations required to evaluate the polynomial P (X) = X**

^{5}+ 4X^{3}+ 6x + 5 for a given value of X, using only one temporary variable is _____..

Correct answer is : 7

Solution :

Take x common repeatedly and form an equation and count the steps.

Question 22

**Consider the following rooted tree with the vertex labelled P as the root**

The order in which the nodes are visited during an in-order traversal of the tree is

The order in which the nodes are visited during an in-order traversal of the tree is

A : SQPTRWUV

B : SQPTUWRV

C : SQPTWUVR

D : SQPTRUWV

.

Correct answer is : A

Solution :

The In order Traversal of Ternary Tree is done as follows:

Left -> Root ->Middle -> Right

So the nodes are visited in SQPTRWUV order.

Question 23

**Suppose depth first search is executed on the graph below starting at some unknown vertex. Assume that a recursive call to visit a vertex is made only after first checking that the vertex has not been visited earlier. Then the maximum possible recursion depth (including the initial call) is _________.**

.

Correct answer is : 19

Question 24

**You have an array of n elements. Suppose you implement quick sort by always choosing the central element of the array as the pivot. Then the tightest upper bound for the worst case performance is**

A : O(n

^{2})

B : O(n logn)

C : θ(n logn)

D : O(n

^{3})

.

Correct answer is : A

Solution :

The Worst case time complexity of quick sort is O (n

^{2}). The central element is chosen as the pivot and not the median so that central element could be an extreme in the final array every time.

Question 25

**The length of the shortest string NOT in the language (over ∑ = {a,b}) of the following regular expression is _________. a*b* (ba)* a***

.

Correct answer is : 3

Solution :

R.E= a * b*(ba)*a *

Length 0 is present as it accepts ∈ all length 1 strings are present (a,b)also aa,ab,ba,bb are present, But 'bab ' is not present. So it is 3

Question 26

**Let S be a finite non-empty alphabet and let * 2S be the power set of S * . Which one of the following is TRUE?**

A : Both 2S * and S * are countable

B : 2S * is countable S * is uncountable

C : 2S * is uncountable and S * is countable

D : Both 2S * and S * are uncountable

.

Correct answer is : C

Question 27

**One of the purposes of using intermediate code in compilers is to**

A : make parsing and semantic analysis simpler.

B : improve error recovery and error reporting

C : increase the chances of reusing the machine-independent code optimizer in other compliers.

D : improve the register allocation.

.

Correct answer is : C

Solution :

Intermediate code is machine independent code which makes it easy to retarget the compiler to generate code for newer and different processors.

Question 28

**Which of the following statements are CORRECT?**

1)Static allocation of all data areas by a compiler makes it impossible to implement recursion.

2)Automatic garbage collection is essential to implement recursion.

3)Dynamic allocation of activation records is essential to implement recursion.

4)Both heap and stack are essential to implement recursion.

1)Static allocation of all data areas by a compiler makes it impossible to implement recursion.

2)Automatic garbage collection is essential to implement recursion.

3)Dynamic allocation of activation records is essential to implement recursion.

4)Both heap and stack are essential to implement recursion.

A : 1 and 2 only

B : 2 and 3 only

C : 3 and 4 only

D : 1 and 3 only

.

Correct answer is : D

Solution :

To implement recursion, activation record should be implemented by providing dynamic memory allocation. This dynamic allocation is done from runtime stack. Heap is essential to allocate memory for data structures at run-time, not for recursion.

So statement 1 and 3 are correct.

Question 29

**In the context of modular software design, which one of the following combinations is desirable?**

A : High cohesion and high coupling

B : High cohesion and low coupling

C : Low cohesion and high coupling

D : Low cohesion and low coupling

.

Correct answer is : B

Solution :

Cohesion is a measure of internal strength within a module, whereas coupling is a measure of inter dependency among the modules. So in the context of modular software design there should be high cohesion and low coupling.

Question 30

**A system uses 3 page frames for storing process pages in main memory. It uses the Least Recently Used (LRU) page replacement policy. Assume that all the page frames are initially empty. What is the total number of page faults that will occur while processing the page reference string given below?**

4, 7, 6, 1, 7, 6, 1, 2, 7, 2

4, 7, 6, 1, 7, 6, 1, 2, 7, 2

.

