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Jharkhand Academic Council (JAC) Class XII Mathematics Set 01 (Foundation Level) English Medium 100% Free Practice Test

JAC Board Class 12 Mathematics: Linear Programming Online Test (Set 01 (Foundation Level)) | Jharkhand Board

Linear Programming — Set 01 (Foundation Level)

Practise free online MCQ mock test for JAC Board Class 12 Mathematics chapter 'Linear Programming'. 20 MCQs with timer countdown, detailed explanations, and instant results as per board syllabus.

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20 MCQs

Questions

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20 Mins

Duration

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20 Marks

Total Marks

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+1.0

Per Correct

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0.0

Negative Mark

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English

Language

Start Test Now (English Medium)

Instant Scorecard Step-by-Step Solutions JCERT / JAC Curriculum

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.

According to the Corner Point Theorem of Linear Programming, where do the Optimal (Maximum or Minimum) values of the objective function Z = ax + by occur in a bounded feasible region?

रैखिक प्रोग्रामन में परिबद्ध सुसंगत क्षेत्र के लिए उद्देश्य फलन Z = ax + by का इष्टतम मान कहाँ प्राप्त होता है?

Always at the origin (0, 0)हमेशा मूल पर (0, 0)

At the center of the feasible regionव्यवहार्य क्षेत्र के केंद्र में

At one of the Corner Points (Extreme / Vertex Points) of the feasible regionसुसंगत क्षेत्र के किसी शीर्ष बिंदु (Corner Point) पर

Anywhere along the perimeter onlyकेवल परिधि के आसपास कहीं भी

Correct Answer: Option C

Explanation:

The Fundamental Theorem of Linear Programming states that if the feasible region is a convex bounded polygon, the optimal value of the linear objective function Z = ax + by always occurs at one of the corner (vertex) points.

कोने के बिंदुओं (Corner Points) पर ही अधिकतम या न्यूनतम मान प्राप्त होता है।

What is the Feasible Region in a Linear Programming Problem (LPP)?

रैखिक प्रोग्रामन समस्या (LPP) में सुसंगत क्षेत्र (Feasible Region) क्या होता है?

The set of points where objective function is zeroउन बिंदुओं का समूह जहां उद्देश्य फ़ंक्शन शून्य है

The area outside the first quadrantप्रथम चतुर्थांश के बाहर का क्षेत्र

The entire coordinate planeसंपूर्ण समन्वय तल

The common region determined by all the given linear inequalities / constraints including non-negative restrictions x ≥ 0, y ≥ 0सभी दी गई व्यवरोधों (Inequalities) तथा अऋणात्मक प्रतिबंधों द्वारा निर्धारित उभयनिष्ठ क्षेत्र

Correct Answer: Option D

Explanation:

The feasible region is the intersection of all half-planes defined by the system of linear constraints, representing all possible candidate solutions satisfying every constraint.

सभी व्यवरोधों को संतुष्ट करने वाला उभयनिष्ठ क्षेत्र सुसंगत क्षेत्र है।

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.

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 Jharkhand Academic Council (JAC) Class XII Mathematics is 100% free to attempt. Students can test their knowledge without any payment or hidden fees.

This page is dedicated to English Medium. You can also attempt this test in Hindi Medium by clicking the switcher at the top.

Absolutely. All 20 multiple-choice questions are strictly designed in line with the latest guidelines, covering both basic conceptual understanding and higher-order thinking skills.

The test contains 20 MCQs to be solved in 20 minutes. Each question carries +1.0 mark for a correct answer, and there is zero (0.0) negative marking for incorrect answers.

Yes. Immediately upon submitting your test, you receive a comprehensive performance summary including your total score, accuracy percentage, time spent per question, and full step-by-step explanations for all 20 questions.

Linear Programming (Set 01 (Foundation Level))

20 MCQs • 20 Mins • 100% Free Practice Test

JAC Board Class 12 Mathematics: Linear Programming Online Test (Set 01 (Foundation Level)) | Jharkhand Board

Chapter Study Guide & In-Depth Notes