৪৯তম বিসিএস ⎯ কম্পিউটার সায়েন্স (CSE) [৯৭১]

চর্যাপদের কবিগণ:
- সুকুমার সেনের 'বাঙ্গালা সাহিত্যের ইতিহাস' (প্রথম খণ্ড) গ্রন্থে চর্যাপদের ২৪ জন পদকর্তার নাম পাওয়া যায়। ড. মুহম্মদ শহীদুল্লাহ সম্পাদিত 'Buddhist Mystic Songs' গ্রন্থে চর্যাপদের ২৩ জন কবির নাম উল্লেখ আছে।

এরা হলেন:
- কাহ্নপা; কুক্কুরীপা; ধর্মপা; ঢেগুণপা; বিরুপা; বীণাপা; ভাদেপা; ভুসুকুপা, মহীধরপা, লুইপা; শবরপা; শান্তিপা; সরহপা; ডোম্বীপা; কম্বলাম্বরপা; গুণ্ডুরীপা; চাটিল্লপা; আর্যদেবপা; দারিকপা; তাড়কপা; কঙ্কণপা; জয়নন্দীপা; তন্ত্রীপা।

উৎস: বাংলা ভাষা ও সাহিত্য জিজ্ঞাসা, বাংলা সাহিত্যের ইতিহাস, মাহবুবুল আলম।

• Love for Love:
- It is a play written by William Congreve.
- এটি মুলত একটি comedy play.
- William Congreve ছিলেন Restoration Period এর একজন বিখ্যাত সাহিত্যিক।
- He wrote some of the most popular plays in English literature.

• William Congreve:
- তিনি একজন English dramatist.
- তিনি comedy of manners এর জন্য বিখ্যাত।
- তিনি Restoration period এর একজন বিখ্যাত সাহিত্যিক।
- He wrote some of the most popular plays in English literature.

• Notable works:
- Love for Love,
- The Double-Dealer,
- The Mourning Bride,
- The Way of the World.

Source: Britannica, Live MCQ Lecture.

- কৌলীন্য প্রথার উদ্ভব পাল শাসনামলে হয়েছিল বলে মনে করা হয়।

কৌলীন্য প্রথা:
- রাঢ় ও বরেন্দ্র এর ব্রাহ্মণদের মধ্যে কৌলীন্য প্রথা অধিক মাত্রায় প্রভাব বিস্তার করেছিল।
- তারা সম্ভবত কান্যকুব্জের পাঁচ ব্রাহ্মণ-রক্ষিতীশ, মেধতিথী, বিতরগ, সুধনিধি এবং সম্ভরি-এর উত্তরসূরি।
- গৌড়ের রাজা শশাঙ্ক এবং বর্মণ রাজা হরিবর্মণ উভয়েই যথাক্রমে শকদ্বীপী ও বৈদিক ব্রাহ্মণ নিয়ে এসেছিলেন বলে জানা যায়।
- বলা হয়ে থাকে, এ ব্রাহ্মণদের সাথে সম্পর্ক সৃষ্টির ফলস্বরূপ বাংলায় সামাজিক প্রথা হিসেবে কৌলিন্য প্রথার সূত্রপাত হয়েছে।
- সেন রাজা বল্লালসেনকেও কৌলিন্য প্রথার স্রষ্টা হিসেবে কৃতিত্ব দেওয়া হয়, যদিও এ দাবির সমর্থনে সেন যুগের কোনো সাহিত্যিক ও উৎকীর্ণলিপি প্রমাণ পাওয়া যায়নি।
- তৃতীয় বিগ্রহপালের বনগাঁ তাম্রশাসনে ইঙ্গিত করা হয়েছে, তাঁর কর্মকর্তা ঘন্তিস-এর প্রো-পিতামহের মাধ্যমে তাঁর পূর্বপুরুষের সাথে কোলঞ্চ (কান্যকুব্জ) ব্রাহ্মণ কচ্ছ-এর যোগসূত্র ছিল।
- ফলে কৌলীন্য প্রথার উদ্ভব পাল শাসনামলে হয়েছিল বলে মনে করা হয়।

উল্লেখ্য,
- কুলীন অর্থ হলো উত্তম পরিবার বা সম্ভ্রান্ত বংশজাত।
- বাচস্পতি মিশ্র-এর মতে, এটি চিহ্নিত হয় আচার (শুদ্ধতা), বিদ্যা (জ্ঞান), বিনয় (শৃঙ্খলাবোধ), প্রতিষ্ঠা (শুদ্ধতার খ্যাতি), তীর্থ-দর্শন (তীর্থযাত্রা), নিষ্ঠা (কর্তব্যনিষ্ঠা), তপস্যা (কঠোর ধ্যান), আবৃত্তি (সমবর্ণে বিবাহ) এবং দান (উদারহস্ত) দিয়ে।

উৎস: বাংলাপিডিয়া।[লিঙ্ক]

• বাংলায় মুঘল শাসন (১৫৭৬-১৭৫৭ সাল):
- সুবাদারি ও নবাবি-এ দুই পর্বে বাংলায় মুঘল শাসন অতিবাহিত হয়।
- বারোভূঁইয়াদের পরাজিত করার পর সমগ্র বাংলা অঞ্চলে মুঘল সুবাদারি প্রতিষ্ঠিত হয়।
- মুঘল প্রদেশগুলো 'সুবা' নামে পরিচিত ছিল।
- বাংলা ছিল মুঘলদের অন্যতম সুবা। সতেরো শতকের প্রথম দিক থেকে আঠারো শতকের শুরু পর্যন্ত ছিল সুবাদারি শাসনের স্বর্ণযুগ।
- সম্রাট আওরঙ্গজেবের পর দিল্লির দুর্বল উত্তরাধিকারীদের সময়ে মুঘল শাসন শক্তিহীন হয়ে পড়ে।
- এ সুযোগে বাংলার সুবাদারগণ প্রায় স্বাধীনভাবে বাংলা শাসন করতে থাকেন।
- মুঘল আমলের এই যুগ 'নবাবি আমল' নামে পরিচিত।

উৎস: বাংলাদেশের ইতিহাস ও বিশ্বসভ্যতা, নবম-দশম শ্রেণি।

জুলাই ঘোষণাপত্র':
- ৫ আগস্ট অন্তর্বর্তী সরকারের প্রধান উপদেষ্টা অধ্যাপক ড. মুহাম্মদ ইউনূস পাঠ করেন ২৮ দফা সংবলিত 'জুলাই ঘোষণাপত্র'।
- ২৪ নং দফায় জুলাই গণঅভ্যুত্থানের সকল শহীদদের জাতীয় বীর হিসেবে ঘোষণা করে।
- শহীদদের পরিবার, আহত যোদ্ধা এবং আন্দোলনকারী ছাত্রজনতাকে প্রয়োজনীয় সকল আইনি সুরক্ষা দেওয়ার অভিপ্রায় ব্যক্ত করেছে।

উৎস: দৈনিক ইত্তেফাক।[লিঙ্ক]

