This is type of problems asked at the JEE (IIT). The purpose of this book is to show students how to handle such problems and give them sufficient practice in solving problems of this type, thus building their confidence. The main features of this book are:Each chapter begins with a summary of facts, formulate and working techniques. Trick, tips and techniques have been clearly marked with the icon.A large number of problems have been solved and explained in each chapter.The exercises contain short-answer, long-answer and objective type questions.Multiple-choice questions in which more than one option may be correct have also been given.Time-bound tests at the end of each chapter will help students practise answering questions in a given time.The book also includes integrated tests, bases on all the chapters.A chapter containing miscellaneous problems has been given at the end of the book. This will help students gain confidence in solving problems without prior knowledge of the chapter(s) to which the problems belong.Table of ContentsAlgebraProgressions, Related Inequalities and SeriesDeterminants and Cramer's RuleEquations, Inequations and ExpressionsComplex NumbersPermutation and CombinationBinomial Theorem for Positive Integral IndexPrinciple of Mathematical Induction (PMI)Infinite SeriesMatricesTrigonometryCircular Functions, IdentitiesSolution of EquationsInverse Circular FunctionsTrigonometrical Inequalities and InequationsLogarithmProperties of TriangleHeights and DistancesCoordinate GeometryCoordinates and Straight LinesPairs of Straight Lines and Transformation of AxesCirclesParabolaEllipse and HyperbolaCalculusFunctionDifferentiationLimit, Indeterminate FormContinuity, Differentiability and Graph of FunctionApplication of dy/dxMaxima and MinimaMonotonic Function and Lagrange's TheoremIndefinite In

    Beginning with the publication of Albert Einstein's theory of relativity, through the wild revolution of quantum mechanics, and up until the physics of the modern day (including the astonishing revelation, in 1998, that the Universe is not only expanding, but doing so at an ever-quickening pace), much of what physicists have seen in our Universe suggests that much of our Universe is unseen—that we live in a dark cosmos.Everyone knows that there are things no one can see—the air you're breathing, for example, or, to be more exotic, a black hole. But what everyone does not know is that what we can see—a book, a cat, or our planet—makes up only 5 percent of the Universe. The rest—fully 95 percent—is totally invisible to us; its presence discernible only by the weak effects it has on visible matter around it.This invisible stuff comes in two varieties—dark matter and dark energy. One holds the Universe together, while the other tears it apart. What these forces really are has been a mystery for as long as anyone has suspected they were there, but the latest discoveries of experimental physics have brought us closer to that knowledge. Particle physicist Dan Hooper takes his readers, with wit, grace, and a keen knack for explaining the toughest ideas science has to offer, on a quest few would have ever expected: to discover what makes up our dark cosmos.

    Here he argues that Canada did not begin in 1867; indeed, its foundation was laid by two visionary men, Louis-Hippolyte LaFontaine and Robert Baldwin. The two leaders of Lower and Upper Canada, respectively, worked together after the 1841 Union to lead a reformist movement for responsible government run by elected citizens instead of a colonial governor.But it was during the "Great Ministry" of 1848—51 that the two politicians implemented laws that created a more equitable country. They revamped judicial institutions, created a public education system, made bilingualism official, designed a network of public roads, began a public postal system, and reformed municipal governance. Faced with opposition, and even violence, the two men— polar opposites in temperament—united behind a set of principles and programs that formed modern Canada. Writing with verve and deep conviction, Saul restores these two extraordinary Canadians to rightful prominence.

    Some of the objects are described by future historians; others through found materials, short stories, or dialogues. All come from a very real future.

