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Delhi University Entrance Test (DUET) 2020 Previous Year Question Paper With Answer Key

This post was last modified on 27 December 2020

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DUET Last 10 Years 2011-2021 Question Papers With Answer Key || Delhi University Entrance Test conducted by the NTA

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Topic:- CS PHD S2N_P1

Consider the following recursive function fun(x, y). What is the value of fun(4, 3)
```
int fun(int x, int y)
{ if (x == 1) return y; return fun(x-1, y+1);
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} 
```
[Question ID = 10768]
1. 13 [Option ID = 43066]
2. 4
3. 6 [Option ID = 43071]
4. 10 [Option ID = 43072]
Correct Answer :- 6 [Option ID = 43071]

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What will be the value of x after execution of the following loop, if the initial value of x was 11?
```
for(int i=x--; i<2*x; x--) { i=i+x; } 
```
[Question ID = 10771]
1. 11 [Option ID = 43078]
2. 0 [Option ID = 43079]
3. Infinite loop [Option ID = 43080]
4. 9 [Option ID = 43081]
Correct Answer :- 9 [Option ID = 43081]

What will be the output of the following code?
```
#include <iostream>
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using namespace std;
int fun(int x = 0, int y = 0, int z)
{ return (x + y + z); } int main()
{ cout << fun(10); return 0;
} 
```
[Question ID = 10772]
1. 10 [Option ID = 43082]
2. 0 [Option ID = 43084]
3. 20 [Option ID = 43086]
4. Compilation Error [Option ID = 43088]
Correct Answer :- Compilation Error [Option ID = 43088]

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Which of the following type of class allows only one object of it to be created? [Question ID = 10775]
1. Virtual class [Option ID = 43093]
2. Abstract class [Option ID = 43095]
3. Singleton class [Option ID = 43096]
4. Friend class [Option ID = 43097]
Correct Answer :- Singleton class [Option ID = 43096]

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What will be the value of z after execution of d = x && y || z++; if initial values of x, y and z are 1, 0 and 5 respectively. [Question ID = 10776]
1. 6 [Option ID = 43098]
2. 5 [Option ID = 43100]
3. 0 [Option ID = 43102]
4. undefined [Option ID = 43104]
Correct Answer :- 6 [Option ID = 43098]

A B-tree of order 4 is built from scratch by 10 successive insertions. What is the maximum number of node splitting operations that may take place? [Question ID = 10779]
1. 7 [Option ID = 43109]
2. 4 [Option ID = 43111]
3. 5 [Option ID = 43112]
4. 6 [Option ID = 43113]
Correct Answer :- 5 [Option ID = 43112]

Given two max heaps of size n each, what is the minimum possible time complexity to make a one max-heap of size 2n from elements of two max heaps? [Question ID = 10780]
1. (log n) [Option ID = 43114]
2. O(log n) but not (log n) [Option ID = 43116]
3. O(n) [Option ID = 43118]
4. O(n²) but not O(n) [Option ID = 43120]
Correct Answer :- O(n) [Option ID = 43118]

Suppose that we have numbers between 1 and 100 in a binary search tree and want to search for the number 55. Which of the following sequences CANNOT be the sequence of nodes examined? [Question ID = 10783]
1. {10, 75, 64, 43, 60, 57, 55} [Option ID = 43125]
2. {90, 12, 68, 34, 62, 45, 55} [Option ID = 43127]
3. (9, 85, 47, 68, 43, 57, 55} [Option ID = 43128]
4. (79, 14, 72, 56, 16, 53, 55} [Option ID = 43129]
Correct Answer :- {9, 85, 47, 68, 43, 57, 55} [Option ID = 43128]

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Which of the following permutation can be obtained in the same order using a stack assuming that input is the sequence 5, 6, 7, 8, 9 in that order? [Question ID = 10784]
1. 7, 8, 9, 5, 6 [Option ID = 43130]
2. 5, 9, 6, 7, 8 [Option ID = 43133]
3. 7, 8, 9, 6, 5
Correct Answer :- 7, 8, 9, 6, 5 [Option ID = 43135]

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The following function reverse() is supposed to reverse a singly linked list. There is one line missing at the end of the function.
```
/* Link list node */
struct node
{ int data; struct node* next;
}; /* head_ref is a double pointer which points to head (or start) pointer
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of linked list */
static void reverse(struct node** head_ref)
{ struct node* prev = NULL; struct node* current = *head_ref; struct node* next; while (current != NULL) { next = current->next; current->next = prev; prev = current; current = next; } /*ADD A STATEMENT HERE*/
} 
```
What should be added in place of "/*ADD A STATEMENT HERE*/", so that the function correctly reverses a linked list. [Question ID = 10787]
1. *head_ref = prev; [Option ID = 43141]
2. *head_ref = current;
3. *head_ref = next; [Option ID = 43144]
4. *head_ref = NULL; [Option ID = 43145]
Correct Answer :- *head_ref = prev; [Option ID = 43141]