Correct answer is : 6

Question 31

**What is the optimized version of the relation algebra expression, where A1, A2 are sets of attributes in with A1 ⊂ A2 and F1, F2 are Boolean expressions based on the attributes in r?**

A : π

_{A1}( ∂ (F1 ∧ F2 ) (r) )

B : π

_{A1}( ∂ (F1 ∨ F2 ) (r) )

C : π

_{A2}( ∂ (F1 ∧ F2 ) (r) )

D : π

_{A2}( ∂ (F1 ∨ F2 ) (r) )

.

Correct answer is : A

Question 32

**A prime attribute of a relation scheme R is an attribute that appears**

A : in all candidate keys of R.

B : in some candidate key of R.

C : in a foreign keys of R.

D : only in the primary key of R.

.

Correct answer is : B

Solution :

A prime attribute or key attribute of a relation scheme R is an attribute that appears in any of the candidate key of R, remaining attributes are known as non-prime or non-key tribute

Question 33

**In the following pairs of OSI protocol layer/sub-layer and its functionality, the INCORRECT pair is**

A : Network layer and Routing

B : Data Link Layer and Bit synchronization

C : Transport layer and End-to-end process communication

D : Medium Access Control sub-layer and Channel sharing

.

Correct answer is : B

Solution :

(a) One of the main functionality of Network Layer is Routing. So Option (a) is CORRECT.

(b) Bit Synchronization is always handled by Physical Layer of OSI model but not Data Link Layer. So Option (b) is INCORRECT.

(c) End – to – End Process Communication is handled by Transport Layer. So Option (c) is CORRECT.

(d) MAC sub layer have 3 types of protocols (Random, Controlled and Channelized Access).

Question 34

**A bit-stuffing based framing protocol uses an 8-bit delimiter pattern of 01111110. If the output bit-string after stuffing is 01111100101, then the input bit-string is**

A : 0111110100

B : 0111110101

C : 0111111101

D : 0111111111

.

Correct answer is : B

Solution :

Given 8 – bit delimiter pattern of 01111110.

Output Bit string after stuffing is 011111

__0__0101

Now, Input String is 0111110101

Question 35

**Host A (on TCP/IP v4 network A) sends an IP datagram D to host B (also on TCP/IP V4 network B). Assume that no error occurred during the transmission of D. When D reaches B, which of the following IP header field(s) may be different from that of the original datagram D?**

(i) TTL

(ii) Checksum

(iii) Fragment Offset

(i) TTL

(ii) Checksum

(iii) Fragment Offset

A : (i) only

B : (i) and (ii) only

C : (ii) and (iii) only

D : (i), (ii) and (iii)

.

Correct answer is : D

Question 36

**An IP router implementing Classless Inter-domain routing (CIDR) receives a packet with address 131.23.151.76. The router’s routing table has the following entries. The identifier of the output interface on which this packet will be forwarded is _____.**

.

Correct answer is : 1

Solution :

Given address 131.23.151.76.coming to the first field of given routing table

131.16.0.0/12

131.0001 0111.151.76

131.0001 0000.0.0 ( given mask bits = 12)

131.16.0.0 Matched

Coming to the 2nd field of given Routing table

131.28.0.0/14

131.0001 0111.151.76

131.0001 0100.0.0 ( given mask bits = 14)

131.20.0.0 Not matched.

Coming to the 3rd field of given Routing table

Error! Not a valid link. 131.19.0.0/16

131.0001 0111.151.76

131.0001 0

Question 37

**Every host in an IPv4 network has a 1-second resolution real-time clock with battery backup. Each host needs to generate up to 1000 unique identifiers per second. Assume that each host has a globally unique IPv4 address. Design a 50-bit globally unique ID for this purpose. After what period (in seconds) will the identifiers generated by a host wrap around?**

.

Correct answer is : 256

Solution :

Given that each host has a globally unique IPv4 Address and we have to design 50 – bit unique Id. So, 50 – bit in the sense (32 + 18). So, It is clearly showing that IP Address (32 – bit) followed by 18 bits.

