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WorksheetsGrand GATE Mock Test
Total questions: 65
Worksheet time: 40mins
Let r be a root of the equation 𝑥^2+ 2𝑥 + 6 = 0.
Then the value of the expression (𝑟 + 2)(𝑟 + 3)(𝑟 + 4)(𝑟 + 5) is
51
-51
126
-126
Select the word that fits the analogy:
Cook : Cook :: Fly : _______
Flyer
Flying
Flew
Flighter
Given below are four statements.
Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not inquisitive.
From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.
Statement 1 and Statement 3
Statement 1 and Statement 2
Statement 2 and Statement 4
Statement 2 and Statement 4
Raman is confident of speaking English _______ six months as he has been practising regularly _______ the last three weeks.
during, for
for, since
for, in
within, for
In a recently conducted national entrance test, boys constituted 65% of those who
appeared for the test. Girls constituted the remaining candidates and they
accounted for 60% of the qualified candidates.
Which one of the following is the correct logical inference based on the
information provided in the above passage?
Equal number of boys and girls qualified
Equal number of boys and girls appeared for the test
The number of boys who appeared for the test is less than the number of girls
who appeared
The number of boys who qualified the test is less than the number of girls who
qualified
A series of natural numbers F1,F2,F3,F4,F5,F6,F7 obeys Fn+1=Fn+Fn-1 for all integers n>=2.
If F6=37 and F7=60 Then what is the value of F1?
4
5
6
7
A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn from the box one at a time. If a green ball is drawn, it is not replaced. If an orange ball is drawn, it is replaced with another orange ball. First ball is drawn. What is the probability of getting an orange ball in the next draw?
1/2
8/25
19/50
23/50
In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rectangle. Out of the total number of the people, the percentage of administrators shall be in the range of _________ .
0 to 15
16 to 30
31 to 45
46 to 60
If values of P=3, R=27, T=243, then find the value of Q+S =
40
80
90
180
The total revenue of a company during 2014−2018 is shown in the bar graph. If the total expenditure of the company in each year is 500 million rupees, then the aggregate profit or loss (in percentage) on the total expenditure of the company during 2014−2018 is _________ .
16.67% profit
16.67% loss
20% profit
20% loss
The Lucas Sequence Ln is defined for recurrence relation
Ln=Ln-1+Ln-2 for n>=3
with L1=1 and L2=3
Which one of the options is TRUE?
Ln=((1+√5)/2)n+((1-√5)/2)n
Ln=((1+√5)/2)n-((1-√5)/2)n
Ln=((1+√5)/2)n+((1-√5)/3)n
Ln=((1+√5)/3)n+((1-√5)/3)n
The grammar S → aSa | bS | c is
LL(1) but not LR(1)
LR(1) but not LR(1)
Both LL(1) and LR(1)
Neither LL(1) nor LR(1)
Which one of the following statements is TRUE for all positive functions f(n)?
f(n2) = θ(f(n)2), when f(n) is a polynomial
f(n2) = o(f(n)2)
f(n2) = O(f(n)2), when f(n) is an exponential function
f(n2) = Ω(f(n)2)
Consider the following array of elements.
〈89,19,50,17,12,15,2,5,7,11,6,9,100〉
The minimum number of interchanges needed to convert it into a max-heap is
4
5
2
3
Match all items in Group 1 with correct options from those given in Group 2.
P-4. Q-1, R-2, S-3
P-3, Q-1, R-4, S-2
P-3, Q-4, R-1, S-2
P-2, Q-1, R-4, S-3
Consider the following recurrence:
f(1) = 1;
f(2n) = 2f(n) -1, for n≥1;
f(2n+1) = 2f(n) +1, for n≥1;
f(2n -1) = 2n-1
f(2n) = 1
f(5. 2n) = 2n+1+1
f(2n +1) = 2n+1
An LALR(1) parser for a grammar G can have shift-reduce (S-R) conflicts if and only if
the SLR(1) parser for G has S-R conflicts
the LR(1) parser for G has S-R conflicts
the LR(0) parser for G has S-R conflicts
the LALR(1) parser for G has reduce-reduce conflicts
A sorting technique is called stable if:
t takes O(n log n) time
It maintains the relative order of occurrence of non-distinct elements.