নজরুল পুরস্কার-২০২৫:
- ২০২৫সালে জাতীয় কবি কাজী নজরুল ইসলামের ১২৬তম জন্মবার্ষিকী ছিল।
- এ বছর পুরস্কার পেয়েছেন নজরুল গবেষক অধ্যাপক আনোয়ারুল হক এবং নজরুল সংগীতশিল্পী শবনম মুশতারী।
- বাংলা একাডেমির আবদুল করিম সাহিত্যবিশারদ মিলনায়তনে অনুষ্ঠিত এক সেমিনারে এ পুরস্কার প্রদান করা হয়।

উল্লেখ্য,
- বাংলা একাডেমির সভাপতি অধ্যাপক আবুল কাসেম ফজলুল হক।
- মহাপরিচালক অধ্যাপক মোহাম্মদ আজম।
- ২০২২ সালে বাংলা একাডেমি নজরুল পুরস্কার চালু করে।
- পুরস্কার হিসেবে দেওয়া হয় ২ লাখ টাকার চেক, সম্মাননাপত্র, সম্মাননা-স্মারক এবং পুষ্পস্তবক।

উৎস: বাংলা একাডেমী ওয়েবসাইট।

স্বল্পোন্নত দেশ:
- ২০১৮ সালে বাংলাদেশ এলডিসি থেকে উত্তরণপ্রক্রিয়ায় প্রবেশ করে।
- সাধারণত ৬ বছরে এ প্রক্রিয়া শেষ হয়।
- কিন্তু কোভিডের কারণে বাংলাদেশসহ অন্য দেশকে আরও দুই বছর সময় দেওয়া হয়।
- ২০২৬ সালের ২৪ নভেম্বর এলডিসি থেকে বের হবে বাংলাদেশ।
- সম্প্রতি, স্বল্পোন্নত দেশের (এলডিসি) তালিকা থেকে বাংলাদেশের উত্তরণের নির্ধারিত সময়সীমা পিছিয়ে দেওয়ার দাবি তুলেছেন ব্যবসায়ীরা।

উৎস: প্রথম আলো।[লিঙ্ক]

• ছাতক সিমেন্ট কোম্পানী:
- দেশের প্রথম সিমেন্ট কারখানা ছাতক সিমেন্ট কোম্পানি লিমিটেড।
- ছাতক সিমেন্ট কোং লিঃ, সুনামগঞ্জ জেলার ছাতকে অবস্থিত দেশের একমাত্র স্বয়ংসম্পূর্ণ সিমেন্ট কারখানা।
- এটি ১৯৩৭ সনে আসাম বেঙ্গল সিমেন্ট কোম্পানী নামে ব্যক্তি মালিকানায় প্রতিষ্ঠিত।
- ১৯৬৫ সনে পাক-ভারত যুদ্ধের পর ব্যক্তি মালিক কর্তৃক কারখনাটি পরিত্যক্ত হয়।
- পরে ১৯৬৬ সন হতে উহা ইপিআইডিসি'র নিয়ন্ত্রনে আসে।
- বাংলাদেশের স্বাধীন হওয়ার পর প্রথমে বিএমওজিসি, বিএমইডিসি ।
- এবং সর্বশেষ ১৯৮২ সালের ১লা জুলাই থেকে বিসিআইসি'র নিয়ন্ত্রণে আসে।

অপরদিকে,
- লাফার্জ সুরমা সিমেন্ট কারখানা:
- ছাতক লাফার্জ সুরমা সিমেন্ট ফ্যাক্টরি বাংলাদেশে তথা এশিয়া মহাদেশের অন্যতম মাল্টি-ন্যাশনাল কোম্পানি।
- ২০০০ সালের পর উক্ত কোম্পানি টি প্রতিষ্ঠিত হয়

উৎস: বাংলাদেশ কেমিক্যাল ইন্ডাস্ট্রিজ কর্পোরেশন।

ছোট সোনামসজিদ:
- গৌড় শহরের দক্ষিণ প্রান্তে বর্তমান ফিরোজাবাদ গ্রামে 'ছোট সোনামসজিদ' নির্মিত হয়েছিল।
- এ মসজিদটি ছিল আকারে ছোট। তবে এ মসজিদেও সোনালি রঙের গিলটির কারুকার্য ছিল।
- সম্ভবত এ কারণেই এটি ছোট সোনা মসজিদ নামে পরিচিত।
- আলাউদ্দিন হুসেন শাহের আমলে জনৈক ওয়ালি মুহাম্মদ এটির নির্মাতা ছিলেন।

উল্লেখ্য,
- বড় সোনা মসজিদের আর এক নাম 'বারোদুয়ারী মসজিদ'।
- এতে বৃহৎ বারোটি দরজা ছিল। এ মসজিদে সোনালি রঙের গিলটি করা কারুকার্য ছিল।
- সম্ভবত এজন্যই এটি সোনা মসজিদ নামে অভিহিত হতো। এ মসজিদটি গৌড়ের বৃহত্তম মসজিদ।
- আসাম বিজয়কে স্মরণীয় করে রাখার জন্য হুসেন শাহ এ মসজিদটি নির্মাণ করেছিলেন।
- ১৫২৭ সালে নসরত শাহ এর নির্মাণ কাজ শেষ করেন।

উৎস: বাংলাদেশের ইতিহাস ও বিশ্বসভ্যতা, নবম-দশম শ্রেণি।

একুশে ফেব্রুয়ারি গান:
- ’’আমার ভাইয়ের রক্তে রাঙানো একুশে ফেব্রুয়ারি”
- গানটির বর্তমান সুরকার- আলতাফ মাহমুদ।
- গানটির রচয়িতা আবদুল গাফ্ফার চৌধুরী।
- এই গানটি প্রথম হাসান হাফিজুর রহমান সম্পাদিত 'একুশে ফেব্রুয়ারি' (১৯৫৩) গ্রন্থে সংকলিত হয়।
- গানটির প্রথম সুরকার ছিলেন আবদুল লতিফ।
- ঢাকা কলেজের নতুন নতুন ছাত্র ইউনিয়নের অভিষেক অনুষ্ঠানে গানটি প্রথম গাওয়া হয়।

উৎস: বাংলাপিডিয়া ও ডেইলী স্টার,।

প্রশ্ন:


সমাধান:

প্রশ্ন: প্রশ্নবোধক স্থানে কোন সংখ্যাটি বসবে?

সমাধান:
(২য় কলাম × ৩য় কলাম) - ১ম কলাম = ৪র্থ কলাম

(6 × 10) - 2 = 60 - 2 = 58
(7 × 11) - 3 = 77 - 3 = 74
(8 × 12) - 4 = 96 - 4 = 92

সুতরাং, প্রশ্নবোধক স্থানে 92 সংখ্যাটি বসবে।

Answer: B) (FFF)_{16
Explanation:}

Answer: (FFF)₁₆

Answer: C) Absorption

Explanation:

Absorption Law: A+AB=A
Reduces redundant terms in SOP/POS.

