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Wed July 23, 2014  

Ans: test purpose

Tue July 22, 2014  

Ans: G i v e n space e q u a t i o n s space m a y space h a v e space a space c o m m o n space r o o t. space a x squared plus b x plus c equals 0 c x squared plus b x plus a equals 0  l e t space p space b e space t h e space c o m m o n space r o o t space f o r space b o t h space e q u a t i o n s comma space w e space g e t a p squared plus b p plus c equals 0 c p squared plus b p plus a equals 0  s u b t r a c t i n g space b o t h space e q u a t i o n s space w e space g e t left parenthesis a minus c right parenthesis p squared plus c minus a equals 0 left parenthesis a minus c right parenthesis p squared equals a minus c a not equal to c space b e c a u s e space b o t h space e q u a t i o n s space b e c o m e space i d e n t i c a l space i f space a equals c rightwards double arrow p squared equals 1 p equals plus-or-minus 1  s u b s t i t u t i n g space p equals 1 space g i v e s space a plus b plus c equals 0 p equals minus 1 comma space g i v e s space a minus b plus c equals 0

Tue July 22, 2014  

Ans: l e t space t w o space p a r t s space b e space x space a n d space 100 minus x g i v e n space s u m space o f space r e c i p r o c a l s space i s space 1 over 24 1 over x plus fraction numerator 1 over denominator 100 minus x end fraction equals 1 over 24 fraction numerator 100 over denominator x left parenthesis 100 minus x right parenthesis end fraction equals 1 over 24 2400 equals 100 x minus x squared x squared minus 100 x plus 2400 equals 0 x equals fraction numerator minus b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction equals fraction numerator 100 plus-or-minus square root of 10000 minus 4 cross times 2400 end root over denominator 2 end fraction equals fraction numerator 100 plus-or-minus 20 over denominator 2 end fraction  x equals 60 comma space 40  T w o space p a r t s space a r e space 60 space a n d space 40

Tue July 22, 2014  

Ans: Following are four important ideals on which the Preamble to the Indian Constitution lays special emphasis: Justice – This ideal implies that citizens of India cannot be discriminated on the basis of caste, religion and gender. It entrusts the Government of India with the removal of social inequalities and the welfare of all, especially the disadvantaged groups. Liberty – This ideal establishes that there are no unreasonable restrictions on Indian citizens in terms of what they think, their manner of expression and the way they wish to follow up their thoughts in action. Equality – It asserts that all Indian citizens are equal before the law of the land. It recognises that the traditional social inequalities are irrelevant and the government is obliged to ensure equality of opportunity for all citizens. Fraternity – It means that all citizens should behave as if they are part of the same family. No one should treat a fellow citizen as inferior.

Tue July 22, 2014  

Ans: Nelson Mandela is recognised as the leader of the democracy movement in South Africa. In 1964, he and seven other associates of his were tried for treason for protesting against the apartheid regime in South Africa and were imprisoned in the Robben Island prison. Mandela spent 28 years in the prison before he was released  in 1990. Despite this long term of imprisonment, Mandela never wavered from his belief in democratic ideals and freedom and fraternity of all South African people. Before and after becoming the first President of the new Republic of South Africa, he worked tirelessly to ensure that the Constitution of South Africa was based on ideal of democratic government and inclusive democratic socialism. As a result of his efforts, South Africa, a State denounced by the entire world till recently as the most undemocratic one is now seen as a model of democracy.

Tue July 22, 2014  

Ans: The Indian constitution was framed by the Indian constituent Assembly.  The making of the Indian constitution was not easy. India had a huge diverse population. The people were emerging as the citizens of the free country. There were also relilgious diversity among the people of the country. During partition, many people were killed in the religious roits. Partition was a traumatic experience for the people of both India and pakistan. One of the major factors for framing the Indian constitution was to provide guidelines to the elected members on the governance. The framers of the Indian constitution while framing the constitution had to frame constitution which could give representation to each section of the society.  Further, the British had drafted the instrument of accession for the princely states in India. This severely threatened the unity of the country. The framers of the constitution thus had to ensure the unity of the country. They also had the reponsibility of transforming the Indian society and politics. Many leaders had different opinions about the political model that had to be adopted in the country. Many social groups in the country were discriminated against. The leaders of the country decided to provide the principles of equality, liberty and justice to all the people of the country irrespective of their caste, class and religion. Thus major factors which contributed to the framing of our constitution were to provide constitutional guideline to the elected representatives, to provide equal repreentation to all and provide liberty, justice and security to the people.