It uses divide and conquers paradigm
It takes O(n) space
Which one or more of the following CPU scheduling algorithms can potentially cause starvation?
First-in First-Out
Round Robin
Priority Scheduling
Shortest Job First
Consider the grammar
S → (S) | a
Let the number of states in SLR(1), LR(1) and LALR(1) parsers for the grammar be n1, n2 and n3 respectively. The following relationship holds good
n1 < n2 < n3
n1 = n3 < n2
n1 = n2 = n3
n1 ≥ n3 ≥ n2
A process executes the code
fork ( );
fork ( );
fork ( );
The total number of child processes created is
3
4
7
8
Let P be a QuickSort Program to sort numbers in ascending order using the first element as pivot. Let t1 and t2 be the number of comparisons made by P for the inputs {1, 2, 3, 4, 5} and {4, 1, 5, 3, 2}, respectively. Which one of the following holds?
t1 = 5
t1 < t2
t1 > t2
t1 = t2
The maximum number of superkeys for the relation schema R(E,F,G,H) with E as the key is
5
6
7
8
In which one of the following page replacement policies, Belady’s anomaly may occur?
Optimal
LRU
MRU
Consider the following tables T1 and T2. In table T1, P is the primary key and Q is the foreign key referencing R in table T2 with on delete cascade and on-update cascade. In table T2, R is the primary key and S is the foreign key referencing P in table T1 with on-delete set NULL and on-update cascade. In order to delete record ⟨3, 8⟩ from table T1, the number of additional records that need to be deleted from table T1 is
(a)
Which of the following is TRUE?
Every relation in 3NF is also in BCNF
A relation R is in 3NF if every non-prime attribute of R is fully functionally dependent on every key of R
Every relation in BCNF is also in 3NF
No relation can be in both BCNF and 3NF
Consider a demand paging system with four-page frames (initially empty) and an LRU page replacement policy. For the following page reference string 7, 2,7,3, 2,5,3, 4,6,7,7,1,5,6,1 the page fault rate, defined as the ratio of number of page faults to the number of memory accesses (rounded off to one decimal place) is_
1.5
0.5
0.6
0.8
Suppose the following functional dependencies hold on a relation U with attributes P, Q, R, S, and
T: • P → QR
• RS → T
Which of the following functional dependencies can be inferred from the above functional dependencies?
PS → T
R → T
P → R
PS → Q
Consider a system with 3 processes that share 4 instances of the same resource type. Each process can request a maximum of K instances. Resource instances can be requested and released only one at a time. The largest value of K that will always avoid deadlock is (a)
The essential content(s) in each entry of a page table is/are:
Virtual page number
Page frame number
Both virtual page number and page frame number
Access the right information
Consider the following deterministic finite automaton (DFA)
The number of strings of length 8 accepted by the above automaton is (a)
Which of the following statements is/are FALSE?
1. For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine.
2. Turing recognizable languages are closed under union and complementation.
3. Turing decidable languages are closed under intersection and complementation.
4. Turing recognizable languages are closed under union and intersection.
1 and 4 only
1 and 3 only
2 only
3 only
A computer has six tape drives, with n processes competing for them. Each process may need two drives. What is the maximum value of n for the system to be deadlock free?
6
5
4
3
Let L = {w (0 + 1)* | w has even number of 1s}, i.e., L is the set of all bit strings with even number of 1s. Which one of the regular expressions below represents L ?
(0* 10* 1)*
0*(10* 10*)*
0*(10* 1)*0*
0* 1(10* 1)* 10*
Consider the following languages: L1 = {ww | w belongs {a, b}*}
L2 = {a^n b^n c^m | m, n >=0}
L3 = {a^m b^n c^n | m, n >= 0}
Which of the following statements is/are FALSE?
L1 is not context – free but L2 and L3 are deterministic context – free.
Neither L1 nor L2 is context – free.
L2, L3 and L2 itersection L3 all are context – free.
Neither L1 nor its complement is context – free
A system has 6 identical resources and N processes competing for them. Each process can request atmost 2 resources. Which one of the following values of N could lead to a deadlock?