1000 unique Ids => 1Sec

2

^{18}/ 1000 = 2

^{8}= 256

Question 38

**An IP router with a Maximum Transmission Unit (MTU) of 1500 bytes has received an IP packet of size 4404 bytes with an IP header of length 20 bytes. The values of the relevant fields in the header of the third IP fragment generated by the router for this packet are**

A : MF bit: 0, Datagram Length: 1444; Offset: 370

B : MF bit: 1, Datagram Length: 1424; Offset: 185

C : MF bit: 1, Datagram Length: 1500; Offset: 370

D : MF bit: 0, Datagram Length: 1424; Offset: 2960

.

Correct answer is : A

Question 39

**Consider the transactions T1, T2, and T3 and the schedules S1 and S2 given below.**

T1 : r1 (X) ; r1 (z) ; w1 (X) ; w1 (z)

T2 : r2 (X) ; r2 (z) ; w2 (z)

T3 : r3 (X) ; r3 (X) ; w3 (Y)

S1: r1(X); r3(Y); r3(X); r2(Y); r2(Z); w3(Y); w2(Z); r1(Z); w1(X); w1(Z)

S2: r1(X); r3(Y); r2(Y); r3(X); r1(Z); r2(Z); w3(Y); w1(X); w2(Z); w1(Z)

Which one of the following statements about the schedules is TRUE?

T1 : r1 (X) ; r1 (z) ; w1 (X) ; w1 (z)

T2 : r2 (X) ; r2 (z) ; w2 (z)

T3 : r3 (X) ; r3 (X) ; w3 (Y)

S1: r1(X); r3(Y); r3(X); r2(Y); r2(Z); w3(Y); w2(Z); r1(Z); w1(X); w1(Z)

S2: r1(X); r3(Y); r2(Y); r3(X); r1(Z); r2(Z); w3(Y); w1(X); w2(Z); w1(Z)

Which one of the following statements about the schedules is TRUE?

A : Only S1 is conflict-serializable

B : Only S2 is conflict-serializable.

C : Both S1 and S2 are conflict-serializable.

D : Neither S1 nor S2 is conflict-serializable.

.

Correct answer is : A

Solution :

Precedence graph for 1 2 S &S are as follows

Only S1 is conflict serializable.

Question 40

**Consider the relational schema given below, where eId of the relation dependentis a foreign key referring to empId of the relation employee. Assume that every employee has at least one associated dependent in the dependent relation.**

employee (

dependent (

Consider the following relational algebra query

πempId(employee) - π empId( employee <> empId=eID) ∧ (emp Age <= depAge) dependent )

The above query evaluates to the set of empIds of employees whose age is greater than that of

employee (

__empId__, empName, empAge)dependent (

__depId, eId,__depName, depAge)Consider the following relational algebra query

πempId(employee) - π empId( employee <> empId=eID) ∧ (emp Age <= depAge) dependent )

The above query evaluates to the set of empIds of employees whose age is greater than that of

A : some dependent.

B : all dependents.

C : some of his/her dependents.

D : all of his/her dependent

.

Correct answer is : D

Solution :

Part A of the above given relational algebra query will give the set of empIds of those employees whose age is less than or equal to the age of some of his/her dependents. Now when set of empIds of all employees minus set of empIds obtained from part A is done, then we get the set of empIds of employees whose age is greater than that of all of his/her dependents.

Question 41

**A system contains three programs and each requires three tape units for its operation. The minimum number of tape units which the system must have such that deadlocks never arise is _________.**

.

Correct answer is : 7

Question 42

**An operating system uses shortest remaining time first scheduling algorithm for pre-emptive scheduling of processes. Consider the following set of processes with their arrival times and CPU burst times (in milliseconds). The average waiting time (in milliseconds) of the processes is _________.**

.

Correct answer is : 5.5

Solution :

Average waiting time = 15 + 0 +3+4 / 4 =5.5

Question 43

**Consider a paging hardware with a TLB. Assume that the entire page table and all the pages are in the physical memory. It takes 10 milliseconds to search the TLB and 80 milliseconds to access the physical memory. If the TLB hit ratio is 0.6, the effective memory access time (in milliseconds) is _________.**

.