সঠিক উত্তর: খ) (A+B+C)(A+B′+C′)(A′+B+C′)(A′+B′+C)
অপশন–ক-তে একটি টার্ম ভুল আছে: AB′C লেখা হয়েছে, কিন্তু হওয়া উচিত AB′C′.
উত্তরপত্রের ইনপুট পরিবর্তন করা হয়েছে। 
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Write minterms
Rule for minterm:
For F=1 row, the minterm is an AND of all variables:

If variable = 1 → write uncomplemented (A)
If variable = 0 → write complemented (A')
Check each row:

Row: 0 0 1 → A=0, B=0, C=1 → minterm = A′B′CA'B'CA′B′C
Row: 0 1 0 → A=0, B=1, C=0 → minterm = A′BC′A'BC'A′BC′
Row: 1 0 0 → A=1, B=0, C=0 → minterm = AB′C′AB'C'AB′C′
Row: 1 1 1 → A=1, B=1, C=1 → minterm = ABCABCABC

Step 3: SOP expression
SOP = Sum (OR) of all midterms:

F(A,B,C)=A′B′C+A′BC′+AB′C′+ABC

Write maxterms
Rule for maxterm:
For F=0 row, the maxterm is (A + B + C) but complemented as per 0 → 1:

If variable = 0 → write as uncomplemented (A)
If variable = 1 → write as complemented (A')
Check each row:

Row: 0 0 0 → A=0, B=0, C=0 → maxterm = (A + B + C)
Row: 0 1 1 → A=0, B=1, C=1 → maxterm = (A + B' + C')
Row: 1 0 1 → A=1, B=0, C=1 → maxterm = (A' + B + C')
Row: 1 1 0 → A=1, B=1, C=0 → maxterm = (A' + B' + C)

Step 3: POS expression
POS = Product (AND) of all maxterms:

F(A,B,C) =(A+B+C)(A+B′+C′)(A′+B+C′)(A′+B′+C)

So , Both are Correct

Answer: C) Full adder

Explanation:

Combinational → output depends only on current input.
Sequential → output depends on input + previous state.
Full adder → combinational Circuit

Answer: C) B
Explanation:

We know,
In K - map, a group of n^m cells eliminates m variables in given expression
here, we made a group of 8 or 2³ cells So 3 variables will be eliminated.

now from K-map , We see that Only B is common within the group
So, Simplified expression is = B

Answer: A

Explanation:

Decoder is a combinational circuit that converts binary code or binary information into human understandable format.

Characteristics of Decoder:
It has ‘n’ input lines and maximum of 2n output lines.
It performs the reverse operation of Encoder.
At any time, only one of outputs can be ‘1’ and rest of the outputs are zero(0).
It is used in output system like display units.
2-to-4 Line Decoder:
Let 2 to 4 Decoder has two inputs X & Y and four outputs D0, D1, D2 & D3. The block diagram of 2 to 4 decoder is shown in the following figure-

→ Needs 2 inverters (NOT) for X′, Y′ and 4 AND gates for each output.

Answer: D) 5
Explanation:
In general, to implement B : 1 MUX using A : 1 MUX , one formula is used to implement the same.
B / A = K1,
K1/ A = K2,
K2/ A = K3

KN-1 / A = KN = 1 (till we obtain 1 count of MUX).

And then add all the numbers of MUXes = K1 + K2 + K3 + .... + K N .
To implement 16 : 1 MUX using 4 : 1 MUX
Using the above formula, we can obtain the same.
16 / 4 = 4
4 / 4 = 1 (till we obtain 1 count of MUX)
Hence, total number of 4 : 1 MUX are required to implement 16 : 1 MUX = 4 + 1 = 5.


To implement 64 : 1 MUX using 4 : 1 MUX
Using the above formula, we can obtain the same.
64 / 4 = 16
16 / 4 = 4
4 / 4 = 1 (till we obtain 1 count of MUX)
Hence, total number of 4 : 1 MUX are required to implement 64 : 1 MUX = 16 + 4 + 1 = 21.

Answer: B) T = 1
T flip-flop changes state on every clock edge when T=1.

Answer: C) Modulo counter

Explanation:
Step 1: Understanding what the question means
"A counter that returns to zero after counting to a maximum"

means:

· It counts sequentially from 0 → 1 → 2 → ... → (N−1),

· then resets back to 0 and repeats.

This “wrap-around” behavior is exactly the definition of a modulo counter (Mod-N counter).

A Mod-N counter is a digital counter that goes through N distinct states (from 0 up to N−1) before resetting to zero.
Examples:
Mod-2 counter: counts 0,1 → resets to 0
Mod-10 counter: counts 0–9 (used in digital clocks, called decade counter)
Mod-16 counter: counts 0–15, common in binary systems
When it reaches its maximum count (N−1), it automatically rolls over (returns to 0).
So:
After max → resets to 0 automatically → repeats the cycle.
This matches the question description perfectly.
Others option:
A) Ring Counter
→A type of shift register counter.
→Circulates a single '1' (or '0') through flip-flops.
→Has N states if it has N flip-flops, but doesn’t count in binary sequence.
→It doesn’t “count to a maximum number” — it rotates a bit pattern.
Not a Modulo binary counter.

B) Johnson Counter (Twisted Ring Counter)
→ Similar to ring counter but with feedback of the inverted output.
→Goes through 2N states for N flip-flops.
→Also doesn’t count in binary; it produces a Gray-like sequence.
Not a Modulo binary counter either.

D) Up/Down Counter
→Can count up or down depending on control input.
→It still may be a Mod-N counter, but the term “up/down” only describes direction — not the automatic return to zero.
The question asks about returning to zero after maximum, not about counting direction.

Answer: D) Higher noise immunity and low power

Explanation:

1) CMOS vs TTL basics
TTL (Transistor-Transistor Logic): Uses bipolar junction transistors (BJTs) for both logic gates.

CMOS (Complementary MOS): Uses complementary pairs of MOSFETs (PMOS and NMOS) in each gate.

Answer: D) Defining multiple functions with the same name but different parameters
Explanation:

1) Definition of Function Overloading

Function overloading is a feature in many programming languages (like C++, Java, Python (limited via default args)) that allows multiple functions to have the same name, but with different parameter lists (different number or types of arguments).

It helps to increase code readability, reusability, and flexibility — because you can perform similar operations with different data types or argument counts under one common function name.

2) Example in C++
#include <iostream>
using namespace std;

void add(int a, int b) {
cout << "Sum (int): " << a + b << endl;
}

void add(double a, double b) {
cout << "Sum (double): " << a + b << endl;
}

void add(int a, int b, int c) {
cout << "Sum (three int): " << a + b + c << endl;
}

int main() {
add(2, 3); // Calls add(int, int)
add(2.5, 3.5); // Calls add(double, double)
add(1, 2, 3); // Calls add(int, int, int)
}

Output:

Sum (int): 5
Sum (double): 6
Sum (three int): 6

All three functions are named add, but the compiler automatically chooses the correct one based on the number and type of arguments.

Answer: C
Explanation: The * and / have the same precedence so associatively.
Then” 5 * 9 / 3 + 9” evaluate as,
5 * 9 is 45 => 45 / 3 + 9
45 / 3 is 15 => 15 + 9
15 + 9 is 24
Hence 24 is the final answer

Answer: B) strcmp()
Explanation:

strcmp(s1, s2)

Compares two strings lexicographically (dictionary order).

