This document contains a tutor marked assignment for a mathematics course. It has 6 questions with varying marks for each question. The first question asks students to answer one part of a multi-part question providing their working and conclusion in 40-60 words. The second question similarly asks students to answer one part of a multi-part mathematics question in 40-60 words. The third question asks students to answer one part of another multi-part mathematics question also in 40-60 words. The fourth question asks students to answer one out of four longer mathematics questions in 100-150 words. Finally, the fifth question repeats this format of answering one out of four mathematics questions but in 100-150 words, and the sixth question asks students to write
This document discusses measuring program objectives for a new Master's in Marketing degree via online assessment. It outlines creating program objectives and mapping them to two direct and two indirect measures. Direct measures include entrance and exit exams, with a goal of 80% of students scoring over 73%. Indirect measures include mid-term and end-of-program surveys, with a goal of 80% of students agreeing or strongly agreeing that they can apply program learning outcomes. The document then discusses using case analysis as one direct measure, outlining four cases and central questions. It provides results from the first exam that were skewed and adjustments made going forward. Finally, it covers setting up the case analysis in an LMS like Blackboard, including why cases
Linda Quinn has over 30 years of experience in nursing education. She currently serves as the Director of the School of Nursing and Professor at Midland University. Her experience also includes roles as an Associate Professor, Student Advancement Coordinator, and Adjunct Professor at Nebraska Methodist College. She holds a PhD in Psychology from Capella University and masters degrees in Counseling and Nursing. Quinn has extensive experience developing, teaching, and revising nursing curriculum to meet accreditation standards. She is published and has presented on topics related to nursing education, leadership, collaboration, and self-care.
Rewood Javacraft merupakan pelopor produsen kacamata kayu di indonesia. Produk rewood eyewear menggunakan bahan kayu limbah atau sisa dari pengrajin mebel ataupun kusen dan akar jati.
This document summarizes oil and gas lease ownership information for a 409-acre property. It lists the lessor and lessee of the original oil and gas lease from 1951, as well as subsequent leasehold owners and their working and net revenue interests. It also provides title notes describing how the lessor acquired the leased acreage and reserving of an overriding royalty interest.
Pangram Financial Services provides accounting, financial reporting, payroll, company establishment, relations with financial institutions, and advisory services to clients. The company aims to act as an "outsourced CFO" by understanding clients' financial needs and handling financial matters so clients can focus on their core business. Pangram is located in Istanbul, Turkey and led by partners with extensive experience in finance roles at multinational companies.
Belcan is an engineering and technical services firm that provides staffing solutions including contract personnel, direct hiring, on-site workforce management, payrolling, and outsourcing. They have a thorough recruiting process that identifies qualified candidates through various sources and screens them based on technical skills, experience, and culture fit. Belcan places candidates onto their payroll quickly after an effective on-boarding process involving screening, hiring, employing, and orienting candidates. They aim to retain employees through competitive benefits, incentives, communication, and a temporary employee care program.
This document discusses measuring program objectives for a new Master's in Marketing degree via online assessment. It outlines creating program objectives and mapping them to two direct and two indirect measures. Direct measures include entrance and exit exams, with a goal of 80% of students scoring over 73%. Indirect measures include mid-term and end-of-program surveys, with a goal of 80% of students agreeing or strongly agreeing that they can apply program learning outcomes. The document then discusses using case analysis as one direct measure, outlining four cases and central questions. It provides results from the first exam that were skewed and adjustments made going forward. Finally, it covers setting up the case analysis in an LMS like Blackboard, including why cases
Linda Quinn has over 30 years of experience in nursing education. She currently serves as the Director of the School of Nursing and Professor at Midland University. Her experience also includes roles as an Associate Professor, Student Advancement Coordinator, and Adjunct Professor at Nebraska Methodist College. She holds a PhD in Psychology from Capella University and masters degrees in Counseling and Nursing. Quinn has extensive experience developing, teaching, and revising nursing curriculum to meet accreditation standards. She is published and has presented on topics related to nursing education, leadership, collaboration, and self-care.
