A coin is tossed successively three times. Find the Probability $(P)$, Event $(E)$, Sample space $(S)$ of getting exactly one head or two heads, where $n$ is number of occurrence.
(A) $n(S)=8$ and $n(E)=4$
(B) $n(E)=6$ and $n(S)=8$
(C) $P(E)=\frac{3}{4}$
(D) $P(E)=\frac{1}{2}$
Choose the correct answer from the options given below :
Sample space for 3 tosses:
$S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}$
Thus
$n(S)=8$
Event: exactly 1 head or 2 heads
1 head → ${HTT,THT,TTH}$
2 heads → ${HHT,HTH,THH}$
So
$n(E)=6$
Probability
$P(E)=\frac{6}{8}=\frac{3}{4}$
Thus correct statements:
(B) and (C)
Consider the given number $(45)_y$ where $y$ is the base of the number. Some of the possible values of $y$ are given below.
(A) 5
(B) 6
(C) 7
(D) 8
Choose the correct answer from the options given below :
In base $y$, digits must be less than base.
Number $(45)_y$ has digit 5.
Thus
$y>5$
Possible bases:
$6,7,8,\dots$
Given options:
6, 7, 8
Thus
(B), (C), (D)
Match List - I with List - II.
| List - I | List - II |
| (A) HTML | (I) Allow for dynamic and interactive web pages. |
| (B) DHTML | (II) Defines the structure of web pages. |
| (C) XML | (III) Object-oriented programming language for web applications. |
| (D) JAVA | (IV) Used for data storage and transport. |
Choose the correct answer from the options given below :
HTML → defines structure of web pages → (II)
DHTML → dynamic interactive web pages → (I)
XML → data storage and transport → (IV)
JAVA → object-oriented programming language → (III)
Thus matching:
(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
Standard compiler phases:
Lexical Analysis
Syntax Analysis
Semantic Analysis
Intermediate Code Generation
Code Optimization
Thus order:
(A) → (C) → (B) → (D) → (E)
Match List - I with List - II.
| List - I (Algorithms) | List - II (Characteristics) |
| (A) First Come First Served (FCFS) | (I) Each process is assigned a priority |
| (B) Shortest Job First (SJF) | (II) Ensures fair allocation of CPU time by assigning time slice |
| (C) Round Robin (RR) | (III) Processes are executed in the order they arrive |
| (D) Priority Scheduling | (IV) Select the process for execution with smallest next burst time |
Typical Software Development Life Cycle (SDLC) activities:
Requirement Analysis ✔
System Design ✔
Implementation / Testing
Deployment ✔
Check options:
(A) Requirement Analysis → ✔
(B) System Design → ✔
(C) Code Refactoring → maintenance activity, not core lifecycle step ✘
(D) Deployment → ✔
(E) Substructure → not SDLC activity ✘
Thus correct:
(A), (B), (D)
(A) True
Constructors can be overloaded.
(B) True
Constructors do not have return type.
(C) False
Constructors are member functions, not friend functions.
(D) False
Destructor is called when object is destroyed.
Thus correct statements:
(A) and (B)
Check dependency preservation
Given FDs:
$P \rightarrow Q$
$Q \rightarrow R$
$R \rightarrow S$
$S \rightarrow Q$
Decomposed relations:
$R_1(P,Q)$
$R_2(Q,R)$
$R_3(Q,S)$
Each dependency is preserved:
$P \rightarrow Q$ → in $R_1$
$Q \rightarrow R$ → in $R_2$
$R \rightarrow S$ → derived via $Q$ in $R_3$
$S \rightarrow Q$ → in $R_3$
Thus dependency preserving
Check lossless join:
Common attribute between relations is Q, which functionally determines other attributes through dependencies.
Hence not lossless join.
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Online Test Series, Information About Examination,
Syllabus, Notification
and More.