Returns:
0 → if both strings are equal.

<0 → if s1 < s2.

>0 → if s1 > s2.

strcpy → Copy
strcmp → Compare
strcat → Concatenate
strlen → Length

Answer: a) 0

Trap Explanation:

· a++ (post increment) → value used = 1, then a=2.

· !1 = 0.

Answer: A) continue

Explanation:

In C (and most programming languages like C++, Java, Python), the continue statement is used inside loops (for, while, do-while) to skip the rest of the current iteration and jump to the next iteration of the loop.

How continue Works

When the continue statement executes:

The remaining statements in the current loop body are skipped.

The control jumps back to the loop’s condition check (in while/do-while) or to the update expression (in for loop).

The loop then continues with the next iteration, if the loop condition is still true.

Example (using for loop)
#include <stdio.h>
int main() {
for (int i = 1; i <= 5; i++) {
if (i == 3)
continue; // skip iteration when i = 3
printf("%d ", i);
}
return 0;
}

Output:
1 2 4 5
Explanation:
When i = 3, the continue statement is executed.
It skips the printf() statement for that iteration.
The loop then moves on to the next iteration (i = 4).

Difference between break and continue
Keyword →→→→→Meaning →→→→→→→→→→→Effect
break →→→ Terminates the entire loop→→ Exits the loop completely
continue→→ → Skips current iteration →→→ Moves to next iteration

Answer: A) To allow code reusability

What is Inheritance?
Inheritance is one of the core principles of Object-Oriented Programming (OOP).
It allows a new class (child/derived class) to acquire the properties and behaviors (data members and member functions) of an existing class (parent/base class).
This means that the derived class does not need to rewrite the code already written in the base class — it can reuse and extend it.

Purpose of Inheritance → Code Reusability
The main goal of inheritance is to reuse existing code.
It helps in avoiding redundancy and promotes maintainability.
The derived class can add new features or override existing ones while keeping the old behavior intact.

Answer: C
Explanation:

Simple Array Queue Problem:

In a linear array-based queue, once the rear pointer reaches the end of the array, no more insertions can be made, even if there is free space at the beginning (due to dequeues).
Example:
Queue size = 5
Elements dequeued from the front → empty slots form at the beginning.
Rear is at end → still shows "overflow" even though space exists.

Circular Queue Solution:
In a circular queue, the queue is treated as circular (last index connects back to the first).
So, if space is available at the beginning (because some elements were dequeued), Circular queues reuse empty slots by connecting end → beginning.
This avoids false overflow and utilizes memory efficiently.

In short:
Simple queue wastes space after several dequeues.
Circular queue reuses space efficiently.
That’s why the advantage = avoids overflow when free space is available

Answer: A) Sorting elements
Explanation:
Valid operations in BST:

1. Searching for an element

Primary use of BST.

Uses the property: Left subtree < Root < Right subtree.

Time complexity: O(h), where h = height of tree.

2. Inserting a new element

Place the new element at the correct position (leaf) while maintaining the BST property.

3. Deleting an element

Remove a node while maintaining BST rules
Three cases:
Node is a leaf → delete directly.
Node has one child → replace with child.
Node has two children → replace with inorder predecessor/successor.

Option A) : Sorting elements

A BST can give sorted elements if we perform an inorder traversal.

But “sorting” itself is not an operation defined on BST.

Sorting is an application, not a built-in operation.

The BST doesn’t provide an explicit sort() function — it only supports dynamic set operations.

Final Note :

Valid BST operations: Insert, Search, Delete, Traverse.

Sorting is not a direct operation, though inorder traversal yields sorted order.

Answer: B) Doubly linked list
Explanation:

Option A) Singly linked list
Each node has data and a single pointer → points to the next node only.
Traversal is one-way only (forward direction). Cannot traverse both ways.

Option B) Doubly linked list
→Data
→Pointer to next node
→Pointer to previous node

This allows movement in both directions:
Forward: using next pointer.
Backward: using previous pointer.
Supports two-way traversal

Option C) Circular linked list
→Last node connects back to the first node (circular connection).

→Can be singly circular (only forward traversal) or doubly circular (both directions).

Option D) Self-referential linked list

A general concept where a structure contains a pointer to itself (used in all linked lists).
Not specifically both-way traversal.

NOTE:
Singly LL → one way.

Doubly LL → two ways (correct answer).

Circular LL → wraps around but usually one way.

Self-referential → just the general pointer structure.

Answer: B) ⌈log₂(n)⌉
Explanation
1. Height of a binary tree:
Height = number of edges on the longest path from root to a leaf.
In a complete binary heap, nodes are filled level by level (except possibly the last).
2. Relationship between nodes and height
At height h, the maximum number of nodes = 2^(h+1) - 1.
At height h, the minimum number of nodes = 2^h.
So if a heap has n nodes:

2^h ≤ n ≤ 2^(h+1) - 1
Take log₂:
h ≤ log₂(n) < h + 1

Therefore: h = ⌊log₂(n)⌋

Since some definitions use height as number of levels - 1, many books/formulas also express it as ⌈log₂(n)⌉ for simplicity.
Example
If n = 15 nodes:

log₂(15) ≈ 3.9 → height = ⌊3.9⌋ = 3.
Indeed, a full binary heap of 15 nodes has height = 3.
If n = 16:

log₂(16) = 4 → height = 4.

Answer: B) Searching
Explanation

Goal of Hashing: Provide fast search operations (average O(1) time).

Hashing uses a hash function to directly compute the storage location of data → no need for linear or binary search.

This makes hashing ideal for searching large datasets like symbol tables, dictionaries, or databases.

Others option:

A) Indexing → Indexing is database technique (e.g., B-trees), not the same as hashing.

C) Encryption → Encryption secures data, hashing is not primarily encryption (though cryptographic hash functions exist).

D) Sorting → Sorting arranges data in order, hashing does not maintain order.

Answer: B) Min-heap
Explanation:

Huffman Coding Overview
Huffman coding is a lossless data compression algorithm.
It works by repeatedly merging two nodes with the smallest frequencies to build a binary tree (Huffman Tree).

2. Why Min-Heap?
At each step, Huffman’s algorithm needs to quickly find the two nodes with the smallest frequency.
A min-heap is a priority queue where:
The root always contains the minimum element.
Insertion and extraction of the minimum element take O(log n) time.

Example:Suppose symbol frequencies: A:5, B:9, C:12, D:13
Build a min-heap with these frequencies: [5, 9, 12, 13]
Extract two smallest (5 and 9) → combine → insert 14 back → min-heap adjusts automatically.
This ensures efficient O(n log n) construction of Huffman tree

A min-heap efficiently extracts two smallest frequency nodes at each step → reduces time complexity to O(n log n).

ANSWER: A
Explanation:
Tree Traversals Overview
Binary tree traversals are methods to visit all nodes:

Preorder: Root → Left → Right
Inorder: Left → Root → Right
Postorder: Left → Right → Root
In all three traversals, the left subtree is always visited before the right subtree.

when the root is visited:
Preorder → before left subtree
Inorder → between left and right subtree
Postorder → after left and right subtree
Hence, the common property = “left subtree visited before right subtree.”