Rewood Javacraft merupakan pelopor produsen kacamata kayu di indonesia. Produk rewood eyewear menggunakan bahan kayu limbah atau sisa dari pengrajin mebel ataupun kusen dan akar jati.
This document summarizes oil and gas lease ownership information for a 409-acre property. It lists the lessor and lessee of the original oil and gas lease from 1951, as well as subsequent leasehold owners and their working and net revenue interests. It also provides title notes describing how the lessor acquired the leased acreage and reserving of an overriding royalty interest.
Pangram Financial Services provides accounting, financial reporting, payroll, company establishment, relations with financial institutions, and advisory services to clients. The company aims to act as an "outsourced CFO" by understanding clients' financial needs and handling financial matters so clients can focus on their core business. Pangram is located in Istanbul, Turkey and led by partners with extensive experience in finance roles at multinational companies.
Belcan is an engineering and technical services firm that provides staffing solutions including contract personnel, direct hiring, on-site workforce management, payrolling, and outsourcing. They have a thorough recruiting process that identifies qualified candidates through various sources and screens them based on technical skills, experience, and culture fit. Belcan places candidates onto their payroll quickly after an effective on-boarding process involving screening, hiring, employing, and orienting candidates. They aim to retain employees through competitive benefits, incentives, communication, and a temporary employee care program.
SSC-CGL Maths Mains Test Paper - 20 by Hansraj AcademyHansraj Academy
SSC-CGL Maths Mains Test Paper - 20 by Hansraj Academy. Hansraj sir unique method of Maths Explanation scores highest marks in Competitive Examinations. Subscribe and Watch maths classes at YouTube Channel.
1. Francis turbine is a radial flow turbine.
2. In laminar, incompressible flow through a circular pipe, the ratio of average to maximum velocity is 1/2.
3. Bernoulli's theorem assumes the fluid is incompressible and flow is frictionless.
The document appears to contain a sample exam paper for the SSC JEN 2011 exam, with questions about engineering concepts in both English and Hindi. It includes 28 multiple choice questions covering topics like materials properties, thermodynamics, heat engines, and internal combustion engines. It also provides contact information to request more exam papers by email or phone.
This document contains an exam paper for a Masters level Economics quantitative methods exam. It consists of 5 questions, with one question from each of 5 units. The units cover topics like linear programming, production functions, regression analysis, time series analysis, index numbers, sampling, chi-square test, estimation, and hypothesis. Students are required to answer all 5 questions in detail, with equal marks given to each.
Class 10 Cbse Maths Sample Paper Term 2 2012Sunaina Rawat
The document provides information about the design of a mathematics question paper for class 10. It includes:
1. The question paper will have 8 multiple choice questions carrying 1 mark each, 6 short answer type 1 questions carrying 2 marks each, 10 short answer type 2 questions carrying 3 marks each, and 10 long answer type 1 questions carrying 4 marks each, totaling to 34 questions and 90 marks.
2. The question paper will include 2-5 marks for value based questions.
3. The topics and their weightage are: Algebra 23%, Geometry 17%, Trigonometry 8%, Probability 8%, Coordinate Geometry 11%, Mensuration 23%.
4. It provides 5 sample multiple choice questions as
1. The document contains 27 multiple choice questions related to mechanical engineering. The questions cover topics like strength of materials, mechanics, thermodynamics, and heat engines.
2. It also contains contact information for an exam preparation service indicating the questions are likely from a past exam paper.
3. The document is advertising additional exam preparation materials and services that can be obtained by contacting the email address provided.
1. The document contains 30 multiple choice questions related to mechanical engineering.
2. Questions cover topics such as laws of motion, stress and strain, fluid mechanics, thermodynamics, heat engines, manufacturing processes and materials.
3. Answers to the questions are not provided, indicating this is a quiz or exam on fundamental mechanical engineering concepts.
The Prime Minister Narendra Modi has directed all his ministers to use social media platforms like Twitter, Facebook actively to publicize and promote their work. The Information and Broadcasting Minister (Independent Charge) Prakash Javadekar said the ministry will help ministers open accounts on social media platforms like Twitter and Facebook as using them extensively is not an easy task. He said the ministry has created a Social Media Communication Hub to help ministers be more active on social media. Javadekar added that ministers can open accounts on these platforms through this hub and it will also help them handle these accounts.
