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Let the required quadratic polynomial is ax² + bx + c. … (1) 

Therefore,

Sum of zeros is \(-\frac{b}{a}\) = −5 (given) 

⇒ b = 5a. 

And product of zeros is \(\frac{c}{a}\) = 6 (given) 

⇒ c = 6a. 

By putting the values of b and c in equation (1), we get the quadratic polynomial.

ax² + 5ax +6a = a(x² + 5x + 6) 

Where a is any real number except zero. 

Hence,

The required polynomial is a(x²+5x+6), a ≠ 0, a∈R.

Given that \(\vec a\)and \(\vec b\)are two vectors such that |\(\vec a\)+ \(\vec b\)| = |\(\vec a\)|.

Now, |\(\vec a\) + \(\vec b\)|² = (\(\vec a\) + \(\vec b\)) ∙ (\(\vec a\) + \(\vec b\)) = \(\vec a\) ∙ \(\vec a\) + \(\vec a\) ∙ \(\vec b\) + \(\vec b\) ∙ \(\vec a\) + \(\vec b\) ∙ \(\vec b\) 

= |\(\vec a\)|² + 2\(\vec a\) ∙ \(\vec b\) + \(\vec b\) ∙ \(\vec b\). 

( \(\because\) \(\vec a\)∙ \(\vec a\) = |\(\vec a\)|² and \(\vec a\) ∙ \(\vec b\)= \(\vec b\)∙ \(\vec a\)) 

⇒ |\(\vec a\) + \(\vec b\)|² = |\(\vec a\) + \(\vec b\)|² + 2\(\vec a\) ∙ \(\vec b\) + \(\vec b\) ∙ \(\vec b\)( \(\because\) |\(\vec a\) + \(\vec b\)| = |\(\vec a\)| (Given)) 

⇒ 2\(\vec a\) ∙ \(\vec b\)+ \(\vec b\) ∙ \(\vec b\) = 0. ... (1)

Now, (2\(\vec a\)+ \(\vec b\)) ∙ \(\vec b\) = 2\(\vec a\) ∙ \(\vec b\)+ \(\vec b\)∙ \(\vec b\)= 0 (By equation (1) ) 

We know that two vectors \(\vec a\) and \(\vec b\) are perpendicular only if  \(\vec a\) ∙ \(\vec b\) = 0. 

Hence, that vector (2\(\vec a\) + \(\vec b\)) is perpendicular to the vector \(\vec b\).

The concept of Friday dressing was introduced in corporate industry of US to relax on the last working day of the week.

Plain and choli cut are examples of sari blouse.

Gandhiji himself accepted the proposition that the Champaran episode was a turning point in his life. It was then that he decided to urge the departure of the British from India. In fact the Champaran episode was the first experiment of civil disobedience in India. When Gandhiji was on his way to Champaran, he stayed in Muzaffarpur, where he met the lawyers who were fighting cases for the sharecroppers. The peasants were so crushed, and fear stricken. that Gandhiji concluded that law courts were useless. The real relief for them was to be free from fear. The spontaneous demonstration by the peasants showed that they were instilled with a new strength and spirit. Gandhiji showed the poor peasants how to fight the British with ‘satyagraha’. He made them aware of their power and the power of ahimsa. All this laid the foundation of his future movements and served as a great source of strength and motivation for all Indians.

Hari Mohan
27, Ranjeet Nagar
Bharatpur
18 July 2020
The Editor
The Indian Express
Bharatpur

Subject: Regarding exploitation of the Indigo farmers at the hands of the English landlords.

Sir,

It’s very painful to inform that most of the Indian farmers were working as sharecroppers in Champaran. They were working on the land of English landlords and were forced to grow indigo on the fifteen per cent area of the total farmland. This whole cultivation was to be surrendered to the landlords as the rent of the land. The British landlords were asking for compensation from the farmers to free them from the agreement. It was an unfair act of the English landlords. They exploited our poor Indian farmers. But due to the efforts of Gandhiji, the English landlords gave in and the exploitation of Indian farmers came to an end. You are respectfully requested to publish this article about the exploitation of the English landlords in your esteemed newspaper.

