This document contains 35 math problems from an unsolved past IITJEE paper from 2001. The problems cover a range of math topics including algebra, geometry, trigonometry, and calculus. They involve finding roots of polynomials, properties of arithmetic and geometric progressions, functions, derivatives, and more. The full document would need to be solved to determine the answers to each individual problem.
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.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
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.
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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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.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
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.
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?
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!
3. 01 Problem Let be the roots of be the roots of are in G.P., then the integral values of p and q respectively, are -2,-32 -2, 3 -6, 3 -6, -32
4. Problem 02 Let and let m(b) be the minimum value of varies, the range of m(b) is a. b. c. d.
5. Problem 03 The number of distinct real roots of in the interval is 0 2 1 3
6. Problem 04 In the binomial expansion of the sum of the 5th and 6th terms is zero. Then equals a. b. c. d.
7. Problem 05 Let denote the number of triangles which can be formed using the vertices of a regular polygon of sides. If ,then n equals 5 7 6 4
8. Problem 06 Let .Then the number of onto functions from E to F is 14 16 12 8
9. Problem 07 Let the positive numbers a,b,c,d be in A.P. Then abc, abd, acd, bcd are NOT in A.P./G.P./H.P in A.P. in G.P. in H.P.
10. 08 Problem If the sum of the first 2n terms of the A.P.2,5,8,…,is equal to the sum of the first n terms of the A.P.57,59,61,…,then n equals 10 12 11 13
11. Problem 09 Let roots of unity which subtend a right angle at the origin. Then must be of the form a. b. c. d.
12. Problem 10 The complex numbers satisfying are the vertices of a triangle which is of area zero right-angled isosceles equilateral obtuse-angled isosceles
16. Problem 14 A man from the top of a 100 meters high tower sees a car moving towards the tower at an angle of depression of 30o.After some time, the angle of depression becomes 60o.The distance (in meters)travelled by the car during this time is a. b. c. d.
17. Problem 15 The number of integer values of m ,for which the x-coordinate of the point of intersection of the lines is also an integer, is 2 0 4 1
18. Problem 16 the equation of the directory of the parabola is a. b. c. d.
19. 17 Problem Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius riff PS and RQ intersect at a point X on the circumference of the circle, then 2r equals a. b. c. d.
20. Problem 18 Let AB be a chord of the circle subtending a right angle at the centre. Then the locus of the centric of the triangle PAB is P moves on the circle is a parabola a circle an ellipse a pair of straight lines
21. Problem 19 Area of the parallelogram formed by the lines equals a. b. c. d.
22. Problem 20 The equation of the common tangent touching the circle and the parabola above the x-axis is a. b. c. d.
23. Problem 21 The triangle formed by the tangent to the curve at the point (1,1)and the coordinate axes, lies in the first quadrant. If its area is 2, then the value of b is -1 3 -3 1