1. The document discusses the need for an ombudsman or Lokpal in India to effectively investigate and prosecute cases of corruption.
2. It outlines some of the key shortcomings of India's existing anti-corruption bodies, including a lack of independence, fragmented structure with overlapping jurisdictions, and lack of transparency and accountability.
3. The document argues that an independent Lokpal institution is necessary to conduct impartial investigations of public officials and ensure corrupt individuals are properly prosecuted and punished.
1. The document discusses a scheme to earn 10 lakhs rupees within 3 months by introducing two people per week to a game or business opportunity.
2. It claims one can earn 1000 rupees in the second week, 2000 rupees in the third week, and so on exponentially as more people are introduced.
3. It asks the reader to purchase a ticket for 3000 rupees to participate, and says they will receive a gift of the reader's choice worth 3113 rupees.
This document contains a syllabus and sample questions for a mathematics summative assessment for class 10. It provides the design of the question paper which will include 90 multiple choice, short answer and long answer questions assessing topics like algebra, geometry, trigonometry, probability, coordinate geometry and mensuration. Sample multiple choice, short answer 1 and 2 mark, and long answer 4 mark questions are provided covering various mathematics concepts to be assessed.
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The document contains 10 multiple choice questions related to mechanical engineering. It provides sample questions that appear to be from an exam for the SSC JEN 2014 recruitment exam. The questions cover topics like fluid mechanics, thermodynamics, hydraulics, metallurgy and manufacturing. Contact information is also provided at the bottom for obtaining more exam papers.
This page is very helpful those students they prepare junior engineer exam like.. SSC JEn, PWD, PHED, RSEB, BSNL JTO, TTA, WRD, DMRC, JMRC, RIICO etc .
The document discusses a tutor marked assignment for Home Science. It contains 4 questions with multiple parts to each question. Students are asked to answer 1 question in 40-60 words. The questions cover topics like planning healthy meals and menus for families, taking care of health, managing resources, adjusting to new families, and more. Guidance is provided on selecting appropriate cooking methods, modifying dishes for different family members' needs, and involving local authorities to care for the ill.
CHEMISTRY 12th Sample Paper 2023-2024.pdf7067634722ps
The document is a sample question paper for chemistry in Hindi. It contains 20 multiple choice and long answer questions divided into sections carrying 1, 2, 3 or 4 marks each. The questions are related to topics like chemical equations, electronic configurations, coordination compounds, reaction mechanisms and organic chemistry. Instructions are given regarding answering all questions, word limits for long answer questions and internal choices for some questions.
This document is a newsletter in Hindi for the Akhil Bharatiya Hindu Mahasabha organization. It provides information on upcoming events, important dates, and articles on topics related to Hinduism and Indian politics. Key details include announcing the annual membership fee of Rs. 100 and notifying readers that the newsletter is published every Wednesday.
(1) This document contains a 75 multiple choice question paper for the subject Library and Information Science. Each question carries 2 marks and all questions must be attempted.
(2) The questions cover topics related to library and information science such as database management systems, binary number system, open system interconnection, spamming, project management techniques, research methods, bibliographic description standards, and information communication modeling.
(3) The paper tests the candidate's knowledge of foundational concepts in libraries, information systems, and research methods.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
SSC-CGL Maths Mains Test Paper - 20 by Hansraj AcademyHansraj Academy
SSC-CGL Maths Mains Test Paper - 20 by Hansraj Academy. Hansraj sir unique method of Maths Explanation scores highest marks in Competitive Examinations. Subscribe and Watch maths classes at YouTube Channel.
1. Francis turbine is a radial flow turbine.
2. In laminar, incompressible flow through a circular pipe, the ratio of average to maximum velocity is 1/2.
3. Bernoulli's theorem assumes the fluid is incompressible and flow is frictionless.
The document appears to contain a sample exam paper for the SSC JEN 2011 exam, with questions about engineering concepts in both English and Hindi. It includes 28 multiple choice questions covering topics like materials properties, thermodynamics, heat engines, and internal combustion engines. It also provides contact information to request more exam papers by email or phone.