The recurrence relation
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T(1) = 2
T(n) =3T(n/4)+n
has solution T(n) equal to [Question ID = 10788]
1. O(n) [Option ID = 43146]
2. O(log n) [Option ID = 43148]
3. O(nlog4(3)) [Option ID = 43150]
4. None of these [Option ID = 43152]
Correct Answer :- O(n) [Option ID = 43146]

The characters a to h have the set of frequencies based on the first 8 Fibonacci numbers as follows:
a:1, b:1, c:2, d:3, e:5, f:8, g:13, h:21
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A Huffman code is used to represent the characters. What is the sequence of characters corresponding to the following code :
110111100111010 [Question ID = 10791]
1. fdheg [Option ID = 43158]
2. ecgdf [Option ID = 43159]
3. dchfg [Option ID = 43160]
4. fehdg [Option ID = 43161]
Correct Answer :- fdheg [Option ID = 43158]

If the tower of Hanoi problem is solved using divide and conquer approach then the running time to solve the problem with 'n' disks is [Question ID = 10793]
1. O(n)
2. O(n²) [Option ID = 43166]
3. O(2ⁿ) [Option ID = 43167]
4. O((1/2) ⁿ) [Option ID = 43169]
Correct Answer :- O(2ⁿ) [Option ID = 43167]

Suppose we have a O(n) time algorithm that finds median of an unsorted array. Now consider a QuickSort implementation where we first find median using the above algorithm, then use median as pivot. What will be the worst case time complexity of this modified QuickSort. [Question ID = 10794]
1. O(n² log n) but not O(n²) [Option ID = 43170]
2. O(n²) but not O(n log n) [Option ID = 43172]
3. O(n log log n) [Option ID = 43174]
4. O(n log n) [Option ID = 43176]
Correct Answer :- O(n log n) [Option ID = 43176]

There are three members: x, y and z; in a committee. An issue will be decided 'yes' if and only if all three of them say 'yes'. Which of the following Boolean expression represents the above problem? [Question ID = 10797]
1. x + y + z
2. xy + xyz + yz
3. xyz
4. x + y + z'
Correct Answer :- xyz [Option ID = 43184]

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_________ shift operation multiplies a signed binary number by 2. [Question ID = 10798]
1. logical left
2. logical right
3. arithmetic left [Option ID = 43191]
4. arithmetic right
Correct Answer :- arithmetic left [Option ID = 43191]

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In a byte-addressable RAM, an instruction at address 1206 is under execution. The address field of this instruction has the value 1755. The value at location 1755 is 2000. Size of an instruction is 2 bytes. What will be the contents of the Program Counter after the fetch phase of the instruction cycle? [Question ID = 10801]
1. 1207 [Option ID = 43197]
2. 1208 [Option ID = 43199]
3. 1755 [Option ID = 43200]
4. 2000 [Option ID = 43201]
Correct Answer :- 1208 [Option ID = 43199]

Let P and Q be two propositions, - (PQ) is equivalent to:
(1) P->Q
(II)-P->Q
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(III)-P->Q
(IV) Q->P
[Question ID = 10802]
1. Only (1) and (II) [Option ID = 43202]
2. Only (II) and (III) [Option ID = 43204]
3. Only (III) and (IV) [Option ID = 43206]
4. Only (III) [Option ID = 43208]
Correct Answer :- Only (1) and (II) [Option ID = 43202]

Consider the graph given below. The two distinct sets of vertices, which make the graph bipartite are:

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[Question ID = 10805]
1. (v1,v4,v6); (v2, v3, v5, v7, v8) [Option ID = 43214]
2. (v1, v4, v7, v8); (v2, v3, v5, v6)
3. (v1, v4, v6, v7); (v2, v3, v5, v8) [Option ID = 43216]
4. (v1, v4, v6, v7, v8); (v2, v3, v5) [Option ID = 43217]
Correct Answer :- (v1, v4, v6, v7); (v2, v3, v5, v8) [Option ID = 43216]

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Let S be a set of n elements. The number of ordered pairs in the largest and the smallest equivalence relation defined on the set S, respectively, are: [Question ID = 10806]
1. n² and n
2. n and n
3. n² and 0
4. n and 1
Correct Answer :- n² and n

How many time is "yes" printed by the following program?
```
main()
{ fork(); fork(); cout << "yes";
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} 
```
[Question ID = 10809]
1. Once [Option ID = 43229]
2. Twice [Option ID = 43231]
3. Four times [Option ID = 43232]
4. Eight times [Option ID = 43233]
Correct Answer :- Four times [Option ID = 43232]

