The definitions in an XML document are said to be ______ when the tagging system and definitions in the DTD are all in compliance.
a.
well-formed
b.
reasonable
c.
valid
Correct Answer
d.
logical
Step-by-Step AI Explanation
Verified Method
An XML document is considered 'well-formed' if it conforms to the basic XML syntax rules. However, when it is also validated against and complies with the rules defined in a DTD (Document Type Definition) or XML Schema, it is said to be **valid**.
Q2mcq
Consider the JavaScript Code :
var y = “12”;
function f( ) {
var y = “6”;
alert (this.y);
function g( ) {alert (y);}
g( );
}
f( );
If $\text{M}$ is the number of alert dialog boxes generated by this JavaScript code and $\text{D}_1$, $\text{D}_2$, ......, $\text{D}_{\text{M}}$ represents the content displayed in each of the $\text{M}$ dialog boxes, then :
1. `f()` is invoked in the global scope where `this` refers to the global object (`window`). Thus, `this.y` accesses the global variable `y = "12"`. The first alert displays `"12"`.
2. Inside `f()`, a local variable `y = "6"` is defined. When `g()` is called, it accesses `y` via lexical scoping, which resolves to the local `y` inside `f()`. Thus, the second alert displays `"6"`.
Hence, $M = 2$, with $D_1$ displaying `"12"` and $D_2$ displaying `"6"`.
Q3mcq
What is the output of the following JAVA program ?
class simple
{
public static void main(String[ ] args)
{
simple obj = new simple( );
obj.start( );
}
void start( )
{
long [ ] P = {3, 4, 5};
long [ ] Q = method (P);
System.out.print (P[0] + P[1] + P[2] + “:”);
System.out.print (Q[0] + Q[1] + Q[2]);
}
long [ ] method (long [ ] R)
{
R[1] = 7;
return R;
}
}// end of class
a.
12 : 15
b.
15 : 12
c.
12 : 12
d.
15 : 15
Correct Answer
Step-by-Step AI Explanation
Verified Method
In Java, arrays are objects and are passed by reference value. Inside `method(long[] R)`, modifying `R[1] = 7` directly alters the original array `P`. Furthermore, `method` returns the reference to `P`, which is assigned to `Q`. Therefore, both `P` and `Q` reference the same array `{3, 7, 5}`. The sum for `P` is $3 + 7 + 5 = 15$, and for `Q` is $3 + 7 + 5 = 15$, producing the output `15:15`.
Q4mcq
What is the output of the following 'C' program ? (Assuming little - endian representation of multi-byte data in which Least Significant Byte (LSB) is stored at the lowest memory address).
#include <stdio.h>
#include <stlib.h>
/* Assume short int occupies two bytes of storage */
int main ( )
{
union saving
{
short int one;
char two [2];
};
union saving m;
m.two [0] = 5;
m.two [1] = 2;
printf ("%d, %d, %d\n", m.two [0], m.two [1], m.one);
}/* end of main */
a.
5, 2, 1282
b.
5, 2, 52
c.
5, 2, 25
d.
5, 2, 517
Correct Answer
Step-by-Step AI Explanation
Verified Method
In a union, all members share the same memory location. In a little-endian system, the least significant byte (LSB) is stored at the lowest memory address:
- `two[0] = 5` is stored at the lower address byte (LSB).
- `two[1] = 2` is stored at the higher address byte (MSB).
Thus, the 2-byte short integer value is:
$$\text{one} = 2 \times 256 + 5 = 512 + 5 = 517$$
Therefore, the output is `5, 2, 517`.
Q5mcq
Given below are three implementations of the swap( ) function in C++ :
| (A) | (B) | (C) |
| :--- | :--- | :--- |
| void swap (int a, int b)<br>{<br> int temp;<br> temp = a;<br> a = b;<br> b = temp;<br>}<br>int main( )<br>{<br> int p = 0; q = 1;<br> swap (p, q);<br>} | void swap (int &a, int &b)<br>{<br> int temp;<br> temp = a;<br> a = b;<br> b = temp;<br>}<br>int main( )<br>{<br> int p = 0, q = 1;<br> swap (p, q);<br>} | void swap (int *a, int *b)<br>{<br> int *temp;<br> temp = a;<br> a = b;<br> b = temp;<br>}<br>int main( )<br>{<br> int p = 0, q = 1;<br> swap (&p, &q);<br>} |
Which of these would actually swap the contents of the two integer variables p and q ?
a.