This document contains an exam paper for a Masters level Economics quantitative methods exam. It consists of 5 questions, with one question from each of 5 units. The units cover topics like linear programming, production functions, regression analysis, time series analysis, index numbers, sampling, chi-square test, estimation, and hypothesis. Students are required to answer all 5 questions in detail, with equal marks given to each.
Class 10 Cbse Maths Sample Paper Term 2 2012Sunaina Rawat
The document provides information about the design of a mathematics question paper for class 10. It includes:
1. The question paper will have 8 multiple choice questions carrying 1 mark each, 6 short answer type 1 questions carrying 2 marks each, 10 short answer type 2 questions carrying 3 marks each, and 10 long answer type 1 questions carrying 4 marks each, totaling to 34 questions and 90 marks.
2. The question paper will include 2-5 marks for value based questions.
3. The topics and their weightage are: Algebra 23%, Geometry 17%, Trigonometry 8%, Probability 8%, Coordinate Geometry 11%, Mensuration 23%.
4. It provides 5 sample multiple choice questions as
1. The document contains 27 multiple choice questions related to mechanical engineering. The questions cover topics like strength of materials, mechanics, thermodynamics, and heat engines.
2. It also contains contact information for an exam preparation service indicating the questions are likely from a past exam paper.
3. The document is advertising additional exam preparation materials and services that can be obtained by contacting the email address provided.
1. The document contains 30 multiple choice questions related to mechanical engineering.
2. Questions cover topics such as laws of motion, stress and strain, fluid mechanics, thermodynamics, heat engines, manufacturing processes and materials.
3. Answers to the questions are not provided, indicating this is a quiz or exam on fundamental mechanical engineering concepts.
The Prime Minister Narendra Modi has directed all his ministers to use social media platforms like Twitter, Facebook actively to publicize and promote their work. The Information and Broadcasting Minister (Independent Charge) Prakash Javadekar said the ministry will help ministers open accounts on social media platforms like Twitter and Facebook as using them extensively is not an easy task. He said the ministry has created a Social Media Communication Hub to help ministers be more active on social media. Javadekar added that ministers can open accounts on these platforms through this hub and it will also help them handle these accounts.
1. The document discusses the need for an ombudsman or Lokpal in India to effectively investigate and prosecute cases of corruption.
2. It outlines some of the key shortcomings of India's existing anti-corruption bodies, including a lack of independence, fragmented structure with overlapping jurisdictions, and lack of transparency and accountability.
3. The document argues that an independent Lokpal institution is necessary to conduct impartial investigations of public officials and ensure corrupt individuals are properly prosecuted and punished.
1. The document discusses a scheme to earn 10 lakhs rupees within 3 months by introducing two people per week to a game or business opportunity.
2. It claims one can earn 1000 rupees in the second week, 2000 rupees in the third week, and so on exponentially as more people are introduced.
3. It asks the reader to purchase a ticket for 3000 rupees to participate, and says they will receive a gift of the reader's choice worth 3113 rupees.
This document contains a syllabus and sample questions for a mathematics summative assessment for class 10. It provides the design of the question paper which will include 90 multiple choice, short answer and long answer questions assessing topics like algebra, geometry, trigonometry, probability, coordinate geometry and mensuration. Sample multiple choice, short answer 1 and 2 mark, and long answer 4 mark questions are provided covering various mathematics concepts to be assessed.
We Are Safalta.com And We Are Providing The Bihar TET Solved Model Question Papers In Hindi.The Solved Model Is Prepared Under The Guidance Of The Experts.
Click Here To Buy Now - http://safalta.com/product/bihar-tet-1st-paper/
The document contains 10 multiple choice questions related to mechanical engineering. It provides sample questions that appear to be from an exam for the SSC JEN 2014 recruitment exam. The questions cover topics like fluid mechanics, thermodynamics, hydraulics, metallurgy and manufacturing. Contact information is also provided at the bottom for obtaining more exam papers.
This page is very helpful those students they prepare junior engineer exam like.. SSC JEn, PWD, PHED, RSEB, BSNL JTO, TTA, WRD, DMRC, JMRC, RIICO etc .
