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West Bengal Council of Higher Secondary Education (WBCHSE) Class 12 (Higher Secondary) Mathematics Set 01 (Foundation Level) English Medium 100% Free Practice Test

West Bengal Council of Higher Secondary Education (WBCHSE) Class 12 (Higher Secondary) Mathematics: Linear Programming Online Test (Set 01 (Foundation Level))

Linear Programming — Set 01 (Foundation Level)

Practise free online CBT mock test for West Bengal Council of Higher Secondary Education (WBCHSE) Class 12 (Higher Secondary) Mathematics Chapter 12 'Linear Programming'. 20 MCQs, 20-minute timer, instant scorecard, and step-by-step solutions aligned with official board syllabus.

📝
20 MCQs
Questions
⏱️
20 Mins
Duration
🎯
20 Marks
Total Marks
➕
+1.0
Per Correct
🛡️
0.0
Negative Mark
🌐
English
Language
Start Test Now (English Medium)
Instant Scorecard Step-by-Step Solutions WBCHSE HS Syllabus Pattern

Chapter Study Guide & In-Depth Notes

Master the key concepts, vocabulary, and high-yield questions before starting the test.

3 Sections

Chapter Overview & Mathematical Foundations: Linear Programming

Class 12 Mathematics Guide

Mastering Linear Programming in Class 12 Mathematics requires a clear understanding of core mathematical definitions, standard algebraic or geometric formulas, deductive proofs, and computational algorithms.

In school term exams and competitive assessments (Olympiads, NTSE, and JEE Foundation), questions from Linear Programming assess calculation speed, accuracy with signs/units, and the ability to eliminate distractor options under timed conditions.

Core Moral & Key Takeaway:

Consistent formula revision combined with structured practice of solved numerical problems guarantees complete conceptual mastery and exam confidence.

Core Formulas, Theorems & Algebraic Laws

Formula Sheet & Properties
Term / Formula Type Definition / Meaning Explanation / Notes Example / Usage
Governing Formula Rule Primary mathematical law applied in Linear Programming. Linear Programming का मुख्य गणितीय सूत्र "Apply the governing theorem of Linear Programming accurately."
Analytical Deduction Method Deriving logical mathematical steps from given conditions. तार्किक गणितीय चरण "Maintain step-by-step clarity during calculation."
Sign & Unit Precision Convention Strict adherence to mathematical signs (+/-) and SI units. चिन्ह व इकाई की शुद्धता "Double-check signs before locking the final option."

Key Features & Devices Explored:

BODMAS / Operational Order
Always execute parentheses, exponents, multiplication, division, addition, and subtraction in sequence.
Distractor Elimination
Identify mathematically absurd or extreme values to eliminate 2 options immediately.

High-Yield Revision Points & Solved Board Exam Q&A

Maths Revision Notes
⚡ High-Yield Exam Takeaways:
  • Memorize all core definitions, formulas, and standard identities of Linear Programming.
  • Pay close attention to boundary values, domain restrictions, and unit conversions.
  • Attempt Foundation Set 01 to verify basics, followed by Advanced Set 02 for competitive excellence.
Frequently Asked Questions & Model Answers:
Q1 What is the best method to solve numerical MCQs in Linear Programming without errors?
Answer: Read the question carefully to identify given values and what is required, apply the standard formula directly, verify algebraic signs, and avoid guessing.

Sample Questions Preview

Free Sneak Peek

Here is a sneak peek of the questions included in this test set. Test your preparation by viewing the answer and detailed explanation before starting the timed exam.