(A) only
b.
(B) only
Correct Answer
c.
(C) only
d.
(B) and (C) only
Step-by-Step AI Explanation
Verified Method
- Implementation (A) uses call-by-value, so the swapping of `a` and `b` only modifies local copies and does not affect `p` and `q`.
- Implementation (B) uses call-by-reference (`int &a, int &b`), which correctly swaps the values stored in variables `p` and `q`.
- Implementation (C) passes pointers, but inside the function it swaps the local pointer variables `a` and `b` instead of dereferencing them (`*a` and `*b`), leaving the original contents of `p` and `q` unchanged.
Therefore, only (B) successfully swaps the contents.
Q6mcq
In Java, which of the following statements is/are TRUE ?
$\text{S}_1$ : The 'final keyword applied to a class definition prevants the class from being extended through derivation.
$\text{S}_2$ : A class can only inherit one class but can implement multiple interfaces.
$\text{S}_3$ : Java permits a class to replace the implementation of a method that it has inherited. It is called method overloading.
Codes :
a.
$\text{S}_1$ and $ ext{S}_2$ only
Correct Answer
b.
$\text{S}_1$ and $ ext{S}_3$ only
c.
$\text{S}_2$ and $ ext{S}_3$ only
d.
All of $\text{S}_1$, $\text{S}_2$ and $\text{S}_3$
Step-by-Step AI Explanation
Verified Method
- $\text{S}_1$ is TRUE: A `final` class cannot be extended (subclassed).
- $\text{S}_2$ is TRUE: Java does not support multiple inheritance with classes (a class can only extend one superclass), but it can implement multiple interfaces.
- $\text{S}_3$ is FALSE: Replacing the implementation of an inherited method is known as method *overriding*, not method overloading.
Q7mcq
Which of the following statements is/are TRUE ?
P : C programming language has weak type system with static types.
Q : Java programming language has a strong type system with static types.
Codes :
a.
P only
b.
Q only
c.
Both P and Q
Correct Answer
d.
Neither P nor Q
Step-by-Step AI Explanation
Verified Method
- Statement P is TRUE: C is statically typed (types are checked at compile time), but weakly typed because it allows implicit type conversions and unchecked pointer type casting.
- Statement Q is TRUE: Java is statically typed and strongly typed (it enforces strict type safety and disallows arbitrary reinterpretations of types/pointers).
Q8mcq
A graphic display system has a frame buffer that is $640$ pixels wide, $480$ pixels high and $1$ bit of color depth. If the access time for each pixel on the average is $200$ nanoseconds, then the refresh rate of this frame buffer is approximately.
a.
16 frames per second
Correct Answer
b.
19 frames per second
c.
21 frames per second
d.
23 frames per second
Step-by-Step AI Explanation
Verified Method
Total number of pixels in one frame:
$$\text{Pixels} = 640 \times 480 = 307,200$$
Time required to access/refresh one frame:
$$T = 307,200 \times 200\text{ ns} = 307,200 \times 200 \times 10^{-9}\text{ s} = 0.06144\text{ seconds}$$
The refresh rate (frames per second) is:
$$\text{Refresh Rate} = \frac{1}{T} = \frac{1}{0.06144} \approx 16.276\text{ frames per second}$$
Thus, it is approximately 16 frames per second.
Q9mcq
Which of the following statements is/are TRUE regarding the solution of the visibility problem in 3D graphics?
$\text{S}_1$ : The Painter's algorithm sorts polygons by depth and then paints (scan - converts) each Polygon on to the screen starting with the most nearest polygon.
$\text{S}_2$ : Backface Culling refers to eliminating geometry with backfacing normals.
Codes :
a.
$\text{S}_1$ only
b.
$\text{S}_2$ only
Correct Answer
c.
Both $\text{S}_1$ and $\text{S}_2$
d.