Correct answer is : 122

Question 44

**Consider the basic block given below.**

a = b+ c

c= a+ d

d= b+ c

e= d+ b

a= e+ b

The minimum number of nodes and edges present in the DAG representation of the above basic block respectively are

a = b+ c

c= a+ d

d= b+ c

e= d+ b

a= e+ b

The minimum number of nodes and edges present in the DAG representation of the above basic block respectively are

A : 6 and 6

B : 8 and 10

C : 9 and 12

D : 4 and 14

.

Correct answer is : A

Question 45

**Which one of the following problems is undecidable?**

A : Deciding if a given context-free grammar is ambiguous.

B : Deciding if a given string is generated by a given context-free grammar.

C : Deciding if the language generated by a given context-free grammar is empty.

D : Deciding if the language generated by a given context-free grammar is finite.

.

Correct answer is : A

Solution :

There were algorithms to find the membership of CFG (using CYK algorithm) and finiteness of CFG (using CNF graph) and emptiness. But there is no algorithm for ambiguity of CFG, so it is undecidable.

Question 46

**Consider the following languages over the alphabet S = {0,1,c}**

L1={0

L2={ wcw

L3={ww

Here wr is the reverse of the string w. Which of these languages are deterministic Contextfree languages?

L1={0

^{n}1^{n}| n>=0 }L2={ wcw

^{r}| w ∈ {0,1} *}L3={ww

^{r}| w ∈ {0,1} *}Here wr is the reverse of the string w. Which of these languages are deterministic Contextfree languages?

A : None of the languages

B : Only L1

C : Only L1 and L2

D : All the three languages

.

Correct answer is : C

Solution :

For the languages L1 and L2 we can have deterministic push down automata, so they are DCFL’s, but for L3 only non-deterministic PDA possible. So the language L3 is not a deterministic CFL.

Question 47

**Suppose you want to move from 0 to 100 on the number line. In each step, you either move right by a unit distance or you take a shortcut. A shortcut is simply a pre-specified pair of integers i, j with i < j. Given a shortcut i, j if you are at position i on the number line, you may directly move to j. Suppose T(k) denotes the smallest number of steps needed to move from k to 100. Suppose further that there is at most 1 shortcut involving any number, and in particular from 9 there is a shortcut to 15. Let y and z be such that T(9) = 1 + min(T(y), T(z)). Then the value of the product yz is _____.**

.

Correct answer is : 150

Solution :

By definition, T(9) = Dist. From 9 to 100

As given, T(9) = 1+min (T(y), T()z) = 1+min (Dist. from y to 100, Dist. From z to 100)

1=Dist. from 9 to y/Dist. From 9 to z

There are only two such values-one is the simple one step on number line i.e. 10, and the other is the shortcut associated with 9 i.e. 15.

Therefore, y and z are 10 and 15 (in any order)

Product yz = 150. Answ

Question 48

**Consider the decision problem 2CNFSAT defined as follows:**

{ ∅ | ∅ is a satisfiable propositional formula in CNF with at most two literal per clause}

For example, ∅ = (x1 ∨ &x2) ∧ (x1 ∨ x3`) ∧ (x2 ∨ x4) is a Boolean formula and it is in 2CNFSAT.

The decision problem 2CNFSAT is

{ ∅ | ∅ is a satisfiable propositional formula in CNF with at most two literal per clause}

For example, ∅ = (x1 ∨ &x2) ∧ (x1 ∨ x3`) ∧ (x2 ∨ x4) is a Boolean formula and it is in 2CNFSAT.

The decision problem 2CNFSAT is

A : NP-Complete.

B : solvable in polynomial time by reduction to directed graph reachability.

C : solvable in constant time since any input instance is satisfiable.

D : NP-hard, but not NP-complete.

.

Correct answer is : B

Question 49

**Suppose we have a balanced binary search tree T holding n numbers. We are given two numbers L and H and wish to sum up all the numbers in T that lie between L and H. Suppose there are m such numbers in T. If the tightest upper bound on the time to compute the sum is O( n**

^{a}log^{b}n + m^{c}log^{d}n , the value of a + 10b + 100c + 1000d is _______..