1
2
3
6
Consider the following definition of a lexical token id for an identifier in a programming language, using extended regular expressions:
letter → [A-Za-z]
digit → [0-9]
id → letter (letter | digit)∗
Which one of the following Non-deterministic Finite-state Automata with ϵ- transitions accepts the set of valid identifiers? (A double-circle denotes a final state)
A 5-stage pipelined processor has Instruction Fetch (IF), Instruction Decode (ID), Operand Fetch (OF), Perform Operation (PO) and Write Operand (WO) stage. The IF, ID, OF and WO stage take 1 clock cycle each for any instruction. The PO stage takes 1 clock cycle for ADD and SUB instructions ,3 clock cycles for MUL instruction, and 6 clock cycles for DIV instruction respectively. Operand forwarding is used in the pipeline. What is the number of clock cycles needed to execute the following sequence of instructions?
Instruction Meaning of Instruction
I0: MUL R2, R0, R1 R2 ← R0*R1
I1: DIV R5, R3, R4 R5 ← R3/R4
I2: ADD R2, R5, R2 R2 ← R5 + R2
I3: SUB R5, R2, R6 R5 ← R2 - R6
13
15
17
19
A multiplexer is placed between a group of 32 registers and an accumulator to regulate data movement such that at any given point in time the content of only one register will move to the accumulator. The number of select lines needed for the multiplexer is (a) . Note - This question was Numerical Type.
Consider a sequential digital circuit consisting of T flip-flops and D flip-flops as shown in the figure. CLKIN is the clock input to the circuit. At the beginning, Q1, Q2 and Q3 have values 0, 1 and 1, respectively
Which one of the given values of (Q1, Q2, Q3) can NEVER be obtained with this digital circuit?
(0, 0, 1)
(1, 0, 0)
(1, 0, 1)
(1, 1, 1)
The value of a float type variable is represented using the single-precision 32-bit floating point format of IEEE-754 standard that uses 1 bit for sign, 8 bits for biased exponent and 23 bits for mantissa. A float type variable X is assigned the decimal value of −14.25. The representation of X in hexadecimal notation is
C1640000H
416C0000H
41640000H
C16C0000H
In 16-bit 2’s complement representation, the decimal number -28 is
1000 0000 1110 0100
0000 0000 1110 0100
1111 1111 1110 0100
1111 1111 0001 1100
In a computer system, four files of size 11050 bytes, 4990 bytes, 5170 bytes and 12640 bytes need to be stored. For storing these files on disk, we can use either 100 byte disk blocks or 200 byte disk blocks (but can't mix block sizes). For each block used to store a file, 4 bytes of bookkeeping information also needs to be stored on the disk. Thus, the total space used to store a file is the sum of the space taken to store the file and the space taken to store the book keeping information for the blocks allocated for storing the file. A disk block can store either bookkeeping information for a file or data from a file, but not both. What is the total space required for storing the files using 100 byte disk blocks and 200 byte disk blocks respectively?
35400 and 35800 bytes
35800 and 35400 bytes
35600 and 35400 bytes
35400 and 35600 bytes
Consider a two-level cache hierarchy with L1 and L2 caches. An application incurs 1.4 memory accesses per instruction on average. For this application, the miss rate of L1 cache is 0.1; the L2 cache experiences on average, 7 misses per 1000 instructions. The miss rate of L2 expressed correct to two decimal places is (a) .
Which one of the following expressions does NOT represent the exclusive NOR of x and y?
xy + x’y’
x⊕y’
x’⊕y
x’⊕y’
Consider the following C program
#include <stdio.h>
int main ( ) {
int m=10 ;
int n, n1;
n=++m ;
n1=m++;
n– –;
– –n1 ;
n–=n1;
printf( ("%d", n);
return 0 ;
}
The output of the program is (a)
Consider a 4-bit Johnson counter with an initial value of 0000. The counting sequence of this counter is
0, 1, 3, 7, 15, 14, 12, 8, 0
0, 1, 3, 5, 7, 9, 11, 13, 15, 0
0, 2, 4, 6, 8, 10, 12, 14, 0
0, 8, 12, 14, 15, 7, 3, 1, 0
An organization requires a range of IP address to assign one to each of its 1500 computers. The organization has approached an Internet Service Provider (ISP) for this task. The ISP uses CIDR and serves the requests from the available IP address space 202.61.0.0/17. The ISP wants to assign an address space to the organization which will minimize the number of routing entries in the ISP’s router using route aggregation. Which of the following address spaces are potential candidates from which the ISP can allot any one of the organization ?