Neither $\text{S}_1$ nor $\text{S}_2$
Step-by-Step AI Explanation
Verified Method
Statement $S_1$ is false because the Painter's algorithm sorts polygons by depth from farthest to nearest (back-to-front), painting the farthest polygons first so that nearer polygons overwrite them. Statement $S_2$ is true because Backface Culling is a technique that removes polygons/surfaces facing away from the camera/viewer by examining the direction of surface normals relative to the viewing vector. Hence, only $S_2$ is true.
Q10mcq
Consider the matrix $\text{M} = \begin{bmatrix} 2 & 0 & 2 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$ representing a set of planar (2D) geometric transformations in homogeneous coordinates. Which of the following statements about the matrix $\text{M}$ is True ?
a.
$\text{M}$ represents first, a scaling of vector $(2, 1)$ followed by translation of vector $(1, 1)$.
b.
$\text{M}$ represents first, a translation of vector $(1, 1)$ followed by scaling of vector $(2, 1)$.
Correct Answer
c.
$\text{M}$ represents first, a scaling of vector $(3, 1)$ followed by shearing of parameters $(-1, 1)$.
d.
$\text{M}$ represents first, a shearing of parameters $(-1, 1)$ followed by scaling of vector $(3, 1)$.
Step-by-Step AI Explanation
Verified Method
Let us check the transformation of a point $(x, y, 1)^T$:
First translation by $(t_x, t_y) = (1, 1)$, followed by scaling by $(s_x, s_y) = (2, 1)$:
$$S \cdot T = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix} = \begin{bmatrix} 2 & 0 & 2 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix} = M.$$
Conversely, scaling followed by translation gives:
$$T \cdot S = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} = \begin{bmatrix} 2 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix} \neq M.$$
Thus, $M$ represents first a translation of vector $(1, 1)$ followed by a scaling of vector $(2, 1)$.
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Assume the following regarding the development of a software system P :
• Estimated lines of code of P : 33, 480 LOC.
• Average productivity for P : 620 LOC per person-month.
• Number of software developers : 6.
• Average salary of a software developer : ₹ 50,000 per month.
If E, D and C are the estimated development effort (in person-months), estimated development time (in months), and estimated development cost (in ₹ Lac) respectively, then (E, D, C) = _________.
a.
$(48, 8, 24)$
b.
$(54, 9, 27)$
c.
$(60, 10, 30)$
d.
$(42, 7, 21)$
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Match the following in Software Engineering :
**List-I**
A. Product Complexity
B. Structured System Analysis
C. Coupling and Cohesion
D. Symbolic Execution
**List-II**
1. Software Requirements Definition
2. Software Design
3. Validation Technique
4. Software Cost Estimation
Codes :
a.
A - 2, B - 3, C - 4, D - 1
b.
A - 3, B - 1, C - 4, D - 2
c.
A - 4, B - 1, C - 2, D - 3
d.
A - 3, B - 4, C - 1, D - 2
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A software system crashed 20 times in the year 2017 and for each crash, it took 2 minutes to restart. Approximately, what was the software availability in that year ?
a.
$96.9924\ \%$
b.
$97.9924\ \%$
c.
$98.9924\ \%$
d.
$99.9924\ \%$
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Match the 5 CMM Maturity levels/CMMI staged representations in List-I with their characterizations in List-II :
List-I
A. Initial
B. Repeatable
C. Defined
D. Managed
E. Optimizing
List-II
1. Processes are improved quantitatively and continually.
2. The plan for a project comes from a template for plans.
3. The plan uses processes that can be measured quantitatively.
4. There may not exist a plan or it may be abandoned.
5. There's a plan and people stick to it.
Codes :
a.
A - 4, B - 5, C - 1, D - 3, E - 2
b.
A - 1, B - 2, C - 4, D - 5, E - 3
c.
A - 5, B - 4, C - 2, D - 3, E - 1
d.
A - 4, B - 5, C - 2, D - 3, E - 1
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Coupling is a measure of the strength of the interconnections between software modules. Which of the following are correct statements with respect to module coupling ?
P : Common coupling occurs when one module controls the flow of another module by passing it information on what to do.
Q : In data coupling, the complete data structure is passed from one module to another through parameters.
R : Stamp coupling occurs when modules share a composite data structure and use only parts of it.
Codes :
a.
P and Q only
b.
P and R only
c.
Q and R only
d.