Answer: D) All of the above

Explanation:

Divide and Conquer divides a problem into smaller subproblems, solves them recursively, and combines the results.

Advantages:

Parallelism: Subproblems can be solved independently.

Simplicity: Breaking problems into smaller parts simplifies logic.

Faster in some cases: Recursive breakdown reduces time complexity (e.g., Merge Sort O(n log n) vs Bubble Sort O(n²)).

Answer: D) Knapsack Problem

Explanation:

Dynamic Programming (DP) solves problems with overlapping subproblems and optimal substructure by storing results of subproblems.

The 0/1 Knapsack problem is a classic DP problem: we decide to include/exclude an item to maximize value.

DFS, Binary Search, and Quick Sort don’t need DP.

Answer: D) O(n²)

The highest degree term dominates → n².

Constants (5) and lower terms (3n, 2) are ignored in asymptotic growth

Answer: B
Explanation:
• Circuit switching (Telephone networks): requires a dedicated path, even if no data is sent → wastes bandwidth.
Packet switching (Internet): data broken into packets, efficient resource usage.

Answer: B) TDMA

Explanation:

GSM (Global System for Mobile Communications) → 2G cellular system.
It uses TDMA (Time Division Multiple Access) to allocate time slots to multiple users.

CDMA (Code Division Multiple Access) is used in some 2G (IS-95) and 3G systems.
CSMA/CA → wireless LAN (Wi-Fi).
WDM → optical fiber communications.

Answer: C) 16

Solution:

· Class C default mask = /24

· New mask = /28 → borrowed bits = 28 – 24 = 4

· Number of subnets = 2^{borrowed bits}=2⁴=16

Answer: C

Explanation:

ATM was designed as a unified transport technology:

Can carry voice, video, and data simultaneously.
Fixed cell size ensures low latency.
Unlike IP, which uses variable-length packets, ATM keeps latency predictable.

Answer: B
Explanation:

Encryption converts plaintext → ciphertext, so only authorized users can read.
Hashing ensures integrity, not confidentiality.
Digital signatures authenticate sender.

Answer: B

Explanation:

Symmetric encryption (e.g., AES, DES): sender & receiver share the same secret key.
Advantage: fast.
Disadvantage: key distribution problem (how to share securely?).

Answer: B) 100 m
Explanation:
UTP cables in Ethernet can transmit up to 100 meters reliably.
Beyond this, attenuation and crosstalk degrade the signal.

Answer: A
Explanation:

Wi-Fi operates on unlicensed ISM bands:

2.4 GHz (longer range, more interference)

5 GHz (higher speed, shorter range).

Latest Wi-Fi 6E adds 6 GHz band.

Answer: C

Explanation:

PSK (esp. QPSK, QAM) is bandwidth efficient because more bits per symbol.

ASK: noise-sensitive.

FSK: requires larger bandwidth.

AM: analog, not efficient.

Answer: C

To reconstruct a band-limited signal without aliasing, the sampling rate must be at least twice the highest frequency.

Called Nyquist rate.

Example: Audio frequency 20 kHz → sampled at ≥ 40 kHz (CD audio uses 44.1 kHz).

Answer: B

TDM assigns time slots to users sequentially.

Synchronous TDM: fixed slots even if idle.

Statistical TDM: slots allocated dynamically → higher efficiency.

Answer: C) CRC (Cyclic Redundancy Check)
Explanation:
What is a burst error?
A burst error occurs when two or more bits in a sequence are corrupted.
Example: 1011101 → one or more consecutive bits flipped.

Why CRC is efficient for burst errors:
Cyclic Redundancy Check (CRC) treats data as a polynomial and divides it by a generator polynomial.
The remainder (CRC value) is transmitted along with the data.
At receiver, polynomial division is performed; if remainder ≠ 0 → error detected.
CRC can detect:

All single-bit errors
All double-bit errors
Any odd number of errors (depending on polynomial)
Most burst errors, especially those shorter than the CRC lengt

Answer: C) 500–600 ms
Explanation:

GEO satellites → ~36,000 km altitude

Propagation delay → 250–270 ms one-way → 500–540 ms round-trip

Causes slight lag in voice or gaming applications

Answer: D) None of the mentioned
Explanation:
Nature of the Error

→ Writing * instead of / is not a syntax error (grammar is still correct).

→ It’s not a semantic error either (types are still valid — multiplying integers is legal).

It is a logical error → the program runs, but gives wrong output compared to programmer’s intention.

Logical errors like using * instead of / cannot be detected by either compiler or interpreter.

They can only be detected during testing/debugging when the output is checked

Answer: A) Every DFA is also an NFA
• DFA ⊆ NFA in expressive power.
• Both recognize exactly regular languages.
• NFAs can be smaller, but after conversion to DFA, state count may explode (but not always)

Answer: (D) Any non-deterministic PDA can be converted to a deterministic equivalent.
Explanation:
Deterministic PDA cannot handle ambiguous languages or grammar, but NDPDA can handle ambiguous languages and any context-free grammar. As a result, no non-deterministic PDA can be converted to a deterministic PDA.

Answer: C) Type mismatch

Lexical Analysis: Reads characters and forms tokens (keywords, identifiers, operators).

Detects unrecognized symbols or invalid characters.
Syntax Analysis (Parsing): Checks if tokens form grammatically correct statements.
Detects missing semicolons, misplaced parentheses, syntax violations.

Semantic Analysis: Ensures the meaning of the program is correct.

Checks type consistency, scope rules, function argument matching, and variable declarations.

Semantic errors occur when the structure is correct, but the meaning is wrong.
Example:
int x;
x = "hello"; // Type mismatch: assigning string to int

Syntactically, x = "hello"; is valid (ends with semicolon, valid tokens).
Semantic analysis detects the type mismatch.

Options option:

a) Missing semicolon: Syntax error → detected during parsing.
c) Unrecognized keyword: Lexical error → detected during lexical analysis.
d) Misplaced parenthesis: Syntax error → detected during parsing.

Answer: B) To make code run faster or use less memory

Explanation:

Optimization improves performance (speed, memory, power consumption).

Must preserve the semantic meaning of the program.

Example: x = 5; y = x * 2; → optimized as y = 10;.

Answer: A) Register allocation

Explanation:

Limited registers → compiler must allocate variables wisely.

Example: in loops, keep frequently used variables in registers to improve speed.

Answer: B) Proving a language is not regular

Explanation:

Pumping Lemma provides a property that all regular languages must satisfy.
If a language violates it, → not regular.
Example: {aⁿ bⁿ | n ≥ 0} fails pumping lemma → not regular.

Answer: D) Expand addressable memory
Explanation:

8086 is a 16-bit processor → 16-bit registers → max 64 KB memory directly addressable.
But Intel wanted 1 MB memory access.
Solution: Segmentation
Memory divided into segments (Code, Data, Stack, Extra).
Physical Address =Segment Register×16+Offset

Allows 20-bit addresses → 1 MB memory access.

Other options:

A) Eliminate registers → segmentation actually uses more registers
B) Simplify programming → segmentation complicates programming, not simplifies.
C) Reduce clock speed → unrelated.