Tue July 22, 2014  

Ans: 'None' and 'Either' are both correct in this context. Though the usage'None… are' is also common and correct, 'None… is' is preferred over it.'None' and 'Each' are both to be used as singular subjects. Similarly, 'Either' means one out of the two('Either of the boys’ would mean one of them). Therefore, it is advisable to treat it as a singular word than plural. In conclusion, ‘Either of the boys is’ and ‘None of the boys is’ are both correct.

Tue July 22, 2014  

Ans: The necessary centripetal force required for the electron to revolve around the nucleus is provided by the electrostatic force of attraction between the nucleus and the electron. If the electrons in an atom were stationary the electrons will be pulled into the nucleus due to the coulomb's attractive force.The structure of the atom can be stable only if the electrons are revolving around the nucleus.   Electrons revolve around nucleus only in certain discrete non radiating stationary orbits.The orbits in which they revolve are those in which the total angular momentum of the revolving electron is an integral multiple of h/2π where h is the Planck,s constant.i.e the anguar momentum of these orbiting electrons are quantised. When the electron revolves in these permitted orbits it does not radiate energy .Since the electrons revolve in a stationary orbit without radiating energy it does not fall into the nucleus. The total energy of electrons in a stationary orbit is negative, which indicates that the electrons are bound to the nucleus and is not free to leave it.

Tue July 22, 2014  

Ans: From the basic definition of One to One function, we know that function never maps distintive elements of its domain to same element   so we are trying to prove the same statement in the different form where we are assuming if f(x1) = f(x2) which means two distintive elements x1 and x2 from domain mapped to same element in codomain. So inorder to have function f, be One to One function both elements should be identical or else the function cant be One to One. Hence for f to be One to One function, if f(x1) = f(x2) => x1=x2 

Tue July 22, 2014  

Ans: square root of open parentheses 2 co t space theta plus fraction numerator 1 over denominator sin squared space theta end fraction close parentheses end root equals square root of open parentheses fraction numerator 2 cos space theta over denominator sin space theta end fraction plus fraction numerator 1 over denominator sin squared space theta end fraction close parentheses end root equals square root of open parentheses fraction numerator 1 plus sin space 2 theta over denominator sin squared space theta end fraction close parentheses end root equals square root of open parentheses fraction numerator sin space theta space plus space cos theta over denominator sin space theta end fraction close parentheses squared end root equals plus-or-minus open parentheses fraction numerator sin space theta space plus space cos theta over denominator sin space theta end fraction close parentheses equals plus-or-minus open parentheses 1 plus c o t space theta close parentheses  g i v e n space theta element of open parentheses fraction numerator 3 straight pi over denominator 4 end fraction comma space straight pi close parentheses space s o space a n s w e r space i s space minus left parenthesis 1 plus space c o t space theta right parenthesis space equals space minus 1 minus c o t space theta space equals space k minus c o t space theta space rightwards double arrow k equals minus 1