All of P, Q and R
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Reasons to re-engineer a software include :
P : Allow legacy software to quickly adapt to the changing requirements.
Q : Upgrade to newer technologies / platforms / paradigm (for example, object-oriented).
R : Improve software maintainability.
S : Allow change in the functionality and architechure of the software.
Code :
a.
P, R and S only
b.
P and R only
c.
P, Q and S only
d.
P, Q and R only
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Which of the following statements is/are True ?
P : Refactoring is the process of changing a software system in such a way that it does not alter the external behavior of the code yet improves the internal architechure. Q : An example of refactoring is adding new features to satisfy a customer requirement discovered after a project is shipped.
Code :
a.
P only
b.
Q only
c.
Both P and Q
d.
Neither P nor Q
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Consider the array $\text{A} = \langle 4, 1, 3, 2, 16, 9, 10, 14, 8, 7 \rangle$. After building heap from the array A, the depth of the heap and the right child of max-heap are ______ and ______.
a.
3, 14
b.
3, 10
c.
4, 14
d.
4, 10
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A hash function h defined $h(\text{key}) = \text{key} \bmod 7$, with linear probing, is used to insert the keys 44, 45, 79, 55, 91, 18, 63 into a table indexed from 0 to 6. What will be the location of key 18 ?
a.
3
b.
4
c.
5
d.
6
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A text is made up of the characters A, B, C, D, E each occuring with the probability 0.08, 0.40, 0.25, 0.15 and 0.12 respectively. The optimal coding technique will have the average length of :
a.
2.4
b.
1.87
c.
3.0
d.
2.15
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Consider the following two Grammars :
$\text{G}_1 : \text{S} \rightarrow \text{SbS} \mid \text{a}$
$\text{G}_2 : \text{S} \rightarrow \text{aB} \mid \text{ab}, \text{A} \rightarrow \text{aAB} \mid \text{a}, \text{B} \rightarrow \text{ABb} \mid \text{b}$
Which of the following option is **correct** ?
a.
Only $\text{G}_1$ is ambiguous
b.
Only $\text{G}_2$ is ambiguous
c.
Both $\text{G}_1$ and $\text{G}_2$ are ambiguous
d.
Both $\text{G}_1$ and $\text{G}_2$ are not ambiguous
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Consider the following statements( ) :
$\text{S}_1$ : There exists no algorithm for deciding if any two Turing machines $\text{M}_1$ and $\text{M}_2$ accept the same language.
$\text{S}_2$ : The problem of determining whether a Turing machine halts on any input is undecidable.
Which of the following options is correct ?
a.
Both $\text{S}_1$ and $\text{S}_2$ are correct
b.
Both $\text{S}_1$ and $\text{S}_2$ are not correct
c.
Only $\text{S}_1$ is correct
d.
Only $\text{S}_2$ is correct
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A slotted ALOHA network transmits 200-bit frames using a shared channel with a $200\text{ Kbps}$ bandwidth. Find the throughput of the system, if the system (all stations put together) produces 250 frames per second.
a.
49
b.
368
c.
149
d.
151
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Which of the following statements are True ?
(1) Advanced Mobile Phone System (AMPS) is a second generation cellular phone system.
(2) IS - 95 is a second generation cellular phone system based on CDMA and DSSS.
(3) The third generation cellular phone system will provide universal personnel communication.
Codes :
a.
(1) and (2) only
b.
(2) and (3) only
c.
(1), (2) and (3)
d.
(1) and (3) only
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Match the following symmetric block ciphers with corresponding block and key sizes :
List-I
A. DES
B. IDEA
C. BLOW FISH
D. AES
List-II
1. Block size 64 and key size ranges between 32 and 448.
2. Block size 64 and key size 64.
3. Block size 128 and key sizes 128, 192, 256.
4. Block size 64 and key size 128.
Codes :
\begin{matrix} & \text{A} & \text{B} & \text{C} & \text{D} \end{matrix}
a.
4 2 1 3
b.
2 4 1 3
c.
2 4 3 1
d.
4 2 3 1
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Which of the following statements are True ?
(A) Three broad categories of Networks are
(i) Circuit Switched Networks
(ii) Packet Switched Networks
(iii) Message Switched Networks
(B) Circuit Switched Network resources need to be reversed during the set up phase.