    Here is the never-before-told story of the nuclear arms race that changed history-and of the visionary American Air Force officer Bernard Schriever, who led the high-stakes effort. A Fiery Peace in a Cold War is a masterly work about Schriever's quests to prevent the Soviet Union from acquiring nuclear superiority, to penetrate and exploit space for America, and to build the first weapons meant to deter an atomic holocaust rather than to be fired in anger. Sheehan melds biography and history, politics and science, to create a sweeping narrative that transports the reader back and forth from individual drama to world stage. The narrative takes us from Schriever's boyhood in Texas as a six-year-old immigrant from Germany in 1917 through his apprenticeship in the open-cockpit biplanes of the Army Air Corps in the 1930s and his participation in battles against the Japanese in the South Pacific during the Second World War. On his return, he finds a new postwar bipolar universe dominated by the antagonism between the United States and the Soviet Union. Inspired by his technological vision, Schriever sets out in 1954 to create the one class of weapons that can enforce peace with the Russians-intercontinental ballistic missiles that are unstoppable and can destroy the Soviet Union in thirty minutes. In the course of his crusade, he encounters allies and enemies among some of the most intriguing figures of the century: John von Neumann, the Hungarian-born mathematician and mathematical physicist, who was second in genius only to Einstein; Colonel Edward Hall, who created the ultimate ICBM in the Minuteman missile, and his brother, Theodore Hall, who spied for the Russians at Los Alamos and hastened their acquisition of the atomic bomb; Curtis LeMay, the bomber general who tried to exile Schriever and who lost his grip on reality, amassing enough nuclear weapons in his Strategic Air Command to destroy the entire Northern Hemisphere; and Hitler's former rocket maker, Wernher von Braun, who along with a colorful, riding-crop-wielding Army general named John Medaris tried to steal the ICBM program. The most powerful men on earth are also put into astonishing relief: Joseph Stalin, the cruel, paranoid Soviet dictator who spurred his own scientists to build him the atomic bomb with threats of death; Dwight Eisenhower, who backed the ICBM program just in time to save it from the bureaucrats; Nikita Khrushchev, who brought the world to the edge of nuclear catastrophe during the Cuban Missile Crisis, and John Kennedy, who saved it. Schriever and his comrades endured the heartbreak of watching missiles explode on the launching pads at Cape Canaveral and savored the triumph of seeing them soar into space. In the end, they accomplished more than achieving a fiery peace in a cold war. Their missiles became the vehicles that opened space for America.

    He explores the growth of a modern consumer society, the impact of immigration, the invention of modern pop music, and the British retreat from empire. He tells the story of the colourful characters of the period, like Harold Macmillan, Kingsley Amis, and Paul McCartney, and brings to life the experience of the first post-imperial generation, from the Notting Hill riots to the first Beatles hits, from the Profumo scandal to the cult of James Bond.

    Topics include the development of counting and numbers systems, the emergence of zero, cultures that don’t have numbers, algebra, solid geometry, symmetry and beauty, perspective, riddles and problems, calculus, mathematical logic, friction force and displacement, subatomic particles, and the expansion of the universe. Great mathematical thinkers covered include Napier, Liu Hui, Aryabhata, Galileo, Newton, Russell, Einstein, Riemann, Euclid, Carl Friedrich Gauss, Charles Babbage, Montmort, Wittgenstein, and many more. The book is beautifully illustrated throughout in full color.

    He was also among the most despised figures in Nazi Germany. As a Jewish homosexual living openly with his male partner, Warburg represented all that the Third Reich abhorred. Yet Hitler and his top advisors dreaded cancer, and protected Warburg in the hope that he could cure it.In Ravenous, Sam Apple reclaims Otto Warburg as a forgotten, morally compromised genius who pursued cancer single-mindedly even as Europe disintegrated around him. While the vast majority of Jewish scientists fled Germany in the anxious years leading up to World War II, Warburg remained in Berlin, working under the watchful eye of the dictatorship. With the Nazis goose-stepping their way across Europe, systematically rounding up and murdering millions of Jews, Warburg awoke each morning in an elegant, antiques-filled home and rode horses with his partner, Jacob Heiss, before delving into his research at the Kaiser Wilhelm Society.Hitler and other Nazi leaders, Apple shows, were deeply troubled by skyrocketing cancer rates across the Western world, viewing cancer as an existential threat akin to Judaism or homosexuality. Ironically, they viewed Warburg as Germany’s best chance of survival. Setting Warburg’s work against the absorbing history of cancer science, Apple follows him as he arrived at his central belief that cancer is a problem of metabolism. Though Warburg’s metabolic approach to cancer was considered groundbreaking, his work was soon eclipsed in the early postwar era, after the discovery of the structure of DNA set off a search for the genetic origins of cancer.Remarkably, Warburg’s theory has undergone a resurgence in our own time, as scientists have begun to investigate the dangers of sugar and the link between obesity and cancer, finding that the way we eat can influence how cancer cells take up nutrients and grow. Rooting his revelations in extensive archival research as well as dozens of interviews with today’s leading cancer authorities, Apple demonstrates how Warburg’s midcentury work may well hold the secret to why cancer became so common in the modern world and how we can reverse the trend. A tale of scientific discovery, personal peril, and the race to end a disastrous disease, Ravenous would be the stuff of the most inventive fiction were it not, in fact, true.