I. 202.61.84.0 / 21
II. 202.61.104.0 / 21
III. 202.61.64.0 / 21
IV. 202.61.144.0 / 21
I and II only
II and III only
III and IV only
I and IV only
Assume that you have made a request for a web page through your web browser to a web server. Initially the browser cache is empty. Further, the browser is configured to send HTTP requests in non-persistent mode. The web page contains text and five very small images. The minimum number of TCP connections required to display the web page completely in your browser is (a) . Note - This question was Numerical Type.
Consider an enterprise network with two Ethernet segments, a web server and a firewall, connected via three routers as shown below.
3
12
6
8
Consider the C function given below.
int f( int j){
static int i = 50 ;
int k ;
if (i==j){
printf ("something");
k=f(i) ;
return 0 }
else
return 0 ;
Which one of the following is TRUE?
The function returns 0 for all values of j.
The function prints the string something for all values of j.
The function returns 0 when j = 50
The function will exhaust the runtime stack or run into an infinite loop when j = 50
Consider the following C program.
#include
int main( ) {
char* c= "GATECSIT2017";
char* p=c ;
printf(“%d ", (int)strlen(c+2[p]–6[p]–1)) ;
return 0 ; }
The output of the program is (a) .
Suppose you are asked to design a new reliable byte-stream transport protocol like TCP. This protocol, named my TCP, runs over a 100 Mbps network with a Round Trip Time of 150 milliseconds and a maximum segment lifetime of 2 minutes. Which of the following is/are valid lengths of the Sequence Number field in the my TCP header?
30
32
34
36
Let A be a square matrix of size n n. Consider the following pseudo code. 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]); (a) (c) (d)
The matrix A itself
Transpose of the matrix A
Adding 100 to the upper diagonal elements and subtracting 100 from lower diagonal elements of A
None of the above
Which one of the following is not a client-server application?
Internet Chat
Web Browsing
ping
Consider a sequence a of elements a0 = 1, a1 = 5, a2 = 7, a3 = 8, a4 = 9, and a5 = 2. The following operations are performed on a stack S and a queue Q, both of which are initially empty.
I: push the elements of a from a0 to a5 in that order into S.
II: enqueue the elements of a from a0 to a5 in that order into Q.
III: pop an element from S.
IV: dequeue an element from Q.
V: pop an element from S.
VI: dequeue an element from Q.
VII: dequeue an element from Q and push the same element into S.
VIII: Repeat operation VII three times.
IX: pop an element from S.
X: pop an element from S.
The top element of S after executing the above operations is (a) .
Which one of the following CIDR prefixes exactly represents the range of IP addresses 10.12.2.0 to 10.12.3.255?
10.12.2.0/23
10.12.2.0/24
10.12.0.0/22
10.12.2.0/22
Consider an Ethernet segment with a transmission speed of 108108 bits/sec and a maximum segment length of 500 meters. If the speed of propagation of the signal in the medium is 2×1082×108 meters/sec, then the minimum frame size (in bits) required for collision detection is (a)
Let
f (x) = x3+ 15x2 − 33x − 36
be a real-valued function.
Which of the following statements is/are TRUE?
f (x) does not have a local maximum.
f (x) has a local maximum.
f (x) does not have a local minimum.
f (x) has a local minimum.
The value of the definite integral
0
1
2
3
A function y(x) is defined in the interval [0, 1] on the
5/6
6/5
13/6
6/13
The product of the non-zero eigenvalues of the matrix
1 0 0 0 1
0 1 1 1 0
0 1 1 1 0
0 1 1 1 0
1 0 0 0 1
4
5
6
7
Which one of the following is NOT necessarily a property of a Group?
Commutativity
Associativity
Existence of inverse for every element
Existence of identity
Let A be the adjacency matrix of the graph with vertices {1, 2, 3, 4, 5}.
Let λ1, λ2, λ3, λ4, and λ5 be the five eigenvalues of A. Note that these eigenvalues need not be distinct.
The value of λ1 + λ2 + λ3 + λ4 + λ5 is
( note :convert it into matrix)
1
2
3
5
An unbalanced dice (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is 90% of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is even given that it is greater than 3 is 0.75, which one of the following options is closest to the probability that the face value exceeds 3?
(note up to 3 digits after point )
(a)