(C) In packet switching there is no resource allocation for packets.
Codes :
a.
(A) and (B) only
b.
(B) and (C) only
c.
(A) and (C) only
d.
(A), (B) and (C)
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At a particular time of computation, the value of a counting semaphore is 10. Then 12 P operations and “x” V operations were performed on this semaphore. If the final value of semaphore is $7, x$ will be
a.
8
b.
9
c.
10
d.
11
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In a paged memory, the page hit ratio is $0.40$. The time required to access a page in secondary memory is equal to $120\text{ ns}$. The time required to access a page in primary memory is $15\text{ ns}$. The average time required to access a page is _______.
a.
105
b.
68
c.
75
d.
78
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In a multi-user operating system, 30 requests are made to use a particular resource per hour, on an average. The probability that no requests are made in 40 minutes, when arrival pattern is a poisson distribution, is :
a.
$\text{e}^{-15}$
b.
$1 - \text{e}^{-15}$
c.
$1 - \text{e}^{-20}$
d.
$\text{e}^{-20}$
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Normally user programs are prevented from handling I/O directly by I/O instructions in them. For CPUs having explicit I/O instructions, such I/O protection is ensured by having the I/O instructions priviledge. In a CPU with memory mapped I/O, there is no-explicit I/O instruction. Which one of the following is true for a CPU with memory mapped I/O ?
a.
I/O protection is ensured by operating system routines.
b.
I/O protection is ensured by a hardware trap.
c.
I/O protection is ensured during system configuration.
d.
I/O protection is not possible.
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Which of the following statements are True ?
(1) External Fragmentation exists when there is enough total memory space to satisfy a request but the available space is contiguous.
(2) Memory Fragmentation can be internal as well as external.
(3) One solution to external Fragmentation is compaction.
Code :
a.
(1) and (2) only
b.
(1) and (3) only
c.
(2) and (3) only
d.
(1), (2) and (3)
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Consider a virtual page reference string $1, 2, 3, 2, 4, 2, 5, 2, 3, 4$. Suppose LRU page replacement algorithm is implemented with 3 page frames in main memory. Then the number of page faults are _______.
a.
5
b.
7
c.
9
d.
10
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Consider the following three processes with the arrival time and CPU burst time given in milliseconds :
\begin{tabular}{ccc}
Process & Arrival Time & Burst Time \\
$P_1$ & 0 & 7 \\
$P_2$ & 1 & 4 \\
$P_3$ & 2 & 8 \\
\end{tabular}
The Gantt chart for preemptive SJF scheduling algorithm is _______.
a.
$P_1$ (0 to 7), $P_2$ (7 to 13), $P_3$ (13 to 21)
b.
$P_1$ (0 to 1), $P_2$ (1 to 5), $P_1$ (5 to 11), $P_3$ (11 to 19)
c.
$P_1$ (0 to 7), $P_2$ (7 to 11), $P_3$ (11 to 19)
d.
$P_2$ (0 to 4), $P_3$ (4 to 12), $P_1$ (12 to 19)
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Consider a relation book (title, price) which contains the titles and prices of different books. Assuming that no two books have the same price, what does the following SQL query list ?
\begin{verbatim}
Select title
from book as B
where (select count (*)
from book as T
where T.price > B.price) < 7
\end{verbatim}
a.
Titles of the six most expensive books.
b.
Title of the sixth most expensive books.
c.
Titles of the seven most expensive books.
d.
Title of the seventh most expensive books.
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Consider the following schedules involving two transactions.
$S_1 : r_1(X); r_1(Y); r_2(X); r_2(Y); w_2(Y); w_1(X)$
$S_2 : r_1(X); r_2(X); r_2(Y); w_2(Y); r_1(Y); w_1(X)$
Which one of the following statements is correct with respect to above ?
a.
Both $S_1$ and $S_2$ are conflict serializable.
b.
Both $S_1$ and $S_2$ are not conflict serializable.
c.
$S_1$ is conflict serializable and $S_2$ is not conflict serializable.
d.
$S_1$ is not conflict serializable and $S_2$ is conflict serializable.
