This document contains a 21 question multiple choice mathematics exam from 2005 on topics including algebra, trigonometry, calculus, and geometry. The exam tests concepts such as functions, derivatives, integrals, polynomials, triangles, ellipses, and systems of equations. For each problem, four possible answers (A, B, C, or D) are given and only one is correct. The document provides the problems and answer choices but no solutions. It directs the reader to an external website to find the solutions.
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We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
1. IIT JEE –PAST PAPER MATHEMATICS- UNSOLVED PAPER - 2005
2. SECTION – I Single Correct Answer Type This section contains 21 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
3. 01 Problem If stands for then value of is a. b. c. d.
4. Problem 02 A rectangle with sides units X units is divided into squares by drawing parallel lines in such a way that distance between two consecutive parallel lines is 1 unit. See Fig. 2005.1. The number of rectangles that can be drawn on the figure such that both the length and the breadth of the rectangle are odd is a. b. c. d.
7. Problem 05 Let the roots of the quadratic equation and If are G.P., then a. b. c. d.
8. Problem 06 Let S denote the set of all polynomials P of degree such that and then a. b. c. d.
9. Problem 07 If a, b and c are three integers such that at least two of them are unequal, and is a cube root of unity, then the least value of the expression is a.0 b. 1 c. d.1/2
10. Problem 08 The shaded region in Fig. 2005.2 is given by a. b. c. d.
11. Problem 09 Let and g be two functions defined from R to R as follows: then the function is One –one but not on to b. Onto but not one-one c. Both one-one and on to d. Neither one-one nor on to
12. Problem 10 Three circular coins each of radii 1 cm are kept in an equilateral triangle so that all the three coins touch each other and also the sides of the triangle. Area of the triangle is a. b. c. d.
13. Problem 11 The function is differentiable at all except at the points a. 1, 0, -1 b. 1 c. 1, -1 d. -1
14. Problem 12 Let X and Y are two nonempty sets. Let be a function. For and define and then a. b. c. d.
15. Problem 13 If f(x) is a continuous and differentiable function such that then a. b. c. d. f(0) = 0 and f’(0) may or may not be zero.
16. Problem 14 If y = y(x) is a function of x satisfying the relation x cos y + y cos x = , then y”(0) equals a. 1 b. -1 -
17. Problem 15 A triangle is formed by a tangent to the ellipse and the coordinate axes. The area of triangle cannot be less than sq. units sq. units sq. units Ab sq. units
18. Problem 16 Let f(x) be a twice differentiable function such that f(x) = x2 for x = 1, 2, 3, then a. b. c. d.
19. Problem 17 Let be such that and the number of pairs of satisfying the above system of equations is 0 1 2 4
20. Problem 18 If a,b,c denote the lengths of the sides of a triangle opposite angles A, B, C of a then correct relation among a,b,c,A, B and C is given by a. b. c. d.
21. Problem 19 The area bounded by the parabolas and and the line y= 1/4 is 1/6 Sq. units 1/3Sq. units 4/3 Sq. units 4 sq. units
22. Problem 20 The solution of the differential equation satisfies the conditions and then value of is a. b. c. d.
23. Problem 21 Tangent to the curve at a point P (1, 7) touches the circle at a point Then the coordinates of are (-9, -13) (-10, -15) (-6, -7) (-6, -7)