The document discusses a tutor marked assignment for Home Science. It contains 4 questions with multiple parts to each question. Students are asked to answer 1 question in 40-60 words. The questions cover topics like planning healthy meals and menus for families, taking care of health, managing resources, adjusting to new families, and more. Guidance is provided on selecting appropriate cooking methods, modifying dishes for different family members' needs, and involving local authorities to care for the ill.
CHEMISTRY 12th Sample Paper 2023-2024.pdf7067634722ps
The document is a sample question paper for chemistry in Hindi. It contains 20 multiple choice and long answer questions divided into sections carrying 1, 2, 3 or 4 marks each. The questions are related to topics like chemical equations, electronic configurations, coordination compounds, reaction mechanisms and organic chemistry. Instructions are given regarding answering all questions, word limits for long answer questions and internal choices for some questions.
This document is a newsletter in Hindi for the Akhil Bharatiya Hindu Mahasabha organization. It provides information on upcoming events, important dates, and articles on topics related to Hinduism and Indian politics. Key details include announcing the annual membership fee of Rs. 100 and notifying readers that the newsletter is published every Wednesday.
(1) This document contains a 75 multiple choice question paper for the subject Library and Information Science. Each question carries 2 marks and all questions must be attempted.
(2) The questions cover topics related to library and information science such as database management systems, binary number system, open system interconnection, spamming, project management techniques, research methods, bibliographic description standards, and information communication modeling.
(3) The paper tests the candidate's knowledge of foundational concepts in libraries, information systems, and research methods.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
South African Journal of Science: Writing with integrity workshop (2024)
7 d.mathematics (311)
1. 21xf.kr (Mathematics)
xf.kr
Mathematics
¼311½
f'k{kd vafdr ewY;kadu i=k
Tutor Marked Assignment
dqy vad % 20
MaximumMarks: 20
fVIi.kh% (i) lHkh iz'uksa ds mÙkj nsus vfuok;Z gSaA iz'u gsrq fu/kkZfjr vad iz'u ds lkeus fn;s x, gSaA
Note: Allquestions are compulsory. The marks allotedfor each question aregivenagainst each.
(ii) mRrj iqfLrdk ds izFke i`"B ij Åij dh vksj viuk uke] vuqØekad] v/;;u dsUnz dk uke]
fo"k; vkfn Li"V 'kCnksa esa fyf[k,A
Write your name, enrolment number, AI name and subject etc. on the top of the first page of the
answer sheet.
1. fuEufyf[kr esa ls fdlh ,d iz'u dk mÙkj yxHkx 40&60 'kCnksa esa nhft;s % 2
Answer anyone ofthe following questions in about 40-60 words :
(a) ;fn 1z gks rks fl) dhft, fd
1
, 1
1
z
z
z
,d 'kq) dkYifud la[;k gSA ;fn 1z gks rks
vkidk fu"d"kZ D;k gksxk
If 1z show that
1
, 1
1
z
z
z
is a pure imaginarynumber. What willyou conclude if 1z ?
(b) diM+s ds ,d VqdM+s dk ewY; 35 : gSA ;fn diMs dh yackbZ 4 eh- vf/kd rFk ewY; 1 : izfr eh- de
gks rks VqdM+s dk ewY; vifjofrZr jgrk gSA VqdM+s dh yackbZ Kkr dhft,A
The cost ofa piece ofclothis Rs. 35. Ifthe piece were 4 mlonger and each meter costs Rs. 1 less, the
cost would remainunchanged. How longis the piece
(c) 45% ek=kk ds 1125 yhVj vEyh; foy;u es fdrus yhVj ikuh feyk;k tk, fd feJ.k es vEy dh
ek=kk 25% ls vf/kd rFkk 30% ls de gks
How many litres ofwater will have to be added to 1125 litres of the 45% solution ofacid so that the
resulting mixturewillcontainmore than25% but less than30% acid content.
(d) 15 fcanq ,d o`Ùk ij fLFkr gSaA bu fcanqvksa ls dqy fdrus pØh; prqHkqZt cuk, tk ldrs gSA
15 points lie on a circle. How manycyclic quadrilaterals can be drawnusing these points.