Yours sincerely

Hari Mohan

Given:-

I = 10

P= 20

Q = 1

⇒P = V × I

⇒ V = \(\frac{P}{I}\) = \(\frac{20}{10}\) = 2V

W = VQ = 2 × 1= 2J 

The energy of each coulomb of charge in the circuit is 2J

From equation: 

P = VI

V = P/I ​= 20/10 ​= 2V

From equation:

V = W/Q

W = VQ 

= 2 × 1 

= 2J

• The Bengali play Nil Darpan 
• It is written by Dinabandhu Mitra 
• The play triggered farmer’s unrest in various parts of the country.

Correct option is A) where she had been the day before

Correct option is C) if I had spent all the money

Correct option is B) what he was going to do

Fermi Energy Level

The reason for the existence of this energy level is due to Pauli’s exclusion principle which states two fermions cannot occupy that same quantum state. So, if a system has more than one fermion, each fermion has a different set of magnetic quantum numbers associated with it.

The Fermi Temperature can be defined as the energy of the Fermi level divided by the Boltzmann’s constant. It is also the temperature at which the energy of the electron is equal to the Fermi energy. It is the measure of the electrons in the lower states of energy in metal.

The four visible spectral lines corresponded to transitions from higher energy levels down to the second energy level (n = 2).

Correct option is D) ages

The peddler was accepted and welcomed to the house as Captain von Stahle. Edla gave the peddler a kind treatment and in spite of kowing the reality, she treated him like a captain. This awakened the latent goodness of his heart and he also behaved in a dignified manner and signed himself as Captain von Stahle.

Correct option is B) sip

The psychiatrist thought that Charley’s stamp collecting was a temporary refuge from reality .Charley did not agree with him because his grandfather for whom things were nice and peaceful and who did not need refuge from reality also collected stamps.

Charley told the psychiatrist about his belief in the existence of the third level at the Grand Central Station but was told that it was only a waking- dream wish fulfillment. The psychiatrist also added that Charley was unhappy because of the insecurity, fear, war, worry and that he just wanted to escape just like everyone else.

(i) has been studying

(ii) have been working

(iii) have you been waiting

(iv) has been cooing

(v) has been learning, has still not learnt

(vi) have been living, have now decided

(vii) has been creating

(viii) has taken up

The images of fishermen not harming the whales in the sea and wars leaving behind no survivors to celebrate the victory show that the poet condemns violence. The poet wants the warmongers to change their bloodstained clothes to clean ones. The poet’s refusal to have any association or dealing with death also shows that he is not in favour of any form of violence.

The poet refers to the sadness which surrounds man due to not having any time for himself, the pain of not understanding what he or his fellow human beings want. He has no time for introspection; as a result, he is unable to analyse his own actions and understand its consequences.

The correct answer is option 1 i.e. India has the largest number of medical colleges in the world.

• India has the highest number of medical colleges in the world at 314.
  • However, India has a doctor-population ratio of 1:1700 against a world average of 1.5:1000.
• Currently (As of 2021), India ranks 3^rd worldwide for production by volume and 14^th by value in the Pharma sector.
• India is the largest provider of generic medicines globally, occupying a 20% share in global supply by volume, and also supplies 62% of global demand for vaccines.
• For more than a decade now, China has been the largest producer of active pharmaceutical ingredients (APIs) in the world.

Source:- https://www.investindia.gov.in/sector/pharmaceuticals#:~:text=India%20is%20a%20prominent%20and,and%2014th%20by%20value.

(i) (C) it influenced a generation to fight against injustice.

(ii) (D) demonstrated utmost strength to oppose the system.