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Consider a system with 32 bit virtual addresses and 1 KB page size. Why is it not possible to use one - level page tables for virtual to physical address translation? [Question ID = 10810]
1. The large memory overhead in maintaining page tables
2. The large computation overhead in the translation process
3. The amount of external fragmentation
4. The amount of internal fragmentation
Correct Answer :- The large memory overhead in maintaining page tables

What is the maximum length of the cable (in km) for transmitting data at a rate of 500 Mbps in an Ethernet LAN with frames of size 10,000 bits? Assume the signal speed in the cable to be 2,00,000 km/s. [Question ID = 10813]
1. 1 [Option ID = 43245]
2. 2 [Option ID = 43246]
3. 2.5 [Option ID = 43248]
4. 5 [Option ID = 43249]
Correct Answer :- 2 [Option ID = 43246]

Consider the following activities related to email
m1: Send an email from mail client to mail server
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m2: Download an email from mailbox server to mail client
m3: Checking email on a browser
Which application level protocol is used in each of the activity: [Question ID = 10814]
1. m1: HTTP; m2: SMTP; m3:POP [Option ID = 43250]
2. m1:SMTP; m2:FTP; m3:HTTP [Option ID = 43252]
3. m1:SMTP; m2: POP; m3: HTTP [Option ID = 43254]
4. m1:POP; m2:SMTP; m3: HTTP [Option ID = 43256]
Correct Answer :- m1:SMTP; m2: POP; m3: HTTP [Option ID = 43254]

There are three coins in a box. One is a two-headed coin, another is a fair coin, and third is a biased coin that comes up heads 75% of the time. When one of the three coins is selected at random and flipped, it shows heads. What is the probability that it was two headed coin? [Question ID = 10817]
1. 1
2. 2/9
3. 4/9
4. 5/9
Correct Answer :- 4/9

An examination paper has 100 multiple choice questions of three mark each, with each question having four choices. Each incorrect answer fetches -1 mark. Suppose 100 students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained by all these students is [Question ID = 10818]
1. 0 [Option ID = 43266]
2. 250 [Option ID = 43267]
3. 752 [Option ID = 43268]
4. 975 [Option ID = 43270]
Correct Answer :- 0 [Option ID = 43266]

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Which of the following is an ethical violation in research?
i. Duplicate publication of research papers
ii. Duplicate submission of research papers
iii. Unrevealed conflicts of interest
iv. Use of selective data to support claims
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[Question ID = 10821]
1. Only i [Option ID = 43275]
2. Only ii [Option ID = 43276]
3. Only i, ii and iv [Option ID = 43279]
4. All i, ii, iii and iv
Correct Answer :- All i, ii, iii and iv

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Which of the following is not a research funding agency in India? [Question ID = 10822]
1. Science and Engineering Research Board [Option ID = 43282]
2. Indian Council of Historical Research [Option ID = 43283]
3. National Science Foundation [Option ID = 43285]
4. Indian Council of Social Science Research [Option ID = 43287]
Correct Answer :- National Science Foundation [Option ID = 43285]

Which of the following is not part of the research design strategy? [Question ID = 10825]
1. Data collection [Option ID = 43292]
2. Data analysis [Option ID = 43294]
3. Algorithm development [Option ID = 43296]
4. Sampling [Option ID = 43297]
Correct Answer :- Data analysis [Option ID = 43294]

During research, review of relevant literature means [Question ID = 10827]
1. To know about the already work done on the topic [Option ID = 43302]
2. To know the concepts and theories applied on the topic [Option ID = 43303]
3. The authors who contributed on the topic [Option ID = 43304]
4. All of the above [Option ID = 43306]
Correct Answer :- All of the above [Option ID = 43306]

The abbreviation et.al., refers to [Question ID = 10830]
1. and others
2. extra and
3. almost
4. extra almost
Correct Answer :- and others

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Consider the following publication data of a journal:

Year No. of Citations No. of Articles Published

2017 121 52

2018 162 50

This journal has ________ impact factor in the year ________ [Question ID = 10832]
1. 2.77, 2018 [Option ID = 43320]
2. 2.77, 2019 [Option ID = 43321]
3. 2.32, 2017 [Option ID = 43323]
4. 3.24, 2018 [Option ID = 43325]
Correct Answer :- 2.77, 2019 [Option ID = 43321]

The number of linearly independent eigen vector(s) of a matrix A=

3 3

3 3

is [Question ID = 10833]
1. 0 [Option ID = 43326]
2. 1 [Option ID = 43328]
3. 2 [Option ID = 43330]
4. Infinite [Option ID = 43331]
Correct Answer :- 1 [Option ID = 43328]

Let A be an m x n matrix, with m < n, and such that every solution of the linear system of equations Ax = 0, is a linear et consistent system of equations. The highest possible rank of A is [Question ID = 10836]
1. 1 [Option ID = 43336]
2. 2 [Option ID = 43338]
3. 3 [Option ID = 43340]
4. 4 [Option ID = 43341]
Correct Answer :- 2 [Option ID = 43338]