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For a database relation $R(a, b, c, d)$ where the domains of a, b, c and d include only atomic values, and only the following functional dependencies and those that can be inferred from them hold :
$a \rightarrow c$
$b \rightarrow d$
The relation is in _______.
a.
First normal form but not in second normal form.
b.
Second normal form but not in third normal form.
c.
Third normal form.
d.
BCNF
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A many-to-one relationship exists between entity sets $r_1$ and $r_2$. How will it be represented using functional dependencies if $\text{Pk}(r)$ denotes the primary key attribute of relation ?
a.
$\text{Pk}(r_1) \rightarrow \text{Pk}(r_2)$
b.
$\text{Pk}(r_2) \rightarrow \text{Pk}(r_1)$
c.
$\text{Pk}(r_2) \rightarrow \text{Pk}(r_1)$ and $\text{Pk}(r_1) \rightarrow \text{Pk}(r_2)$
d.
$\text{Pk}(r_2) \rightarrow \text{Pk}(r_1)$ or $\text{Pk}(r_1) \rightarrow \text{Pk}(r_2)$
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Database system that store each relation in a separate operating system file may use the operating system's authorization scheme, instead of defining a special scheme themselves. In this case, which of the following is false?
a.
The administrator enjoys more control on the grant option.
b.
It is difficult to differentiate among the update, delete and insert authorizations.
c.
Cannot store more than one relation in a file.
d.
Operations on the database are speeded up as the authorization procedure is carried out at the operating system level.
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Let $R_1(a, b, c)$ and $R_2(x, y, z)$ be two relations in which a is the foreign key of $R_1$ that refers to the primary key of $R_2$. Consider following four options.
(1) Insert into $R_1$
(2) Insert into $R_2$
(3) Delete from $R_1$
(4) Delete from $R_2$
Which of the following is correct about the referential integrity constraint with respect to above ?
a.
Operations (1) and (2) will cause violation.
b.
Operations (2) and (3) will cause violation.
c.
Operations (3) and (4) will cause violation.
d.
Operations (4) and (1) will cause violation.
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Consider a hash table of size seven, with starting index zero, and a hash function $(7x + 3) \bmod 4$. Assuming the has table is initially empty, which of the following is the contents of the table when the sequence $1, 3, 8, 10$ is inserted into the table using closed hashing ? Here "______" denotes an empty location in the table.
In heuristic search algorithms in Artificial Intelligence (AI), if a collection of admissible heuristics $h_1, \dots, h_m$ is available for a problem and none of them dominates any of the others, which should we choose ?
a.
$h(n) = \max \{h_1(n), \dots, h_m(n)\}$
b.
$h(n) = \min \{h_1(n), \dots, h_m(n)\}$
c.
$h(n) = \text{avg} \{h_1(n), \dots, h_m(n)\}$
d.
$h(n) = \text{sum} \{h_1(n), \dots, h_m(n)\}$
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Consider following sentences regarding A*, an informed search strategy in Artificial Intelligence (AI).
(1) A* expands all nodes with $f(n) < C^*$.
(2) A* expands no nodes with $f(n) \ge C^*$.
(3) Pruning is integral to A*.
Here, $C^*$ is the cost of the optimal solution path.
Which of the following is correct with respect to the above statements ?
a.
Both statement (1) and statement (2) are true.
b.
Both statement (1) and statement (3) are true.
c.
Both statement (2) and statement (3) are true.
d.
All the statements (1), (2) and (3) are true.
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Consider the following statements :
(1) $\text{False} \models \text{True}$
(2) If $\alpha \models (\beta \wedge \gamma)$ then $\alpha \models \beta$ and $\alpha \models \gamma$
Which of the following is correct with respect to the above statements ?
a.
Both statement (1) and statement (2) are false.
b.
Statement (1) is true but statement (2) is false.
c.
Statement (1) is false but statement (2) is true.
d.
Both statement (1) and statement (2) are true.
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Consider the following English sentence :
“Agra and Gwalior are both in India”.
A student has written a logical sentence for the above English sentence in First-Order Logic using predicate. $\text{In }(x, y)$, which means $x$ is in $y$, as follows :
$\text{In}(\text{Agra}, \text{India}) \vee \text{In}(\text{Gwalior}, \text{India})$
Which one of the following is correct with respect to the above logical sentence ?
a.