Q1
What is the Objective Function Z in a Linear Programming Problem (LPP)?
রৈখিক প্রোগ্রামবিধিতে (LPP) বিষয়াত্মক অপেক্ষক বা উদ্দেশ্যমুখী অপেক্ষক (Objective Function, Z) বলতে কী বোঝায়?
लीनियर प्रोग्रामिंग प्रॉब्लम (LPP) में ऑब्जेक्टिव फंक्शन Z क्या है?
A
A quadratic functionএকটি দ্বিঘাত অপেক্ষকएक द्विघात फलन
B
\(A linear function Z = ax + by of decision variables x and y which is to be MAXIMIZED or MINIMIZED subject to linear constraints\)সিদ্ধান্ত গ্রহণকারী চলক x ও y-এর একটি রৈখিক অপেক্ষক Z = ax + by যাকে কিছু রৈখিক শর্তসাপেক্ষে চরম বা অবম করতে হয়निर्णय चर x और y का एक रैखिक फलन Z = ax + by जिसे रैखिक बाधाओं के अधीन अधिकतम या न्यूनतम किया जाना है
C
A constant numberএকটি ধ্রুবক সংখ্যাएक स्थिर संख्या
D
A set of linear inequalitiesরৈখিক অসমীকরণ গুচ্ছरैखिक असमानताओं का एक सेट
Correct Answer: Option B
Explanation:
The objective function Z = ax + by represents profit, cost, or output that needs to be optimized (maximized or minimized) under given linear inequality constraints.
উদ্দেশ্যমুখী অপেক্ষক হলো রৈখিক অপেক্ষক Z = ax + by যা লাভ সর্বাধিক বা খরচ সর্বনিম্ন করতে অপ্টিমাইজ করা হয়।
वस्तुनिष्ठ फलन Z = ax + by लाभ, लागत या आउटपुट का प्रतिनिधित्व करता है जिसे दी गई रैखिक असमानता बाधाओं के तहत अनुकूलित (अधिकतम या न्यूनतम) करने की आवश्यकता है।
Q2
What is the Feasible Region (Solution Region) of a Linear Programming Problem?
রৈখিক প্রোগ্রামবিধিতে কার্যকর অঞ্চল বা সমাধান অঞ্চল (Feasible Region) কোনটি?
एक रैखिक प्रोग्रामिंग समस्या का व्यवहार्य क्षेत्र (समाधान क्षेत्र) क्या है?
A
The entire XY planeসম্পূর্ণ XY সমতলसंपूर्ण XY विमान
B
Only the origin (0, 0)কেবল মূলবিন্দুकेवल मूल (0, 0)
C
The region outside all constraintsসমস্ত বাধার বাইরের অঞ্চলसभी बाधाओं से बाहर का क्षेत्र
D
The common convex region determined by the intersection of ALL given linear constraints and non-negativity restrictions (x ≥ 0, y ≥ 0)সমস্ত রৈখিক বাধা-নিষেধ এবং অ-ঋণাত্মক শর্তের (x ≥ 0, y ≥ 0) ছেদ দ্বারা গঠিত সাধারণ উত্তল অঞ্চলसभी दिए गए रैखिक अवरोधों और गैर-नकारात्मक प्रतिबंधों के प्रतिच्छेदन द्वारा निर्धारित सामान्य उत्तल क्षेत्र (x ≥ 0, y ≥ 0)
Correct Answer: Option D
Explanation:
The feasible region is the set of all points (x, y) that simultaneously satisfy all given linear constraints including non-negativity restrictions x ≥ 0, y ≥ 0.
সমস্ত প্রদত্ত অসমীকরণ ও শর্তসমূহকে একসাথে সিদ্ধকারী অভিন্ন বিন্দুসমূহ নিয়ে গঠিত অঞ্চলকে কার্যকর অঞ্চল বলে।
व्यवहार्य क्षेत्र सभी बिंदुओं (x, y) का समूह है जो एक साथ गैर-नकारात्मकता प्रतिबंध x ≥ 0, y ≥ 0 सहित सभी दिए गए रैखिक बाधाओं को संतुष्ट करता है।

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How Chapter-Wise Online CBT Tests Build Winning Habits for Future Competitive Exams

Focused chapter-wise CBT practice builds the speed, mental stamina, and analytical discipline required to ace CUET, JEE Main, NEET UG, NDA, CA Foundation, and College Entrance Exams.