Answer: C) Modified Harvard with EU and BIU
Explanation:
8086 split into:
Bus Interface Unit (BIU): Fetches instructions, handles queue (6 bytes prefetch).
Execution Unit (EU): Decodes and executes instructions.
Works like Harvard (separate fetch and execute), but shares same memory.
Key feature: Instruction prefetch → basic pipelining.

Answer: B) 8255A chip

Explanation:
1. What is 8255A?

Intel 8255A = Programmable Peripheral Interface (PPI) chip. Provides programmable parallel I/O ports for microprocessors like 8085, 8086.

It has 3 ports:
Port A (8-bit)
Port B (8-bit)
Port C (8-bit, split into two 4-bit parts
These ports can be programmed as input or output, depending on the control word written to the control register.

Widely used for interfacing keyboards, LEDs, printers, displays, switches, etc.

8237 → DMA Controller
8255A → I/O interface.
8259A → Interrupt controller.
8253/8254 → Timer/counter.

Answer: B
Explain:

What is a Hazard in Pipelining?
In a pipelined CPU, hazards are conditions that prevent the next instruction from executing in the next cycle.
Three major types:

Data Hazard → Dependency on the result of a previous instruction.
Structural Hazard → Hardware resource conflict.
Control Hazard → Arises due to branch/jump instructions.

2. What is a Control Hazard?
Control hazard = Branch hazard.
Happens when the CPU does not know which instruction to fetch next because of a branch or jump decision.
So, Answer: B) Branch and jump instructions

Others option:
Cache misses: his is a memory access delay, not a pipeline control hazard.
Divide-by-zero: This causes an exception/interrupt, not a control hazard.
Resource sharing: This leads to structural hazards, not control hazards.

Answer: D
Explanation:
Control signals orchestrate all data movement and processing inside CPU. They tell ALU what to compute, which registers to load, and when to read/write memory.

Answer: A
Explanation:
• Pipelining allows multiple instructions to overlap in execution.
Latency per instruction doesn’t improve, but overall throughput (instructions per unit time) increases.

Answer: B) Checkpointing and rollback

Explanation:
1. Fault-tolerant computing basics:
Fault tolerance = ability of a system to continue correct operation even when faults occur.
Approaches can be hardware-based or software-based.

2. Software approach – Checkpointing and Rollback
Checkpointing = saving the state of a process/program at certain intervals.
If a fault occurs, the system rolls back to the most recent checkpoint instead of restarting from the beginning.
Example: Long-running computations in distributed systems (like supercomputers).
This is a software-level technique, because the system state management and recovery logic are handled in software, not hardware.

Checkpointing and rollback = software approach to fault tolerance.
TMR, ECC memory, systolic arrays = hardware techniques.

Answer: C
Explanation:
• Parallelism suffers from synchronization overhead, communication delays, and dependencies (Amdahl’s law).
• Limits maximum achievable speedup

Answer: b) Store metadata about data

What is a Data Dictionary?

A data dictionary is like the “catalog” or “blueprint” of a database.

It contains metadata → data about data.

It does not store actual user data (like names, salaries, etc.), but stores:

→Table names

→Column names & data types

→Constraints (Primary Key, Foreign Key, etc.)

→Indexes

→Relationships between tables

→Access permissions

Answer: D) Both (A) and (B)
Explanation:
Virtual memory can be implemented by paging (fixed-size blocks) or segmentation (variable-size).
In modern OS, paging (sometimes segmentation + paging) is dominant.

(C) Swapping is process-level, not directly VM implementation

Answer: A
Explanation:

Table = Relation.
Row = Tuple.
Column = Attribute

Answer: A) Roll_No → Student_Name
Explain:
Functional dependency in a database management system (DBMS) defines a relationship between attributes in a table, where one attribute uniquely determines another. It is denoted as X → Y, meaning the value of attribute X determines the value of attribute Y.

Roll_No uniquely determines Student_Name.
Functional dependency is always one-way (not necessarily reversible)

Answer: B) Every record

Dense Index
In a dense index, a record is created for every search key valued in the database. This helps you to search faster but needs more space to store index records. In this Indexing, method records contain search key value and points to the real record on the disk.
Pros: Fast search.
Cons: Large index size, high maintenance overhead.


Sparse Index: Index has one entry per block of records, smaller but slower for search.

Answer: B) Transitive dependency
Explain:
Definitions of normal forms:

1NF (First Normal Form) →All attributes are atomic (no repeating groups or multivalued attributes).
2NF (Second Normal Form)
→Relation is in 1NF.
→No partial dependency → no non-key attribute depends on part of a composite primary key.
3NF (Third Normal Form)
→Relation is in 2NF.
→No transitive dependency → non-key attribute must depend only on the primary key, not on another non-key attribute.

BCNF (Boyce–Codd Normal Form) →Even stricter: for every functional dependency X → Y, X must be a super key.

Transitive Dependency:
Definition: A non-key attribute depends on another non-key attribute instead of directly on the primary key.
Example Table:
Student(RollNo, DeptID, DeptName)
RollNo → DeptID
DeptID → DeptName
⇒ RollNo → DeptName (through DeptID) = transitive dependency

Why 3NF Eliminates Transitive Dependency:
In 3NF, all non-key attributes must depend directly on the key.
To fix the above example:
Split into two relations:
Student(RollNo, DeptID)
Department(DeptID, DeptName)

Now,
RollNo → DeptID (direct)
DeptID → DeptName (direct in another relation)
This removes redundancy and anomalies.

Answer: A) Fraction of tuples that satisfy selection condition
Explanation:

Selectivity = (Result size) ÷ (Total relation size). Lower selectivity → fewer tuples returned → cheaper.

Answer: C) DELETE
Explanation:

DELETE is a DML (Data Manipulation Language) command used to remove specific rows from a table based on a condition.

Syntax:

DELETE FROM Students WHERE Age < 18;
Only rows satisfying the WHERE condition are deleted.
If WHERE is omitted, all rows are deleted, but table structure remains.

DELETE (DML)→ selective row removal.
TRUNCATE (DDL) → removes all rows fast.
DROP (DDL) → deletes the table entirely.
CLEAR→ NOT valid SQL command

Answer: C) JOIN

JOIN connects tables using keys.
Example:
· SELECT Orders.order_id, Customers.name

· FROM Orders

· JOIN Customers ON Orders.customer_id = Customers.id;

UNION combines results vertically.
INTERSECT finds common rows

Answer: B) User Mode
Explanation

User Mode is the CPU mode in which regular application programs run.

Characteristics:

Restricted access to hardware and critical system resources.

Cannot execute privileged instructions (like I/O or memory management) directly.

Any request for system resources is made via system calls, which temporarily switch the CPU to kernel mode.

Examples:
Word processors, web browsers, media players all execute in user mode.