Tue July 22, 2014  

Ans: G i v e n space t h a t space t h e space p e r i m e t e r space o f space a space c i r c l e space a n d space a space c i r c l e space a n d space a space s q u a r e space i s space K K equals 2 πr plus 4 straight a rightwards double arrow 4 straight a equals straight K minus 2 πr rightwards double arrow straight a equals fraction numerator straight K minus 2 πr over denominator 4 end fraction.... left parenthesis 1 right parenthesis The space sum space of space the space areas space of space the space circle space and space square space is space given space by straight A equals πr squared plus straight a squared rightwards double arrow straight A equals πr squared plus open parentheses fraction numerator straight K minus 2 πr over denominator 4 end fraction close parentheses squared fraction numerator d straight A over denominator d straight r end fraction equals 2 πr plus 2 open parentheses fraction numerator straight K minus 2 πr over denominator 16 end fraction close parentheses open parentheses minus 2 straight pi close parentheses rightwards double arrow fraction numerator d straight A over denominator d straight r end fraction equals 2 πr minus straight pi open parentheses fraction numerator straight K minus 2 πr over denominator 4 end fraction close parentheses For space minimum comma space fraction numerator d straight A over denominator d straight r end fraction equals 0 2 πr minus straight pi open parentheses fraction numerator straight K minus 2 πr over denominator 4 end fraction close parentheses equals 0 rightwards double arrow 2 straight r equals fraction numerator straight K minus 2 πr over denominator 4 end fraction rightwards double arrow 8 straight r equals straight K minus 2 πr rightwards double arrow 8 straight r plus 2 πr equals straight K rightwards double arrow straight r open parentheses 8 plus 2 straight pi close parentheses equals straight K rightwards double arrow straight r equals fraction numerator straight K over denominator open parentheses 8 plus 2 straight pi close parentheses end fraction.... left parenthesis 2 right parenthesis Now space let space us space find comma space fraction numerator d squared straight A over denominator d straight r squared end fraction space fraction numerator d squared straight A over denominator d straight r squared end fraction equals 2 straight pi plus straight pi over 2 greater than 0 Thus comma space area space is space minimum space when comma space straight r equals fraction numerator straight K over denominator open parentheses 8 plus 2 straight pi close parentheses end fraction straight a equals fraction numerator straight K minus 2 straight pi cross times fraction numerator straight K over denominator open parentheses 8 plus 2 straight pi close parentheses end fraction over denominator 4 end fraction rightwards double arrow a equals fraction numerator straight K minus straight pi cross times fraction numerator straight K over denominator open parentheses 4 plus straight pi close parentheses end fraction over denominator 4 end fraction rightwards double arrow a equals fraction numerator straight K open parentheses 4 plus straight pi close parentheses minus K straight pi over denominator 4 open parentheses 4 plus straight pi close parentheses end fraction rightwards double arrow a equals fraction numerator 4 straight K over denominator 4 open parentheses 4 plus straight pi close parentheses end fraction rightwards double arrow a equals fraction numerator straight K over denominator open parentheses 4 plus straight pi close parentheses end fraction.... left parenthesis 3 right parenthesis F r o m space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e straight a equals fraction numerator straight K minus 2 πr over denominator 4 end fraction rightwards double arrow 4 a equals K minus 2 πr rightwards double arrow 2 πr equals straight K minus 4 straight a rightwards double arrow straight r equals fraction numerator straight K minus 4 straight a over denominator 2 straight pi end fraction.... left parenthesis 4 right parenthesis Substituting space the space value space of space straight a space from space equation space left parenthesis 3 right parenthesis space in space equation space left parenthesis 4 right parenthesis comma space we space have comma straight r equals fraction numerator straight K minus 4 cross times fraction numerator straight K over denominator 4 plus straight pi end fraction over denominator 2 straight pi end fraction straight r equals fraction numerator straight K over denominator 2 open parentheses 4 plus straight pi close parentheses end fraction... left parenthesis 5 right parenthesis From space equations space left parenthesis 3 right parenthesis space and space left parenthesis 5 right parenthesis comma space it space is space clear space that space a equals 2 r

Tue July 22, 2014  

Ans: Solution: 2Fe (s)     +    3H 2 O (g)               Fe 2 O 3(s)      +      3H 2(g) 2x56g              3x18g 3x18g H 2 O    = 2X 56 g Fe So 18g H 2 O   = 2 X 56   =  37.3g                              3

Tue July 22, 2014  

Ans: A rheostat is a variable resistor or an adjustable resistor.Its resistance can be varied as desired.It is a continuous resistance varying device used to change the magnitude of current in a circuit by changing the length of the resistance wire inserted into the circuit.The main use of a rheostat is as variable resistance .

Tue July 22, 2014  

Ans: Dear pannalal.malakar@gmail.com

Thanks for asking us a question in Ask the Expert section of TopperLearning.com.   In case of multiple questions within a query, please post each question individually and let us know where you are getting stuck so that we would be able to explain things better.

  Solution for your first query, Electronegativity is the ability of molecule to attract an electron of the covalent bond. It deals with atoms in a molecule and their tendency to attract bonding pair of electrons. Electron affinity is the amount of energy released when an electron is gained by some atom. It deals with an isolated atom. Regards

Topperlearning Team.

Tue July 22, 2014  

Ans: Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.

Tue July 22, 2014  

Ans: Significant figure does not convey the magnitude of the reading uncertainty for any specific scale. Significant figure neglect the operator error, systematic error which occurs during the real experiments so there will be more uncertainty than what the significant figure of the measurements would suggest.

Tue July 22, 2014  

Ans: Dear pannalal.malakar@gmail.com

Thanks for asking us a question in Ask the Expert section of TopperLearning.com.
We have not understood the query that you have posted. You have not mentioned which law to derive from what other law. We would like you to state the law to be derived and the law from which that law is to be derived.

Regards

Topperlearning Team.

Tue July 22, 2014  

Ans: Newton's law of gravitation is defined as "The force between two objects is directly proportional to the product of the masses and inversely proportional to the square of the distance between them" It is expressed from the statement itself and there is no direct derivation for the law. Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.

Tue July 22, 2014  

Ans: Dear crys.tiwari@gmail.com

Thanks for asking us a question in Ask the Expert section of TopperLearning.com.
We have not understood the query that you have posted. We would request you to clarify / provide additional details so that we may answer this to the best of the ability.