Correct answer is : 110

Solution :

It takes (log n ) time to determine numbers n1 and n2 in balanced binary search tree T such that

1. n1 is the smallest number greater than or equal to L and there is no predecessor n’1 of n1 such that n’1 is equal to n1.

2. n2 is the largest number less than or equal to H and there is no successor of n’2 of n2 such that is equal to n2.

Since there are m elements between n1 and n2, it takes ‘m’ time to add all elements between n1 and n2.

So time complexity is O (log n + m)

Question 50

**Consider a hash table with 100 slots. Collisions are resolved using chaining. Assuming simple uniform hashing, what is the probability that the first 3 slots are unfilled after the first 3 insertions?**

A : (97 × 97 × 97)/100

^{3}

B : (99 × 98 × 97)/100

^{3}

C : (97 × 96 × 95)/100

^{3}

D : (97 × 96 × 95)/(3! × 100

^{3})

.

Correct answer is : A

Question 51

**Consider the pseudocode given below. The function Dosomething () takes as argument a pointer to the root of an arbitrary tree represented by the leftMostChild-rightSibling representation. Each node of the tree is of type treeNode.**

typedef struct treeNode* treeptr; struct treeNode { treeptr leftMostChild, rightSibling; }; int DoSomething (treeptr tree) { int value=0; if (tree != NULL) { if (tree->leftMostChild == NULL) value = 1; else value = DoSomething(tree->leftMostChild); value = value + DoSomething(tree->rightSibling); } return(value); }

A : number of internal nodes in the tree.

B : height of the tree.

C : number of nodes without a right sibling in the tree.

D : number of leaf nodes in the tree.

.

Correct answer is : D

Solution :

The key to solving such questions is to understand or detect where/by what condition the value (or the counter) is getting incremented each time.

Here, that condition is if (tree->leftMostchild == Null)

Which means if there is no left most child of the tree (or the sub-tree or the current nodeas called in recursion)

Which means there is no child to that particular node (since if there is no left most child, there is no child at all).

Which means the node under consideration is a leaf node

Question 52

**Consider the C function given below. Assume that the array listA contains n (> 0) elements, sorted in ascending order.**

int ProcessArray (int * listA, int x, int n)

{

Int 1, j, k;

i = 0;

j = n – 1;

do { k = (i + j) /2;

if (x < = listA [k]) j = k – 1;

If (listA [k] < = x) i = k+1;

}

while (1 < = j);

If (listA [k] = = x)

return (k) ;

else return -1;

}

Which one of the following statements about the function ProcessArray is CORRECT?

int ProcessArray (int * listA, int x, int n)

{

Int 1, j, k;

i = 0;

j = n – 1;

do { k = (i + j) /2;

if (x < = listA [k]) j = k – 1;

If (listA [k] < = x) i = k+1;

}

while (1 < = j);

If (listA [k] = = x)

return (k) ;

else return -1;

}

Which one of the following statements about the function ProcessArray is CORRECT?

A : It will run into an infinite loop when x is not in listA.

B : It is an implementation of binary search

C : It will always find the maximum element in listA.

D : It will return – 1 even when x is present in listA.

.

Correct answer is : B

Solution :

By the logic of the algorithm it is clear that it is an attempted implementation of Binary Search. So option C is clearly eliminated. Let us now check for options A and D.

A good way to do this is to create small dummy examples (arrays) and implement the algorithm as it is. One may make any array of choice. Running iterations of the algorithm would indicate that the loop exits when the x is not present. So option A is wrong. Also, when x is present, the correct index is indeed returned. D is

Question 53

**An instruction pipeline has five stages, namely, instruction fetch (IF), instruction decode and register fetch (ID/RF), instruction execution (EX), memory access (MEM), and register writeback (WB) with stage latencies 1 ns, 2.2 ns, 2 ns, 1 ns, and 0.75 ns, respectively (ns stands for nanoseconds). To gain in terms of frequency, the designers have decided to split the ID/RF stage into three stages (ID, RF1, RF2) each of latency 2.2/3 ns. Also, the EX stage is split into two stages (EX1, EX2) each of latency 1 ns. The new design has a total of eight pipeline stages. A program has 20% branch instructions which execute in the EX stage and produce the next instruction pointer at the end of the EX stage in the old design and at the end of the EX2 stage in the new design. The IF stage stalls after fetching a branch instruction until the next instruction pointer is computed. All instructions other than the branch instruction have an average CPI of one in both the designs. The execution times of this program on the old and the new design are P and Q nanoseconds, respectively. The value of P/Q is __________.**

.

