# GATE Numerical Answer Questions

Question 1

**The exports and imports (in crores of Rs.) of a country from the year 2000 to 2007 are given in the following bar chart. In which year is the combined percentage increase in imports and exports the highest?**

.

Correct answer is =206

Solution :

Increase in exports in 2006= (100-70)/70 = 42.8%

Increase in imports in 2006=(120-90)/90 = 33.3%

which is more than any other year

Question 2

**Given a has table T with 25 slots that stores 2000 elements, the load factor for T is ___________.**

.

Correct answer is =80

Solution :

Load factor = no of elements / no of slots = 2000/25 = 80

Question 3

**Consider a software project with the following information domain characteristics for calculation of function point metric.**

Number of external inputs (I) = 30

Number of external outputs (O) = 60

Number of external inquiries (E) = 23

Number of files (F) = 08

Number of external interfaces (N) = 02

It is given that the complexity weighting factors for I, O, E, F and N are 4,5,4,10 and 7, respectively. It is also given that, out of fourteen value adjustment factors that influence the development effort, four factors are not applicable, each of the other four factors have value 3, and each of the remaining factors have value 4. The computed value of function point metric is _________.

Number of external inputs (I) = 30

Number of external outputs (O) = 60

Number of external inquiries (E) = 23

Number of files (F) = 08

Number of external interfaces (N) = 02

It is given that the complexity weighting factors for I, O, E, F and N are 4,5,4,10 and 7, respectively. It is also given that, out of fourteen value adjustment factors that influence the development effort, four factors are not applicable, each of the other four factors have value 3, and each of the remaining factors have value 4. The computed value of function point metric is _________.

.

Correct answer is =612.06

Question 4

**The number of 4 digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set {1,2,3} is _____ .**

.

Correct answer is =15

Solution :

4-digit numbers with first digit ‘1’

1111, 1112, 1113, 1122, 1123, 1133, 1222, 1223, 1233, 1333 i.e., 10

4 digit numbers with first digit 2 : 2222, 2223, 2233, 2333 i.e, 4

4 digit numbers with first digit 3: 3333 i.e, 1

Question 5

**Consider a software program that is artificially seeded with 100 faults. While testing this program, 159 faults are detected, out of which 75 faults are from those artificially seeded faults. Assuming that both are and seeded faults are of same nature and have same distribution, the estimated number of undetected real fault is _____ .**

.

Correct answer is =175

Question 6

**Consider a binary tree T that has 200 leaf nodes. Then, the number of nodes in T that have exactly two children are ____ .**

.

Correct answer is =199

Solution :

Let the number of leaf nodes of a binary tree with ‘n’ vertices be ‘p’ then the tree has

(i) ‘p’ vertices of degree ‘1’

(ii) one vertex (i.e. root of T) of degree ‘2’.

(iii) 'n - p - 1' vertices of degree ‘3’

(iv) 'n - 1' edges

By Handshaking theorem,

p×1+1× 2 + (n - p - 1)×3 = 2(n - 1)

n=2p-1

=399 as p =200

Number of nodes having exactly two children are n - p i.e., 199

Question 7

**Consider a B+ tree in which the search Answeris 12 bytes long, block size is 1024 bytes, record pointer is 10 bytes long and block pointer is 8 bytes long. The maximum number of keys that can be accommodated in each non-leaf node of the tree is ____ .**

.

Correct answer is =50

Solution :

Suppose that ‘k’ is order of the non-leaf node

k(8)+(k-1)12 <= 1024

20k<=1036

k<=|_1036/20_| => k<=51

As the order is 51, maximum we can store 50 keys.

Question 8

**Suppose Xi for i=1,2,3 ar independent and identically distributed random variables whose probability mass functions are Pr [Xi = 0] = Pr [Xi =1] =1/ 2 for i =1,2,3. Define another random variable Y = X1 X2 ⊕ X , where ⊕ denotes XOR.Then Pr [Y = 0| X3 = 0] = _____ .**

.

Correct answer is =0.75

Question 9

**The total number of prime implicates of the function**

f (w,x, y,z) = ∑ (0,2,4,5,6,10) is ____ .

f (w,x, y,z) = ∑ (0,2,4,5,6,10) is ____ .

.

Correct answer is =3

Solution :

There are three groups, and all the containing esential-1, so all are prime implicants as well as essential prime implicants also.

Question 10

**Consider the equation (43)**

_{x}= (y3)_{8}where x and y are unknown. The number of possible solution is_______ ..

Correct answer is =5

Solution :

(43)

_{x}= (y3)

_{8}

3+4x = 3+8y=> 4x = 8y

=> x = 2y

x>=5 and y<= 7

Therefore 5 solutions are possible which are (14,7), (12,6), (10,5), (8,4) and (6,3)

Question 11

**Suppose c = (c[0],....,c[k - 1]) is an array of length k, where all the entries are from the set {0, 1}. For any positive integers a and n, consider the following pseudo code. DOSOMETHING (c, a, n)**

z <- 1

for - <- 0 to k-1

do z <- z

ifc[i]=1

then z <- (z*a) mod n

return z

If k = 4, c =( 1.0,1,1 ), a=2 and n = 8, then the output of DOSOMETHING (c, a, n) is _____________.

z <- 1

for - <- 0 to k-1

do z <- z

^{2}mod nifc[i]=1

then z <- (z*a) mod n

return z

If k = 4, c =( 1.0,1,1 ), a=2 and n = 8, then the output of DOSOMETHING (c, a, n) is _____________.

.