Year	No. of Citations	No. of Articles Published
2017	121	52
2018	162	50

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In the software testing, the cumulative number of faults m(t) can be modelled using an ODE
m'(t) = [a-m(t)]; where 'a' is initial fault in the software and 'b' is constant. Assuming m(0) = 0; the solution of the differential equation is given by [Question ID = 10837]
1. m(t) = a[1-e^-bt] [Option ID = 43342]
2. m(t) = a[1-(1+bt)e^-bt] [Option ID = 43343]
3. m(t) = a(1+bt)e^bt [Option ID = 43344]
4. m(t) = a / (1+bt) [Option ID = 43345]
Correct Answer :- m(t) = a[1-(1+bt)e^-bt] [Option ID = 43343]

Which of the following is a possible solution of the differential equation d²y/dx² + 4 dy/dx + 4y = 0 [Question ID = 10840]
1. e^-3x [Option ID = 43353]
2. xe^-x [Option ID = 43355]
3. xe^-2x [Option ID = 43356]
4. x²e^-2x [Option ID = 43357]
Correct Answer :- xe^-2x [Option ID = 43356]

Consider the real vector space R³. Then the coordinate vector of (3,1, -4) relative to the basis {(1,1,1), (0,1,1), (0,0,1)} is [Question ID = 10842]
1. (3, 1, -4)
2. (3, -2, -4)
3. (3, -2, -5)
4. (3, -2, -6)
Correct Answer :- (3, -2, -5)

lim_x?0 (tan x sin x) / x³ equals [Question ID = 10843]
1. 1/2
2. -1/2
3. 5/6
4. -5/6
Correct Answer :- -1/2

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The condition for the system of equations x+2y-3z = a, 2x+6y-11z = b, x-2y+7z = c to be consistent is [Question ID = 10846]
1. a + b - c = 0
2. 3a + 2b + c = 0
3. 5a-2b-c = 0
4. None of these
Correct Answer :- 5a-2b-c = 0

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The inverse of the matrix

3 5

5 9

in GL(2,Z11) is [Question ID = 10847]
1. (9,2)
2. (10,3)
3. (10,8)
4. none of these
Correct Answer :- (10,8)

lim_x?0+ x² ln x equals [Question ID = 10850]
1. 1 [Option ID = 43392]
2. 0 [Option ID = 43394]
3. -1 [Option ID = 43396]
4. does not exist [Option ID = 43397]
Correct Answer :- 0 [Option ID = 43394]

Choose the correct statement for the sequence {(-1)^n-1}: [Question ID = 10851]
1. sequence is monotonically increasing [Option ID = 43398]
2. sequence is monotonically decreasing [Option ID = 43399]
3. sequence is bounded [Option ID = 43400]
4. limit of the sequence exists [Option ID = 43401]
Correct Answer :- sequence is bounded [Option ID = 43400]

What is the value of the integral ?^a_-a dx? [Question ID = 10854]
1. 0
2. a/2
3. a
4. 2a
Correct Answer :- a/2

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The area enclosed between the curves y² = 4x and x² = 4y is [Question ID = 10855]
1. 16/3
2. 8
3. 32/3
4. 16
Correct Answer :- 16/3

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Topic:- CS PHD S2N_P2

Next Question is based on the following passage
According to philosopher J. Krishnamurthi, "Listening is an art not easily come by, but in it there is beauty and great understanding. We listen with the various depths of our being, but our listening is always with a preconception or from a particular point of view. We do not listen simply; there is always the intervening screen of our own thoughts, conclusions, and prejudices. To listen there must be an inward quietness, a freedom from the strain of acquiring, a relaxed attention. This alert yet passive state is able to hear what is beyond the verbal conclusion. Words confuse; they are only the outward means of communication; but to commune beyond the noise of words, there must be in listening, an alert passivity. However, most of us are after results, achieving goals; we are forever overcoming and conquering, and so there is no listening. It is only in listening that one hears the song of the words."
J. Krishnamurthi says it is not easy to learn the art of listening because, [Question ID = 10862]
1. We do not listen with an open and receptive mind
2. We do not realize the beauty and great understanding it brings to
3. We only hear but do not listen
Correct Answer :- We do not listen with an open and receptive mind

Next Question is based on the following passage
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According to philosopher J. Krishnamurthi, "Listening is an art not easily come by, but in it there is beauty and great understanding. We listen with the various depths of our being, but our listening is always with a preconception or from a particular point of view. We do not listen simply; there is always the intervening screen of our own thoughts, conclusions, and prejudices. To listen there must be an inward quietness, a freedom from the strain of
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This post was last modified on 27 December 2020

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