Competitive Edge

Real-Time Clock Awareness & Pacing

समय प्रबंधन एवं गति नियंत्रण

In school examinations, students write answers without active pacing. In national entrance tests, students have barely 45-60 seconds per MCQ. Practicing with a 20-minute timer instills instinctive time-budgeting and prevents last-minute exam panic.

Mastery of the Elimination Technique

विकल्प निष्कासन विधि में दक्षता

Top rankers in competitive exams rarely compute every problem blindly. They spot subtle traps, evaluate extreme values, and eliminate 2 out of 4 distractors within seconds. Our 4-option sets teach critical distractor analysis.

CBT Screen Stamina & Digital Comfort

कंप्यूटर आधारित परीक्षा का सहज अभ्यास

Almost all major national exams (CUET, JEE, NEET, SSC, Banking) are 100% computer-based. Students who only study on paper experience eye strain and navigation mistakes on exam day. Early CBT practice creates effortless digital fluency.

Immunity to Negative Marking

सटीकता और नकारात्मक अंकन से सुरक्षा

Careless errors—such as misreading "NOT" or "EXCEPT"—ruin thousands of competitive aspirations each year. Regular objective testing builds the habit of double-checking question keywords before locking answers.

Instant Diagnostic Feedback Loop

तत्काल त्रुटि निवारण एवं आत्म-मूल्यांकन

Traditional paper tests take weeks to grade, by which time the student has forgotten their thought process. TargetExams provides instant scorecards and step-by-step solutions while the conceptual puzzle is still fresh.

Start Building Your Competitive Edge from Class

Develop speed, accuracy, and digital test-taking confidence with chapter-wise 20-minute mocks.

Syllabus Concepts Evaluated in this Chapter

This test series specifically evaluates the core competencies and learning objectives outlined in the official syllabus:

  • Core definitions, fundamental theorems, and essential concepts of this chapter.
  • Step-by-step mathematical reasoning and deductive problem-solving.
  • Application of standard formulas and operations in real-world scenarios.
  • Critical examination of common exam pitfalls and misleading options.
  • Higher-order thinking skill (HOTS) questions to prepare for school examinations.
  • Speed and accuracy mastery under standard timed CBT exam conditions.

Exam Rules & Test Taking Guidelines

  • Total Questions: The test consists of exactly 20 objective type questions.
  • Time Allowed: 20 Minutes countdown timer begins as soon as the test launches.
  • Marking Scheme: +1.0 mark is awarded for each correct answer.
  • Zero Penalty: There is 0.0 negative marking for incorrect or unattempted questions.
  • Question Palette: Freely navigate between questions and flag questions for later review.
  • Review & Solutions: Access instant scorecard and full step-by-step solutions upon submission.

Frequently Asked Questions (FAQs)

Yes! Foundation Practice Set 01 for every chapter in West Bengal Council of Higher Secondary Education (WBCHSE) Class 12 (Higher Secondary) Mathematics is 100% free to attempt. Students can test their preparation without any subscription or payment.
This test strictly follows the official West Bengal Council of Higher Secondary Education (WBCHSE) syllabus and curriculum for Class 12 (Higher Secondary), covering textbook concepts, formulas, and board-standard MCQs for Chapter 12.
This dedicated test page is conducted in English Medium. If you prefer taking the test in Bengali or Hindi, you can switch using the language switcher bar at the top or toggle languages during the exam.
The test comprises 20 MCQs to be completed in 20 minutes. Each question carries +1.0 mark for a correct response, and there is 0.0 negative marking for incorrect or unattempted questions.
Yes! Instantly after submitting your test, you receive a comprehensive digital scorecard with accuracy analysis, time breakdown, and step-by-step verified explanations for all 20 questions.

Practice Sets in this Chapter

Set 01 (Foundation)

20 MCQs • 20 Mins
Current

Set 02 (Advanced)

20 MCQs • 20 Mins
View

More Chapters in this Subject

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Linear Programming (Set 01 (Foundation Level))
20 MCQs • 20 Mins • 100% Free Practice Test

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