2. fuEufyf[kr esa ls fdlh ,d iz'u dk mÙkj yxHkx 40&60 'kCnksa esa nhft;s % 2
Answer anyone ofthe following questions in about 40-60 words :
(a) 50 O;fDr;ksa ds ,d lewg es 35 fganh] 25 fganh o vxzsth nksuksa RkFkk izR;sd O;fDr nksuks Hkk"kkvksa es ls
de ls de ,d Hkk"kk vo'; cksyrk gSA fdrus O;fDr dsoy vaxzsth cksyrs gSa rFkk fganh ugh cksyrs
fdrus O;fDr vaxzsth cksyrs gSA
2. 22 xf.kr (Mathematics)
In a group of50 people;35 speak Hindi, 25 speak both English and Hindiand allpeople speak at least
one of the two languages. How many people speak only English and not Hindi? How many people
speak English?
(b) ,d f=kHkqt dh Hkqtkvksa dk vuqikr a: b: c = 7: 8: 9 gks rks n'kkZb, fd cosA: cosB: cosC = 14: 11: 6
gksxkA
Ifthe ratio ofthree sides ofa triangle is a: b: c = 7: 8: 9 then show that cosA: cosB: cosC = 14: 11: 6.
(c) A rFkk B }kjk ,d leL;k dks Lora=k :Ik ls gy djus dh izkf;drk Øe'k% ½ o 1/3 gSA ;fn nksuksa
Lora=k :Ik ls leL;k dks gy djsa rks (i) leL;k gy gksus (ii) fdlh ,d }kjk leL;k gy djus] dh
izkf;drk Kkr dhft,A
Probabilities ofsolving a problemindependentlybyAand B are ½ and 1/3 respectively. Ifbothtryto
solvethe problemindependentlyfind the probabilitythat (i) theproblemissolved (ii)exactlyoneofthem
solves the problem
(d) [kehj es cSDVhfj;k dh la[;k 1,00,000 gSA 2 ?kaVs es la[;k 10% c<+ tkrh gSA ;fn cSDVhfj;k dh
la[;k dh o`f) nj la[;k ds lekuqikrh gks rks fdrus ?kaVs esa cSDVhfj;k dh la[;k 2,00,000 gks
tk,xhA
In yeast the bacteria count is 1,00,000. The number isincreased by10% in2 hours. Inhow manyhours
willthe count reach 2,00,000 ifthe rate ofgrowth ofbacteria is proportionalto the numbers present.
3. fuEufyf[kr esa ls fdlh ,d iz'u dk mÙkj yxHkx 40&60 'kCnksa esa nhft;s % 2
Answer anyone ofthe following questions in about 40-60 words :
(a) 95 ij 14% LVkWd vFkok 105 ij 15% LVkWd es ls dkSu lk vf/kd ykHkizn gSA
Which is a better investment 14% stock at 95 or 15% stock at 105
(b) 2005 dks vk/kkj o"kZ ekudj o"kZ 2005, 2006, 2007, 2008 ,oa 2009 ds fy, lwpdkad dh x.kuk
dhft,A
Compute the index number for the years 2005, 2006, 2007, 2008 and 2009 taking 2005 as base year
o"kZ Year 2005 2006 2007 2008 2009
ewY; Price 120 144 168 204 216
(c) xksys 2 2 2
49x y z ij ry 2 3 5 14 0x y z }kjk dkVs x, o`Ùkkdkj Hkkx dh f=kT;k
Kkr dhft,A
Find the radius of the circular section of the sphere 2 2 2
49x y z by the plane
2 3 5 14 0x y z
(d) ,d ABC ds Å/oZ B rFkk C js[kk
2 1 0
2 1 4
x y z
ij fLFkr gSA ;fn A ds funsZ'kkad 1, 1,2
rFkk js[kk [k.M BC dh yackbZ 5 bdkbZ gks rks ABC dk {ks=kQy Kkr dhft,A
Vertices B and C ofa ABC lie along the line
2 1 0
2 1 4
x y z
. Find the area ofthe triangle given
thatAhas Coordinates 1, 1,2 and line segment BC has length 5 units.