Regards

Topperlearning Team.

Tue July 22, 2014  

Ans: limit as x rightwards arrow infinity of open parentheses fraction numerator x over denominator x plus 3 end fraction close parentheses to the power of 3 x end exponent equals e to the power of limit as x rightwards arrow infinity of 3 x. log open parentheses fraction numerator x over denominator x plus 3 end fraction close parentheses end exponent equals e to the power of limit as x rightwards arrow infinity of 3 x. log open parentheses 1 plus fraction numerator x over denominator x plus 3 end fraction minus 1 close parentheses end exponent equals e to the power of limit as x rightwards arrow infinity of 3 x. log open parentheses 1 plus fraction numerator x minus x minus 3 over denominator x plus 3 end fraction close parentheses end exponent equals e to the power of limit as x rightwards arrow infinity of 3 x. log open parentheses 1 minus fraction numerator 3 over denominator x plus 3 end fraction close parentheses end exponent equals e to the power of limit as x rightwards arrow infinity of 3 x. fraction numerator log open parentheses 1 minus fraction numerator 3 over denominator x plus 3 end fraction close parentheses over denominator begin display style fraction numerator minus 3 over denominator left parenthesis x plus 3 right parenthesis end fraction end style end fraction. fraction numerator minus 3 over denominator left parenthesis x plus 3 right parenthesis end fraction end exponent equals e to the power of limit as x rightwards arrow infinity of fraction numerator log open parentheses 1 minus fraction numerator 3 over denominator x plus 3 end fraction close parentheses over denominator begin display style fraction numerator minus 3 over denominator left parenthesis x plus 3 right parenthesis end fraction end style end fraction. limit as x rightwards arrow infinity of fraction numerator minus 9 x over denominator left parenthesis x plus 3 right parenthesis end fraction end exponent equals e to the power of limit as fraction numerator minus 3 over denominator x plus 3 end fraction rightwards arrow 0 of fraction numerator log open parentheses 1 minus fraction numerator 3 over denominator x plus 3 end fraction close parentheses over denominator begin display style fraction numerator minus 3 over denominator left parenthesis x plus 3 right parenthesis end fraction end style end fraction. limit as x rightwards arrow infinity of fraction numerator minus 9 x over denominator left parenthesis x plus 3 right parenthesis end fraction end exponent open square brackets I f space x rightwards arrow infinity comma space t h e n space fraction numerator minus 1 over denominator x plus 3 end fraction rightwards arrow 0 space & fraction numerator minus 3 over denominator x plus 3 end fraction rightwards arrow 0 space close square brackets  equals e to the power of open square brackets limit as fraction numerator minus 3 over denominator x plus 3 end fraction rightwards arrow 0 of fraction numerator log open parentheses 1 minus fraction numerator 3 over denominator x plus 3 end fraction close parentheses over denominator begin display style fraction numerator minus 3 over denominator left parenthesis x plus 3 right parenthesis end fraction end style end fraction close square brackets. limit as x rightwards arrow infinity of fraction numerator minus 9 x over denominator left parenthesis x plus 3 right parenthesis end fraction end exponent equals e to the power of limit as fraction numerator minus 3 over denominator x plus 3 end fraction rightwards arrow 0 of fraction numerator log open parentheses 1 minus fraction numerator 3 over denominator x plus 3 end fraction close parentheses over denominator begin display style fraction numerator minus 3 over denominator left parenthesis x plus 3 right parenthesis end fraction end style end fraction. limit as x rightwards arrow infinity of fraction numerator minus 9 x over denominator left parenthesis x plus 3 right parenthesis end fraction open square brackets limit as x rightwards arrow 0 of fraction numerator log left parenthesis 1 plus x right parenthesis over denominator x end fraction equals 1 close square brackets end exponent equals e to the power of 1 cross times limit as x rightwards arrow infinity of fraction numerator minus 9 x over denominator left parenthesis x plus 3 right parenthesis end fraction end exponent equals e to the power of limit as x rightwards arrow infinity of fraction numerator minus 9 over denominator left parenthesis 1 plus begin display style 3 over x end style right parenthesis end fraction end exponent equals e to the power of fraction numerator minus 9 over denominator left parenthesis 1 plus begin display style 3 over infinity end style right parenthesis end fraction end exponent equals e to the power of fraction numerator minus 9 over denominator left parenthesis 1 plus begin display style 0 end style right parenthesis end fraction end exponent equals e to the power of minus 9 end exponent  T h e space b e s t space w a y space i s space t o space t a k e space log space o n space b o t h space s i d e s space f o r space t h e s e space s u m s.
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