Key Point:

User mode = safe execution for applications

Kernel mode = full access for OS services

Answer: D) Real-Time OS
Explanation
Real-Time Operating System (RTOS) is designed to guarantee predictable and deterministic response times.
Embedded systems, like pacemakers, industrial robots, and avionics, require that the OS responds within strict deadlines.
Key Features of RTOS for Embedded Systems:

→Deterministic timing – tasks execute within guaranteed deadlines.
→Fast context switching – critical for handling multiple time-sensitive tasks.
→Minimal latency – ensures hardware responses happen on time.
→Reliability and fault tolerance – essential for life-critical applications like pacemakers.

Why not the others?
A) Batch OS → Executes jobs sequentially without interaction; not suitable for real-time.
B) Time-Sharing OS → Provides interactive response but cannot guarantee strict timing.
C) Distributed OS → Manages multiple machines as a single system; irrelevant for small embedded devices.


Embedded systems = real-time response critical → RTOS is required

Answer: A) Shortest Job First (SJF)
Explanation:
1. What is SJF Scheduling?
Shortest Job First (SJF) schedules the process with the shortest CPU burst time next.
Can be non-preemptive (once a process starts, it runs to completion) or preemptive (Shortest Remaining Time First, SRTF).

2. Why SJF Minimizes Average Waiting Time
Average waiting time (AWT) is the mean time a process spends in the ready queue before execution.
By executing short processes first, longer processes do not block multiple short processes.
This reduces total waiting time for all processes.

Example:
Processes with CPU bursts: P1=2, P2=4, P3=6 (time units)
FCFS order: P1 → P2 → P3

Waiting times: P1=0, P2=2, P3=6 → Avg = 2.67
SJF order: P1 → P2 → P3 (already sorted, same in this case)
If bursts were unsorted, SJF always optimizes AWT.
Key Point:
SJF = Optimal scheduling algorithm for minimizing average waiting time when CPU burst times are known.
Drawback: Can cause starvation for long processes.

Answer: B) Avoiding thrashing
Explanation
1. What is the Working Set?
The working set of a process is the set of pages actively used by the process during a certain period of execution.
Denoted as W(t, Δ), where Δ is the time window.
Idea: If all pages in the working set are in memory, the process executes efficiently with minimal page faults.

2. How the Working Set Model Prevents Thrashing
Thrashing occurs when the sum of working sets of all processes exceeds physical memory, causing excessive page faults.
Working set model approach:
→OS tracks the working set of each process
→Ensures enough frames are allocated to hold the working set
→Only loads processes whose working set can fit → prevents thrashing
This ensures processes run efficiently without constant paging.
Key Point:
Working set = actively used pages of a process
Goal: Keep the working set in memory → avoid thrashing

Answer: B) Multithreading

Why Multithreading is More Efficient
Threads within the same process share data and resources → no need to allocate separate memory for each thread.
Context switching between threads is faster than switching between processes.
CPU utilization improves because threads can execute while others are waiting (e.g., I/O operations).

Answer: C) Deadlock
Explanation:

Deadlock = resource allocation issue, not a security threat.
Trojan, Worm, Virus = malicious security threats.

Answer: D) All of the above
Explanation:

A) Poor estimation of project cost and schedule
One of the most frequent risks.
Leads to cost overrun, missed deadlines, and scope reduction.
Root cause: inaccurate requirements, lack of metrics, or over-optimism.

B) Ambiguous or changing user requirements
Known as requirements volatility.
Causes scope creep, rework, and delays because the target keeps changing.
Often arises from poor communication with clients or unclear vision.

C) Lack of top management support
Without executive backing, teams may face budget cuts, resource shortages, and low morale.
Also weakens decision-making and project prioritization.
All three contribute to project risk, hence the best answer is (d) All of the above.

Key Concept:
In software project management, risk categories typically include:

Project risks → Cost, schedule, resource, and planning failures.
Technical risks → Technology limitations, integration issues, performance problems.
Business risks → Changing user needs, budget issues, or organizational instability.
Good managers identify, analyze, and mitigate these risks early through proper risk management planning.

Answer: A) ER Diagram (Entity–Relationship Diagram)
Explanation:

What is an ER Diagram?
An Entity–Relationship (ER) Diagram) is a data modeling technique used to visually represent:

Entities → real-world objects or concepts (like Student, Course, Employee)

Attributes → properties of entities (like Name, ID, Salary)

Relationships → how entities are connected (like enrolls in, manages, teaches)

In other words, ER diagrams model how data is stored, related, and organized within a system — forming the foundation for database design.

Purpose of ER Diagrams

Define data structure clearly before implementation.

Show relationships among entities (one-to-one, one-to-many, many-to-many).

Help transform the conceptual model into a relational database schema.

Example:
A simple Student–Course ER Diagram:

[STUDENT] ──<enrolls>── [COURSE]

Here:

Entities: STUDENT, COURSE

Relationship: enrolls

Attributes: Student_ID, Student_Name, Course_ID, Course_Name

Answer: C) Polymorphism
Explanation:
A) Encapsulation: Data hiding, not multiple forms.
B) Inheritance: Enables hierarchy and reuse, but not multiple forms by itself.
C) Polymorphism: Allows objects to respond differently to the same message depending on their type. Example: method overriding in subclasses. (Correct)
D) Aggregation: Represents “has-a” relationships, unrelated to polymorphism

Answer: B) High dependability and fault tolerance
Explanation

What Are Critical Systems?

A critical system is one where failure can lead to serious consequences, such as:

→Loss of life (e.g., medical, aviation, or nuclear control systems)

→Major financial loss (e.g., banking or stock trading systems)

→Environmental damage (e.g., chemical plant monitoring systems)

Hence, these systems must operate reliably and safely under all conditions So, High Dependability and Fault Tolerance is required in Critical system

Critical systems are designed with dependability as their top priority.

Dependability includes several key attributes:

Reliability → System performs its function correctly and continuously.

Availability → System remains operational with minimal downtime.

Safety → System operates without causing unacceptable harm.

Security → Protection from unauthorized access or malicious actions.

Maintainability → Faults can be detected and repaired quickly.

Fault Tolerance ensures that even when part of the system fails, it can continue functioning correctly (e.g., redundant components, backup systems, error detection and recovery mechanisms).

Example:

An Aircraft control system must keep functioning even if one sensor or processor fails.

A hospital ventilator system must remain reliable during power interruptions — using backup circuits.

Answer: D) Waterfall development
Explanation:

Waterfall is a development methodology, NOT a fault-tolerance technique.

The others are explicitly designed to detect, mask, or recover from faults.

Answer: C

Explanation:

A) Corrective: Fixes defects, not performance improvements.
B) Adaptive: Adjusts to new environments or platforms.
C) Perfective: Focuses on enhancing software features, performance, readability, and maintainability after delivery. (Correct.)
D) Preventive: Avoids future problems but not specifically improving performance.

Answer: B) Iterative, incremental, with strong user involvement

Explanation
What Is Agile Software Development?

Agile is a software development methodology that emphasizes:

→Iterative and incremental development – the product is built in small, manageable pieces.

→Customer collaboration – continuous involvement of users/stakeholders to refine requirements.

→Flexibility and adaptability – changes are welcomed even late in development.

→Working software over comprehensive documentation – focus on delivering functional code.