It is syntactically valid but does not express the meaning of the English sentence.
b.
It is syntactically valid and expresses the meaning of the English sentence also.
c.
It is syntactically invalid but expresses the meaning of the English sentence.
d.
It is syntactically invalid and does not express the meaning of the English sentence.
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Consider the following two sentences :
(1) The planning graph data structure can be used to give a better heuristic for a planning problem.
(2) Dropping negative effects from every action schema in a planning problem results in a relaxed problem.
Which of the following is correct with respect to the above sentences ?
a.
Both sentence (1) and sentence (2) are false.
b.
Both sentence (1) and sentence (2) are true.
c.
Sentence (1) is true but sentence (2) is false.
d.
Sentence (1) is false but sentence (2) is true.
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A knowledge base contains just one sentence, $\exists x \, \text{AsHighAs} (x, \text{Everest})$. Consider the following two sentences obtained after applying existential instantiation.
(1) $\text{AsHighAs} (\text{Everest}, \text{Everest})$
(2) $\text{AsHighAs} (\text{Kilimanjaro}, \text{Everest})$
Which of the following is correct with respect to the above sentences ?
a.
Both sentence (1) and sentence (2) are sound conclusions.
b.
Both sentence (1) and sentence (2) are unsound conclusions.
c.
Sentence (1) is sound but sentence (2) is unsound.
d.
Sentence (1) is unsound but sentence (2) is sound.
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Consider the set of all possible five-card poker hands dealt fairly from a standard deck of fifty-two cards. How many atomic events are there in the joint probability distribution ?
a.
$2,598,960$
b.
$3,468,960$
c.
$3,958,590$
d.
$2,645,590$
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$\text{E}$ is the number of edges in the graph and $\text{f}$ is maximum flow in the graph. When the capacities are integers, the runtime of Ford-Fulkerson algorithm is bounded by :
a.
$O(\text{E} * \text{f})$
b.
$O(\text{E}^2 * \text{f})$
c.
$O(\text{E} * \text{f}^2)$
d.
$O(\text{E}^2 * \text{f}^2)$
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Digital data received from a sensor can fill up to $32$ buffers. Let the sample space be $\text{S} = \{0, 1, 2, \dots, 32\}$ where the sample $j$ denote that $j$ of the buffers are full and $p(i) = \frac{1}{561}(33-i)$. Let $\text{A}$ denote the event that the even number of buffers are full. Then $p(\text{A})$ is :
a.
$0.515$
b.
$0.785$
c.
$0.758$
d.
$0.485$
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Match the following in List-I and List-II, for a function $f$ :
**List-I**
A. $\forall x \, \forall y \, (f(x) = f(y) \rightarrow x = y)$
B. $\forall y \, \exists x \, (f(x) = y)$
C. $\forall x \, f(x) = k$
**List-II**
1. Constant
2. Injective
3. Surjective
a.
A - 1, B - 2, C - 3
b.
A - 3, B - 2, C - 1
c.
A - 2, B - 1, C - 3
d.
A - 2, B - 3, C - 1
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Match the terms in List-I with the options given in List-II
**List-I**
A. Decoder
B. Multiplexer
C. Demultiplexer
**List-II**
1. 1 line to $2^n$ lines
2. n lines to $2^n$ lines
3. $2^n$ lines to 1 line
4. $2^n$ lines to $2^{n-1}$ lines
a.
A - 2, B - 1, C - 3
b.
A - 2, B - 3, C - 1
c.
A - 2, B - 1, C - 4
d.
A - 4, B - 2, C - 1
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Match the items in List-I and List-II :
\begin{tabular}{|l|l|l|l|}
\hline
& \textbf{List - I} & & \textbf{List - II} \\
\hline
A. & Interrupts which can be delayed when a much highest priority interrupt has occured & 1. & Normal \\
\hline
B. & Unplanned interrupts which occur while executing a program & 2. & Synchronous \\
\hline
C. & Source of interrupt is in phase with the system clock & 3. & Maskable \\
\hline
& & 4. & Exception \\
\hline
\end{tabular}
a.
A - 2, B - 1, C - 4
b.
A - 2, B - 4, C - 3
c.
A - 3, B - 1, C - 2
d.
A - 3, B - 4, C - 2
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