Notes and Study material for Exams
Rahul Raj Number system 1. Basic Formulae (a + b)(a – b) = (a2 – b2) (a + b)2 = (a2 + b2 + 2ab) (a – b)2 = (a2 + b2 – 2ab) (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) (a3 + b3) = (a + b)(a2 – ab + b2) (a3 – b3) = (a – b)(a2 + ab + b2) (a3 + b3 + c3 – 3abc) = (a + b + c)(a2 + b2 + c2 – ab – bc – ac) When a + b + c = 0, then a3 + b3 + c3 = 3abc 2. Types of Numbers I. Natural Numbers Counting numbers 1,2,3,4,5,…1,2,3,4,5,… are called natural numbers … Read more
The National Ganga Council: A Catalyst for the Rejuvenation of India’s Sacred River The Ganga, revered as a lifeline and a symbol of faith for millions in India, has faced severe environmental challenges for decades. Pollution, depletion, and ecological degradation have threatened the river’s health and the livelihoods of those who depend on it. Recognizing … Read more
Satyagraha – A holistic approach towards life, based on the ideals of truth and moral courage. Satyagraha’s goal is winning over people’s hearts, and this can be achieved only with tremendous patience, Satyagraha is more than a political tool of resistance. The similarities of the Satyagraha to some of the greatest philosophical and … Read more
Elementary idea of LASER Laser, a device that stimulates atoms or Molecules to emit Light at particular wavelengths and amplifies that light, typically producing a very narrow beam of radiation. The emission generally covers an extremely limited range of visible, infrared, or ultraviolet wavelengths. Many different types of lasers have been developed, with … Read more
Urban Indian economy after 1858 During this period, the Indian economy essentially remained stagnant, growing at the same rate (1.2%) as the Population. India also experienced deindustrialization during this period. Compared to the Mughal era, India during the British colonial era had a lower per-capita income, a large decline in the Secondary Sector, and lower … Read more
Kalidasa: The Bard of Sanskrit Literature Kalidasa, the celebrated poet, playwright, and dramatist, stands as a towering figure in the history of Sanskrit literature. His works, imbued with profound insights into human nature, intricate poetic imagery, and a masterful command of language, have captivated audiences for centuries. While shrouded in mystery, his legacy continues to … Read more
Yoga, aims to remind us of the simple joy and profound benefits of laughter. The Origins of World Laughter Day The concept of World Laughter Day was born in 1998, inspired by Dr. Kataria’s belief in the transformative power of laughter. He observed that even forced laughter could trigger physiological changes similar to genuine laughter, … Read more
The Travels of Ibn Battuta: A Journey Through Time and Space Introduction Ibn Battuta, born in 1304 in Tangier, Morocco, stands as one of history’s most remarkable travelers. His epic journey, spanning over three decades and covering an estimated 75,000 miles, took him across vast swathes of the known world, from the bustling cities of … Read more
Navigating the Complexities of Advanced Pricing Agreements (APAs) The globalized nature of modern business has led to an increasing complexity in international tax matters. Multinational corporations (MNCs) often face challenges in determining the appropriate transfer pricing for transactions between their subsidiaries in different countries. This can lead to disputes with tax authorities, resulting in costly … Read more