Agile Manifesto Principles:

→Individuals and interactions over processes and tools

→Working software over comprehensive documentation

→Customer collaboration over contract negotiation

→Responding to change over following a plan

Answer: B) Model Checking (most standard technique)

Explanation
What Is Formal Verification?
Formal verification is the process of proving or disproving the correctness of a system’s design or program with respect to a formal specification using mathematical and logical methods.

Goal: Ensure that the system behaves exactly as intended and satisfies all requirements.
Especially important for critical systems (aircraft, medical devices, nuclear plants) where errors are unacceptable.

Common Techniques for Formal Verification
→Model Checking
→Theorem Proving
→Abstract Interpretation

Analyzes program properties using approximate models to detect potential errors like buffer overflows, deadlocks, or race conditions.

A) Code walkthroughs: Informal verification, not formal.
C) User surveys: Validation tool, not formal verification.
D) Unit testing: Dynamic verification, not formal.

Answer: A) Alpha is performed by developers; Beta by end users
Explanation:

The key distinction lies in who performs the testing and where it’s done.

Alpha:
→By developers/testers at developer site
→Controlled environment

Beta:
→By actual users at user site
→Real environment, realistic feedback

Other options:

b) Both after deployment → They occur before final release.
c) Alpha tests usability only → Alpha tests both functionality and usability.
d) No difference →They differ in purpose, performers, and environment.

Answer: B)
Explanation

Halstead’s Software Science Metrics
Developed by: Maurice H. Halstead (1977)
Purpose: To measure software complexity, volume, and effort based on operators and operands in the source code.
Key Concepts:
n1​: number of distinct operators
n2​: number of distinct operands
N1​: total number of operators
N2​: total number of operands
Volume (V):
V=(N1+N2) × log⁡2(n1+n2)
Effort (E):
E=V/S where
S = “programmer’s ability” factor.
Use: Measures code complexity, effort to implement or understand, and sometimes potential number of bugs.

Answer: D) p∨¬p

Explanation:

A tautology is a statement that is true for all truth values of its variables.

For any proposition p:
if p is true → p∨¬p=T∨F=T.

If p is false → F∨T=T.

So, it is always true.

Others option:

A) p∧¬p → always false (contradiction).
B) p∧q → not always true; true only if both true.
C) p∨q → not always true; depends on values of p,q.

Answer: A) One

Empty set (∅): A set that contains no elements.

Example: ∅ = {}

Power set (P(S)): The set of all subsets of a set S.

If a set has n elements,
then the power set has 2n subsets.

In empty Set, n=0 elements.

Formula: Number of subsets =2n =20=1
So, the power set of ∅ = { ∅ }

 Answer: B)
Explanation:
•    Order = number of past terms on which current term depends.
•    Example: F(n) = F(n-1) + F(n-2) → order = 2.

 Answer: A) [−1,1]

Explanation:

if x∈R , for any value of x Sine function  f(x)=sinx oscillates between -1 and 1.

Hence the range is [-1,1].

Answer: B

Explanation:
Partial pivoting rearranges rows so the pivot (diagonal element) has the largest magnitude. This minimizes numerical instability and round-off error.

Answer: B) Parabolas

Explanation:
Simpson’s 1/3 rule fits a second-degree polynomial (parabola) through each pair of subintervals.

A) Straight lines
 used in Trapezoidal Rule where the function between two points is approximated by a straight line.

C) Cubic polynomial
Used in Simpson’s 3/8 Rule, which fits a cubic polynomial through four points.

D) Circle
A circle has no relation to numerical integration approximation methods.

Answer: C) Both A & B

Differential equations can be solved using both

1. Euler’s Method, and
2. Runge–Kutta Method.

Answer: C) Identity matrix

Answer: B) Linear interpolation 

Answer: C) Numerical integration

Explanation:

Key Points:

Numerical differentiation → finds the derivative from tabulated values.

Numerical integration → estimates the area under the curve using the tabulated values.

Quadrature → is another term for numerical integration.

Numerical value → just a number, not a method.

Answer: B) Procedural knowledge

Explanation:

Knowledge can be categorized in several ways:

1. Declarative knowledge – “knowing what” Facts, concepts, rules
                                           Example: “Paris is the capital of France.”

2. Procedural knowledge – “knowing how” Knowledge of how to perform tasks or procedures
                                          Example: “How to ride a bicycle” or “How to solve a linear equation.”

3. Heuristic knowledge – “rules of thumb” Strategies or shortcuts for problem solving
                                           Example: “Try the simplest approach first.”

4. Semantic knowledge – General understanding of concepts and meanings
                                           Example: Understanding the meaning of “gravity” in physics.

Procedural knowledge is action-oriented — it’s applied knowledge for performing tasks, NOT just knowing facts.

Answer: A) Handling uncertainty and incomplete information
Explanation:

        Real-world knowledge is often incomplete, ambiguous, or uncertain.

       Techniques like fuzzy logic, probabilistic reasoning, Bayesian networks help deal with uncertainty.

Answer: B) Fuzzy logic or probability

Explanation:

Expert systems often need to reason with incomplete, ambiguous, or uncertain information, because real-world situations rarely provide perfect or exact data. Expert systems use fuzzy logic or probabilistic methods to reason under uncertainty.

How uncertainty is handled:

Fuzzy Logic:
Deals with degrees of truth rather than just true/false.
Example: “The patient is somewhat feverish” → truth value between 0 and 1.

Probability / Certainty Factors:
Assigns a confidence level to each rule or fact.
Example: “There is an 80% chance of bacterial infection.”

Other options:

Boolean logic → only true/false, cannot model uncertainty.

Assembly language → programming language, unrelated to reasoning.

Graphical interface → only for user interaction, does not handle uncertainty.

Answer: b) Fuzzy logic or probability

Answer: C) Utility-based agent

Explanation:

In Artificial Intelligence (AI), agents are classified based on how they make decisions:
1. Random Agent
Takes actions randomly without reasoning

2. Model-based Agent
Maintains an internal model of the world to make decisions
Does not necessarily evaluate multiple outcomes quantitatively

3. Utility-based Agent
Chooses actions to maximize a given utility function
Can evaluate trade-offs between different choices
Example: Google Maps evaluates time, distance, traffic conditions and recommends the fastest route

4. Simple Reflex Agent
Acts only based on current percept
No consideration of future consequences or environment model
Example: Automatic light sensor

Google Maps considers multiple factors (traffic, distance, speed limits) and selects the route that maximizes utility (shortest travel time). This is the hallmark of a utility-based agent.

Answer: D) All of the above
Explanation:

FOL reasoning uses:

Forward chaining: Data-driven reasoning (facts → conclusion)

Backward chaining: Goal-driven reasoning (goal → required facts)

Resolution: Proof by refutation using clauses

Answer: A) Natural language generation (NLG)
Explanation:
    NLG = generating human-like text from internal representations or prompts.
•   Used in chatbots, report generation, dialogue systems.

Answer: B) Computer vision
Explanation:
    Cameras + sensors capture images → AI models recognize objects, lanes, signals, and pedestrians.

Answer: A) Expert system
Explanation:
    Uses rules and knowledge base: IF income > threshold AND credit score > threshold → approve loan.
Decision-making is rule-based, like expert systems