Correct answer is =0

Question 12

**The velocity v (in kilometer/minute) of a motorbike which start from rest, is given at fixed intervals of time t (in minutes as follows.**

The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson’s 1/3rd rule is ________.

t | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |

10 | v | 18 | 25 | 29 | 32 | 20 | 11 | 5 | 2 | 0 |

The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson’s 1/3rd rule is ________.

.

Correct answer is =309.33

Solution :

Let ‘S’ be the distance covered in 20 minutes, then by simpson’s 1/3rd rule

= 2/3[(0+0)+4(10+25+32+11+2)+2(18+29+20+5)]

=309.33km (Here length of each of the subinterval is h = 2)

Question 13

**Consider the following C program**

#include

int main ()

{

static int a =[10, 20, 30 40, 50] ;

static int * p =[a, a+ 3, a+ 4, a +1, a+ 2] ;

int **ptr =p;

ptr++ ;

printf( "%d%d", ptr- p, **ptr) ;

}

The output of the program is __________.

#include

int main ()

{

static int a =[10, 20, 30 40, 50] ;

static int * p =[a, a+ 3, a+ 4, a +1, a+ 2] ;

int **ptr =p;

ptr++ ;

printf( "%d%d", ptr- p, **ptr) ;

}

The output of the program is __________.

.

Correct answer is =140

Question 14

**Let G be a connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a minimum spanning tree becomes __________.**

.

Correct answer is =995

Solution :

G has 100 verticles => spanning tree contain 99 edges given, weight of a minimum spanning tree of G is 500 since, each edge of G is increased by five

Weight of a minimum spanning tree becomes 500 + 5 × 99 = 995

Question 15

**Consider a network connected two systems located 8000 kilometers apart. The bandwidth of the network is 500 × 10**

^{6}bits per second. The propagation speed of the media is 4 × 10^{6}meters per second. It is needed to design a Go-Back-N sliding window protocol for this network. The average packet size is 10^{7}bits. The network is to be used to its full capacity. Assume that processing delays at nodes are negligible. Then the minimum size in bits of the sequence number field has to be ___________..

Correct answer is =8

Question 16

**Consider the following reservation table for a pipeline having three stages S1, S2, and S3.**

The minimum average latency (MAL) is ________.

The minimum average latency (MAL) is ________.

.

Correct answer is =*

Question 17

**In the network 200.20.11.144/27, the fourth octet (in decimal) of the last IP address of the network which can be assigned to a host is ________.**

.

Correct answer is =158

Solution :

Given IP address 200.20.11.144/27

To find out the loss address in a block, we have to set (32-n) no. of right most bits to 1.

n=27

32 - n = 32 - 27 = 5

200.20.11.10010000

200.20.11.10011111

200.20.11.159

CIDR Address range is 200.20.11.128/27-200.20.11.159/27

But w.r.t the question, the value of the last octet of last host in this network is 200.10.11.158.

Question 18

**Consider the following C program ( )**

#inclue

int main

{

int i, j, k 0;

j= 2*3 /4+ 2.0 / 5 +8 / 5;

k-= - - j;

for (i= 0; i< 5; i + +)

{

Switch (i + k)

{

case1:

case 2 : printf ("\ n%d", i+k);

case 3: printf( "\ n%d", i+ k);

default : printf( "\ n%d", i+ k) ;

}

Return 0:

}

The number of times printf statement is executed is _________.

#inclue

int main

{

int i, j, k 0;

j= 2*3 /4+ 2.0 / 5 +8 / 5;

k-= - - j;

for (i= 0; i< 5; i + +)

{

Switch (i + k)

{

case1:

case 2 : printf ("\ n%d", i+k);

case 3: printf( "\ n%d", i+ k);

default : printf( "\ n%d", i+ k) ;

}

Return 0:

}

The number of times printf statement is executed is _________.

.

Correct answer is =10

Solution :

j and k will be evaluated to 2 and -1 respectively.

In for loop:

When i = 0; 1 time printed (-1)

When i = 1; 1 time printed (0)

When i = 2; 3 times printed (1,1,1)

When i = 3; 3 times printed (2,2,2)

When i = 4; 2 times printed (3,3)

on the whole printf is executed 10 times

Question 19

**Consider the following C program.**

#include

int f1 (void) ;

int f 2 (void)

; int x 10;

int main ()

{

int x 1;

x +=f1()+ f2()+ f3()+ f2() ;

printf( "%d", x) ;

return 0;

}

int f1() { int x 25; x++ ; return x;}

int f2()

{ static int x 50; x++ ; return x;}

int f3(){ x* 10; return x ;}

The output of the program is_________.

#include

int f1 (void) ;

int f 2 (void)

; int x 10;

int main ()

{

int x 1;

x +=f1()+ f2()+ f3()+ f2() ;

printf( "%d", x) ;

return 0;

}

int f1() { int x 25; x++ ; return x;}

int f2()

{ static int x 50; x++ ; return x;}

int f3(){ x* 10; return x ;}

The output of the program is_________.

.

Correct answer is =230

Solution :

static variable in f2() will be initialized only once & it retains value in between function calls.

Question 20

**Two hosts are connected via a packet switch with 10**

^{7}bits per second links. Each link has a propagation. Delay of 20 microseconds. The switch begins forwarding a packet 35 microseconds after it receives the same. If 1000 bits of data are to be transmitted between the two hosts using a packet size of 5000 bits, the time elapsed between the transmission of the first bit of data and the reception of the last of the data in microsecond is _________..

Correct answer is =1575

**MY REPORT**

TOTAL = 20 | |||

ANSWERED = | |||

CORRECT / TOTAL = | /20 | ||

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