    People knew the basics: men and women had sex, and sometimes babies followed. But beyond that the origins of life were a colossal mystery. The Seeds of Life is the remarkable and rollicking story of how a series of blundering geniuses and brilliant amateurs struggled for two centuries to discover where, exactly, babies come from. Taking a page from investigative thrillers, acclaimed science writer Edward Dolnick looks to these early scientists as if they were detectives hot on the trail of a bedeviling and urgent mystery. These strange searchers included an Italian surgeon using shark teeth to prove that female reproductive organs were not 'failed' male genitalia, and a Catholic priest who designed ingenious miniature pants to prove that frogs required semen to fertilize their eggs. A witty and rousing history of science, The Seeds of Life presents our greatest scientists struggling-against their perceptions, their religious beliefs, and their deep-seated prejudices-to uncover how and where we come from.

    Reprint. NYT.

    It identifies ten types of supposed truth and explains how easily each can become the midwife of falsehood. There is no species of truth that we can rely on unquestioningly, but that does not mean the truth can never be established. Attaining truth is an achievement we need to work for, and each chapter will end up with a truth we can have some confidence in.This history builds into a comprehensive and clear explanation of why truth is now so disputed by exploring 10 kinds of truth:1. Eternal truths.2. Authoritative truths.3. Esoteric truths.4. Reasoned truths.5. Evidence-based truths.6. Creative truths.7. Relative truths. 8. Powerful truths9. Moral truths.10. Holistic truths. Baggini provides us with all we need to restore faith in the value and possibility of truth as a social enterprise. Truth-seekers need to be sceptical not cynical, autonomous not atomistic, provisional not dogmatic, open not empty, demanding not unreasonable.

    In this selection from The Body, Bill Bryson introduces us to the mysterious, and often devastating, world of disease.

    

    In his newest volume, he takes on a fundamental concept of modern physics: nothing. The physics of stuff—protons, neutrons, electrons, and even quarks and gluons—is at least somewhat familiar to most of us. But what about the physics of nothing? Isaac Newton thought of empty space as nothingness extended in all directions, a kind of theater in which physics could unfold. But both quantum theory and relativity tell us that Newton’s picture can’t be right. Nothing, it turns out, is an awful lot like something, with a structure and properties every bit as complex and mysterious as matter. In his signature lively prose, Weatherall explores the very nature of empty space—and solidifies his reputation as a science writer to watch.

    The tipping point, Mirbat, South Oman, 19 July 1972 is one of the least-known yet most crucial battles of modern times. If the SAS had been defeated at Mirbat, the Russian and Chinese plan for a communist foothold in the Middle East would have succeeded, with catastrophic consequences for the oil-hungry West. OPERATION STORM is a page-turning account of courage and resilience. Mirbat was a battle fought and won by nine SAS soldiers and a similar number of brave local people - some as young as ten years old - outnumbered by at least twenty-five to one. Roger Cole, one of the SAS soldiers who took part, and writer Richard Belfield have interviewed every SAS survivor who fought in the battle from the beginning to the end - the first time every single one of them has revealed their experience. OPERATION STORM is a classic story of bravery against impossible odds, minute by minute, bullet by bullet.