3. 23xf.kr (Mathematics)
4. fuEufyf[kr esa ls fdlh ,d dk mÙkj yxHkx 100-150 'kCnksa esa nhft,A 4
Answer anyone out ofthe followingfour questions in about 100 to 150 words
(a) nks izdkj ds QfVZykbtj 1F rFkk 2F miyC/k gSaA 1F esa 10% ukbVªkstu rFkk 6% QkjLQksfjd vEy
vkSj 2F es 5%ukbVªkstu rFkk 10% QkLQksfjd vEy gSA feV~Vh dh tkap ls fdlku dks Kkr gksrk gS
fd mls Qly ds fy, U;wure 14 fdxzk ukbVªkstu rFkk 14 fdxzk QkLQksfjd vEy dh vko';drk
gSA ;fn 1F dk ewY; 6 :0 izfr fdxzk rFkk 2F dk ewY; 5 :0 izfr fdxzk gks rks Kkr dhft, fd
fdl izdkj ds QfVZykbtj dks fdl ek=kk es iz;ksx fd;k tk, dh Qly dh vko';drk dks
U;wure ewY; esa iwjk fd;k tk ldsA
There are two typesoffertilizers 1F and 2F . 1F consists of10% nitrogenand 6%phosphoric acid and
2F consists of5% nitrogen and 10% phosphoric acid. After testing the soilconditions, a farmer finds
that he atleast needs 14 kg. ofnitrogenand 14 kg ofphosphoric acid for the crop. If 1F costs Rs. 6 per
kg. and 2F costs Rs. 5 per kg., determine how much of each type of fertilizer should be used so that
nutrient requirementsare met at aminimumcost.
(b) ,d leckgq f=kHkqt dh ,d Hkqtk 24 lseh gSA bldh Hkqtkvksa ds e/; fcnqavks dks feykdj ,d nwljk
f=kHkqt cuk;k x;k gSA bl nwljs f=kHkqt dh Hkqtkvksa ds e/; fcUnqvksa dks feykdj ,d vkSj f=kHkqt
cuk;k tkrk gSA ;g izfØ;k vlhfer :Ik ls pyrh jgrh gSA bl izfØ;k es cuus okys f=kHkqtksa ds
ifjekiksa dk ;ksx Kkr dhft,A
One sideofanequilateraltriangleis 24 cm. Themid points ofits sides are joined to formanothertriangle
whosemid pointsinturnare joinedto formstillanother triangle. Theprocesscontinuesindefinitely. Find
the sumofthe perimeters ofallthe triangles.
(c) funsZ'kkad T;kfefr dk iz;ksx djds fl) dhft, fd v/kZo`r es cuk dks.k ledks.k gksrk gSA
Using Coordinate geometryprove that angle ina semicircle is a right angle.
(d) 4 fdxzk I;kt] 3 fdxzk xsagwa o 2 fdxzk pkoy dk ewY; 60 :0 gSA 2 fdxzk I;kt] 4 fdxzk xsagwa o 6 fdxzk
pkoy dk ewY; 90:0 gSA 6 fdxzk I;kt 2 fdxzk xsagwa o 3 fdxzk pkoy dk ewY; 70 :0 gSA vkO;wg
dk iz;ksx djrs gq, rhuksa oLrqvksa dk izfr fdxzk ewY; Kkr dhft,A
The cost of4 kg onion, 3 kg wheat and 6 kg rice is Rs 60. The cost of2 kg onion, 4kg wheat and 6kg
rice is Rs. 90. The cost of6 kg. onion, 2 kg wheat and 3kg rice is Rs. 70. Findthe cost ofeachitemper
kg. usingmatrix.
5. fuEufyf[kr esa ls fdlh ,d dk mÙkj yxHkx 100-150 'kCnksa esa nhft,A 4
Answer anyone out ofthe followingfour questions in about 100 to 150 words
(a) ,d f[kM+dh vk;rkdkj gS ftlds mij ,d v/kZo`Ùk gSA f[kM+dh dk ifjeki 10 ehVj gSA f[kM+dh
dh foek,a Kkr dhft, rkfd vf/kdre laHko izdk'k dh ek=kk vanj vk ldsA
Awindowis inthe formofrectangle surmounted bya semi-circle. Thetotalperimeter ofthewindow is
10 m. Find the dimensionsofthe window to admit maximumlight throughthe whole opening.