(iii) (A) his countrymen

(iv) (B) committed

(v) (B) oppression

The Soldier-"The Soldier" is composed by the poet Rupert Brooke who was the most handsome young man in England. The poet is  saying that when he would die he would he given a come of a field on the earth hidden from dust. when the war had started the dust starts to hid everything and was washed away by the rivers. when war started he wanted a flower which would give love without knowing the definite way where he is to go. He always contacts with English air of England. He was walking, thinking about dispute in war. He thought himself that not a single evil word came in his mind. A small vibraion touahed his mind would last for ever...He wanted a peaceful country. It is his dream and always had seen this type of sight that there woudl be no war between two countries. Everyone should life a peaceful life. It seemed like a heaven in England to think over it.

Nanukaka was coming from Delhi to see some minister. 

The poet wants that the children of the slums should get rid of their dismal lives. They should be educated and brought out from their ugly surroundings. He feels that it is the responsibility of the affluent classes to free these poor children from the life of hunger and misery.

India Through a Traveller's Eyes 

India through a traveller's Eyes is an extract from 'My Several Worlds' written by Pearl S Buck. Pearl S. Buck was an American by birth but was educated in China. India has been the part of the background of Pearl S. Buck's life. She heard the stories of India and Indians from her family doctor and his wife. She was very eager to see India. She has seen many countries in the world. But she is very impressed with Indians. Since was an earnest desire to know India and Indians is Pearl's heart. She came to know India and saw the Taj Mahal in the moonlight. She saw the Fatehpur Sikari and Delhi. But she could not understand India and Indians. She met the young intellectual in the cities and the poor peasants in the villages. By talking and listening the youth of the cities and the poor farmers of the country she understood Indians and then she said that India could not be understood by seeing its monument but it can be understood by talking and listening the young intellects in the cities and poor peasants in the villages. This is the proper way to know India. She says that the customs and rituals of India is very impressing. She feels that Indians are restless for their freedom. They plan to achieve their freedom from the slavery of the British rule.

(c) heaven can be seen in the harvest and moonlight

At Nara in Japan, a deer created the impression that it bowed to the author.

'The Waste Land' had been composed by T.S. Eliot.

The poet refers to the ‘‘sadness’’ which we form out of our own thinking and actions. We understand a lot of things but do not understand himself and his actions. His rush and hurry cause us troubles. He is bent up creating wars against humanity. He is the creator of all disasters. This is the ‘sadness’ that the poet refers to in the poem. Let us introspect ourselves and create mutual understanding.

New varielies of English that have that have emerged in different parts of the world is called New English.

Correct option is C) power

Correct option is D) grows up

36, Gandhi Road 

Chennai – 45 

04 August 2018

Dear Ramesh, 

How are you? I feel sad to inform you that my house was burgled last week when I was on a holiday. Burglars might have known from the accumulated newspaper pile that I had gone away. When I came back last Sunday, I found the back-door lock broken. I could have forgotten to bolt the back-door from inside and they should have entered through it. My room was ransacked. They took my laptop and other valuables. I must have deposited the jewellery in a bank locker to avoid this loss. I should have informed my neighbours about my week-long trip. Well, I have registered an FIR with the police. They are investigating the case. They have assured that I would get my jewels back. The burglars will be caught very soon. Convey my regards to all at home.

Yours lovingly, 

Murali 

Address on the envelope : 

Mr. Ramesh, 

50, Bharathiyar Street, 

Namakkal.

Correct option is C) ordinary

Correct option is B) courageous

Correct option is B) coward

density \(\rho\) = 1.29kg/m³

p = 1 bar

T = 273 k°

Pv = RT

R/M = P/\(\rho.T\)

R/M = \(\frac1{1.29\times10^{-3}\times273}\)

R/M = \(\frac{1000}{1.29\times273}\) 

R/M = 2.83 kJ/kg. k

Milk purchased by tea stall – Intermediate good as milk will be used as an input to make the final product i.e. tea.

Since the milk purchased by a tea stall involves further processing before it is sold as tea or coffee, it is considered as an intermediate good. Final goods are those goods which are purchased for final consumption. They are not meant for resale and is not processed further.

A. the work done by the gas is the same as the energy absorbed as heat 

These entrepreneurs either create a new market for their services or provide a service in an existing market