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Three Dimensional Geometry (part - 2) , The Planes | study material for IIT JEE | concept booster, chapter highlights/

THREE DIMENSIONAL GEOMETRY (PART - 2), THE PLANES










THE PLANESPlane is the surface such that if any two points are taken on it, then the line joining the two points lies on it.
General equation of plane is given as -  ax + by + cz + d = 0 , where a ,b and c is not equal to zero.
           POINTS TO BE REMEMBERED 1). a, b and c are the directions ratios of the normal to the plane ax + by + cz + d = 0.

2). Equation of the yz - plane is x = 0

3). Equation of the zx - plane is y = 0

 4). Equation of the xy - plane is z = 0

5). Equation of the any plane parallel to the xy - plane is z = c. Similarly for Planes parallel to yz and zx is x = c and y = c
EQUATION OF THE PLANE IN NORMAL FORMVECTOR FORMIf n̂ be a unit vector normal to a given plane and d be the length of the perpendicular from the origin to the plane, then the equation of the plane is given by -                           r.n̂ = d CARTESIAN FORMIf l, m, n are the directions cosines of the normal to the plane and d is the perpendicular distan…

Metamorphosing Sociopolitical Matrix of India under rule of East India Company

Metamorphosing Sociopolitical Matrix of India under the Regime of East India Company till 1857






Under the colonial rule of the British Imperial Legislative Government and East India Company, the sociopolitical structure of India had undergone a massive change at several levels. East India Company was evolving as a crucial political strength in India by late eighteenth century after deposing prominent regional powers like Bengal, Bombay etc. The Company introduced repressive policies for expansion of territories as elaborated in the article Emergence of East India Company as an Imperialist Political Power in India.
Functioning as an administrative and political entity in India, EIC launched numerous political, social and education-related policies that considerably affected various sections of society like peasants, women, children, industrial sectors and handicrafters. The prime objective of this article is to shed light on the sociopolitical matrix of British India to understand the sta…

Partnership & Work and wages problems tricks in Hindi | fast track formulae for problem solving.

WORK AND WAGES PROBLEMS TRICKS IN HINDI
1). कुल वेतन = कुल दिन × 1 दिन का वेतन
2). यदि X , Y, Z किसी कार्य को d1 , d2 , d3 दिनों में कर सकते हैं, तो उनके वेतनो का अनुपात =       d2d3 : d3d1 : d1d2 
3). यदि A और B किसी कार्य को x और y दिनों में कर सकते हैं, तथा उनके वेतनो का अनुपात y : x है, तो A और B के वेतन क्रमशः , A = y [कुल वेतन/(x+y)] ,              B = x[कुल वेतन/(x+y)]
4). यदि A , B और C किसी कार्य को x,y व z दिनों में कर सकते हैं, तथा उनके वेतनो का अनुपात yz : xz : xy है, तब A , B और C के वेतन क्रमशः -
A = yz [कुल वेतन/(yz : xz : xy)] B = zx [ कुल वेतन/(yz : xz : xy)] C =  xy [ कुल वेतन/(yz : xz : xy)]
5). निश्चित व्यक्ति द्वारा निश्चित कार्य करके कमाया गया कुल वेतन = (1 व्यक्ति का 1 दिन का वेतन) × ( व्यक्तियों की संख्या) × (दिनों की संख्या). तो आवश्यक व्यक्तियों की संख्या =  कुल वेतन/(1 व्यक्ति का 1 दिन का वेतन) × (दिनों की संख्या).
6). A किसी कार्य को x दिन में कर सकता है, तथा B की सहायता से A किसी कार्य को y दिन में कर सकता है, तब A का हिस्सा तथा B का हिस्सा , यदि वे ₹ a प्राप्त करते है…

Was East India Company supremely functioning as a Colonial Trading Group till 1857?

Was British East India Company supremely functioning as a Colonial Trading Group till 1857?

After acquiring the royal charter from the ruler of England in 1600, the British East India Company attained a monopoly on trade with East. The company eliminated competition in business; asserted control over Bengal after Battle of Plassey 1757; achieved Diwani rights ( i.e. revenue collection rights over Bengal, Bihar and Orisha) after Treaty of Allahabad 1765 and emerged as a supreme political power by the middle eighteenth century. But interestingly, the company experienced financial collapse by the second half of the eighteenth century because of nepotism and persistence of corruption in company officials. ( Such corrupt officials were often referred as nabobs- an anglicised form of the nawab.)
British Parliamentary Government investigated the inherent functioning of the company and introduced several acts to induce discipline in the company officials. Regulating Act/ Charter Act (1773):Thi…

True Discount and Banker's Discount problems tricks in Hindi | fast track formulae for problem solving.

TRUE DISCOUNT AND BANKER'S DISCOUNT TRICKS IN HINDI

TRUE DISCOUNT 1). वास्तविक बट्टा = मिश्रधन - वर्तमान धन
2). यदि ब्याज की दर r% वार्षिक , समय t व वर्तमान धन (pw) है, तो वास्तविक बट्टा = PW×r×t/100
3). यदि r% तथा समय t के बाद देय धन A है, तो तत्काल धन pw = 100×A/(100+r.t)
4). यदि देय धन A पर r% व समय t दिए गए है, तो वास्तविक बट्टा = A.r.t /(100+r.t)
5). यदि किसी निश्चित समय के पश्चात निश्चित वार्षिक दर पर, देय धन पर वास्तविक बट्टा (TD) व समान समय व दर के लिए साधारण ब्याज (SI) हैं, तो देय धन A =      SI × TD/(SI - TD)
6). यदि t समय पश्चात r% वार्षिक दर पर, देय धन पर वास्तविक बट्टा (TD) व साधारण ब्याज (SI) है , तो -  SI - TD = TD×r×t/100
7). t वर्ष बाद r% चक्रवृद्धि दर पर देय धन A का तत्काल धन (PW) = A/(1+r/100)^t   व वास्तविक बट्टा = A - PW
BANKER'S DISCOUNT1). महाजनी बट्टा = शेष समय (समाप्त न हुए समय) के लिए बिल पर ब्याज = बिल की राशि × दर × शेष समय /100
2). महाजनी लाभ = महाजनी बट्टा - वास्तविक बट्टा
3). यदि बिल का मान / अंकित मूल्य A है, समय t व दर r% है, तो महाजनी बट्टा = A×r×t/100
4).…