Correct answer is : 1.54

Question 54

**The memory access time is 1 nanosecond for a read operation with a hit in cache, 5 nanoseconds for a read operation with a miss in cache, 2 nanoseconds for a write operation with a hit in cache and 10 nanoseconds for a write operation with a miss in cache. Execution of a sequence of instructions involves 100 instruction fetch operations, 60 memory operand read operations and 40 memory operand write operations. The cache hit-ratio is 0.9. The average memory access time (in nanoseconds) in executing the sequence of instructions is __________.**

.

Correct answer is : 1.68

Solution :

Total instruction= 100 instruction fetch operation + 60 memory operand read operation + 40 memory operand write op;

= 200 instructions (operations)

Time taken for fetching 100 instructions (equivalent to read) = 90*1ns +10*5ns =140ns

Memory operand Read operations = 90%(60)*1ns +10%(60)×5ns = 54ns + 30ns = 84ms

Memory operands write operation time = 90%(40)*2ns +10%(40)*10ns = 72ns + 40ns =112ns

Total time taken for executing 200 instructions =140 + 84 +112 = 336ns

Average memo

Question 55

**The below given synchronous sequential circuit built using JK flip-flops is initialized with Q2Q1Q0 = 000. The state sequence for this circuit for the next 3 clock cycles is**

A : 001, 010, 011

B : 111, 110, 101

C : 100, 110, 111

D : 100, 011, 001

.

Correct answer is : C

Question 56

**With respect to the numerical evaluation of the definite integral, K= ∫**

(I) The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral.

(II) The value of K obtained using the Simpson’s rule is always equal to the exact value of the definite integral.

^{b}a x^{2}dx, where a and b are given, which of the following statements is/are TRUE?(I) The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral.

(II) The value of K obtained using the Simpson’s rule is always equal to the exact value of the definite integral.

A : I only

B : II only

C : Both I and II

D : Neither I and II

.

Correct answer is : C

Question 57

**The value of the integral given below is**

A : -2π

B : π

C : -π

D : 2π

.

Correct answer is : A

Question 58

**Let S be a sample space and two mutually exclusive events A and B be such that A ∪ B = S. If P(.) denotes the probability of the event, the maximum value of P(A)P(B) is ______ A**

.

Correct answer is : 0.25

Question 59

**Consider the set of all functions f :{0,1,...,2014}->{0,1...,2014} such that f (f (i)) = i, for 0 <= i<= 2014 .**

Consider the following statements.

P. For each such function it must be the case that for every i, f(i) = i,

Q. For each such function it must be the case that for some i,f(i) = i,

R. Each such function must be onto.

Which one of the following is CORRECT?

Consider the following statements.

P. For each such function it must be the case that for every i, f(i) = i,

Q. For each such function it must be the case that for some i,f(i) = i,

R. Each such function must be onto.

Which one of the following is CORRECT?

A : P, Q and R are true

B : Only Q and R are true

C : Only P and Q are true

D : Only R is true

.

Correct answer is : B

Solution :

Let us consider a function (counter example) as

f(0)=1,f(1) =0,f(2)=3,f(3)=2,.........,f(2012)=2013,f(2013)=2012 andf(2014)=2014

Clearly f (f (i))= i for 0<= i <=2014

Here f(i) ≠ i for every i and f(i) = i for some i

Also f is onto

Hence , only Q and R are true

Question 60

**There are two elements x,y in a group (G,*) such that every element in the group can be written as a product of some number of x’s and y’s in some order. It is known that**

x * x = y * y = x * y *x * y = y* x * y *x = e

where e is the identity element. The maximum number of elements in such a group is _________________.

x * x = y * y = x * y *x * y = y* x * y *x = e

where e is the identity element. The maximum number of elements in such a group is _________________.