4. 24 xf.kr (Mathematics)
(b) Lkekdy dk iz;ksx djds o`Ùk 2 2
16x y ds ml Hkkx dk {ks=kQy Kkr dhft, tks ijoy;
2
6y x ds cfgHkkZx es fLFkr gSA
Using integralfindthe area ofthat part ofcircle 2 2
16x y whichis exterior to theparabola 2
6y x
(c) ,d QeZ dk ykxr Qyu 2 31
300 10
3
C x x x x gSA tgka x mRikfnr bdkbZ;ksa dh la[;k gSA
The cost functionofa firmis given by 2 31
300 10
3
C x x x x
Kkr dhft,
Find
(i) lhekar ykxr Qyu
Marginalcost function
(ii) vkSlr ykxr Qyu
Average cost function
(iii) mRikn] ftl ij lhekar ykxr] vkSlr ykxr ds leku gSA
The out put at whichmarginalcost is equalto average cost.
(d) fcanq 1,6,3 dk js[kk
1 2
1 2 3
x y z
s esa izfrfcEc Kkr dhft,A fcanq rFkk blds izfrfcEc dks
feykus okyh js[kk dk lehdj.k Kkr dhft,A
Find the image of the point 1,6,3 in the line
1 2
1 2 3
x y z
. Also find the equation of the line
joining the givenpoint and its image.
6. uhps nh xbZ pkj ifj;kstukvksa dh lwph esa ls dksbZ ,d ifj;kstuk 500 'kCnksa esa rS;kj dhft, 6
Make anyone project out ofthe four given below in 500 words.
(a) 'kadq dk iz;ksx djds n'kkZb, fd fdl izdkj fofHkUu izdkj ds 'kadq ifjPNsnksa dh mRifÙk gksrh gSA
Using cone illustrate how different types ofconicsections are generated
(b) eqEcbZ LVkWd ,Dlpst es lwphc) dksbZ 10 daifu;k pqfu,A bu daifu;ks dk (i) 2012-13 es 'ks;j
ewY; es ifjorZu (ii) 2012-13 esa vftZr ykHk (iii) 'ks;j /kkjdkas dks fn;k x;k ykHkka'k] ds vk/kkj ij
v/;;u dhft,A D;k vki bu rhuksa esa dksbZ laca/k ikrs gSaA ;fn gka rks mldh O;k[;k dhft,A
Choose any10 companies listed inBombaystock exchange. Studythe performance ofthese companies
in respect of(i) change intheir share value in2012-13 (ii) profit in2012-13 (iii) dividend givento share
holders. Do you find some relationship between the above mentioned three parameters. If yes then
explainit.
5. 25xf.kr (Mathematics)
(c) lHkh 6 f=kdks.kferh; Qyuksa rFkk izfrykse f=kdks.kferh; Qyuksa ds xzkQ cukb,A ;fn buesa dksbZ
laca/k gS rks mls LFkkfir dhft,A buds izkar o ifjlj es lca/k dh O;k[;k dhft,A
Make a graph ofallsix trigonometric and inverse trigonometric functions. Establish the relationship
betweenthemifany. Also explainthe relationship intheir respectivedomainand range.
(d) lfn'k xq.kuQy dh T;kferh; O;k[;k dhft, A bldk iz;ksx djds rhu fHkUu f=kHkqtksa rFkk rhu
fHkUu lekarj prqHkqZtksa ds {ks=kQy Kkr dhft,A T;kfefr ds iz;ksx ls Hkh bu vkÑfr;ksa ds {ks=kQy
Kkr dhft, A bu nks fof/k;ksa ls Kkr {ks=kQyksa dh rqyuk dhft,A
Interpret the geometrical significance ofvector product. Using this interpretation find area ofthree
different trianglesand three different parallelograms. Also find the area ofthese figuresusing geometry.
Compare the areas calculated bythese two methods.