.

Correct answer is : 4

Question 61

**If G is a forest with n vertices and k connected components, how many edges does G have?**

A : [n / k]

B : [n / k]

C : n-k

D : n-k+1

.

Correct answer is : C

Solution :

Let n1 ,n2 ,.....nk be the number of vertices respectively in K connected components of a forest G, then n1 ?1,n2 ?1,.....,nk ?1 be the number of edges respectively in K connected components and n1 + n2 + ..... + nk = n (number of vertices in G)

Hence, number of edges in G = number of edges in K connected components

(n1-1)+(n2-1)+..........+(nk-1) = n-k

Question 62

**Let d denote the minimum degree of a vertex in a graph. For all planar graphs on n vertices with d>=3, which one of the following is TRUE?**

A : In any planar embedding, the number of faces is at least n/2 +2

B : In any planar embedding, the number of faces is less than n/2 +2

C : There is a planar embedding in which the number of faces is less than n /2 +2

D : There is a planar embedding in which the number of faces is at most n /d +1

.

Correct answer is : A

Solution :

We know that v + r = e + 2e = n + r ? 2 ...(1)

Where V= n(number of vertices); r =number of faces and e =number of edges

Given d>=3 then 3n <=2e

e>=3n/2

n+r-2>=3n/2 (using(1))

r>=3n/2 -n +2 => r>= n/2 +2

No.of faces is atleast n/2 + 2

Question 63

**The CORECT formula for the sentence, “not all rainy days are cold” is**

A : ∀d (Rainy(d) ∧ ~Cold(d))

B : ∀d ( ~Rainy(d)->Cold(d))

C : ∃d(~Rainy(d) -> Cold(d))

D : ∃d (Rainy(d) ∧ Cold(d))

.

Correct answer is : D

Question 64

**Consider the following relational schema:**

Employee (empId, empName, empDept )

Customer (custId,custName, salesRepId, rating)

SalesRepId is a foreign key referring to empId of the employee relation. Assume that each employee makes a sale to at least one customer. What does the following query return?

SELECT empName

FROM employee E

WHERE NOT EXISTS (SELECT custId

FROM customer C

WHERE C. salesRepId = E. empId

AND C. rating < > ‘GOOD’)

Employee (empId, empName, empDept )

Customer (custId,custName, salesRepId, rating)

SalesRepId is a foreign key referring to empId of the employee relation. Assume that each employee makes a sale to at least one customer. What does the following query return?

SELECT empName

FROM employee E

WHERE NOT EXISTS (SELECT custId

FROM customer C

WHERE C. salesRepId = E. empId

AND C. rating < > ‘GOOD’)

A : Names of all the employees with at least one of their customers having a ‘GOOD’ rating.

B : Names of all the employees with at most one of their customers having a ‘GOOD’ rating.

C : Names of all the employees with none of their customers having a ‘GOOD’ rating.

D : Names of all the employees with all their customers having a ‘GOOD’ rating.

.

Correct answer is : D

Solution :

The outer query will return the value (names of employees) for a tuple in relation E, only if inner query for that tuple will return no tuple (usage of NOT EXISTS).

The inner query will run for every tuple of outer query. It selects cust-id for an employee e, if rating of customer is NOT good. Such an employee should not be selected in the output of outer query.

So the query will return the names of all those employees whose all customers have GOOD rating.

Question 65

**Let ⊕ denote the Exclusive OR (XOR) operation. Let ‘1’ and ‘0’ denote the binary constants. Consider the following Boolean expression for F over two variables P and Q.**

F(P,Q) = ((1⊕P)⊕(P⊕Q))⊕((P⊕Q)⊕(Q⊕0))

The equivalent expression for F is

F(P,Q) = ((1⊕P)⊕(P⊕Q))⊕((P⊕Q)⊕(Q⊕0))

The equivalent expression for F is

A : P+Q

B : (P+Q)`

C : P ⊕ Q

D : (P ⊕Q)`

.

Correct answer is : D

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