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21151.

In which of the following ways does the hydride ion tend to function ?A. an electrophileB. A nucleophileC. A free radicalD. An acid

Answer» Correct Answer - B
Hydride ion is formed when hydrogen aaccepts an electron, so it has a tendency to donate electron, hence it function as nucleophile.
21152.

The wavelength of electron waves in two orbits `(lambda_(1) : lambda_(2))`A. `25 : 9`B. `5 : 3`C. `9 : 25`D. `3 : 5`

Answer» Correct Answer - A
`lambda=(h)/(sqrt(2mKE)), (lambda_(1))/(lambda_(2))=sqrt((KE_(2))/(KE_(1))), (3)/(5)=sqrt((KE_(2))/(KE_(1))),(KE_(1))/(KE_(2))=(25)/(9)`
21153.

Most stable radical isA. `CH_(2) = overset(*)CH`B. `CH_(2)= CH overset(*) CH_(2)`

Answer» Correct Answer - D
`3^(@)` allylic radical.
21154.

If the electron gain enthalpy of S and Se are `-200` KJ `" mol"^(-1)` and `-195 KJ " mol"^(-1)` respectively. Wha is the electron gain enthalpy of O atom?A. `-250 KJ " mol"^(-1)`B. `-198 KJ " mol"^(-1)`C. `-141 KJ " mol"^(-1)`D. `-225 KJ " mol"^(-1)`

Answer» Correct Answer - C
Order of electron affinity :
`{:(,S,gt,Se,gt,Te,gt,Po,gt,O),(E.G.E.,-200,,-195,,-190,,-174,,-141):}`
21155.

The structural formula of 2-oxo-3-methyl-(N-bromo) butanamide isA. `CH_(3)-CH_(2)-CO- CO-NH-Br`B. `CH_(3)-overset(CH_(3)) overset(|)(CH)-CO-NH-Br`C. `CH_(3)CH-CO-CO-overset(CH_(3)) overset(|)(NOBr)`D. `(CH_(3))_(3)C-CO-CO-NHBr`

Answer» Correct Answer - B
2-oxo-3-methyl-(N-bromo) butanamide is
`H_(3)underset(4)C-H overset(H_(3)C)overset(|)underset(3)C-overset(O)overset(||)underset(2)C-overset(O)overset(||)underset(1)C-underset(H) underset(|)N-Br`
21156.

Democracy’s ability to generate its own support is itself an outcome that cannot be ignored.’ Support the statement with examples. OR ‘There is an overwhelming support for the idea of democracy in South Asia.’ Support the statement with examples.

Answer»

(i) Democracy ensures that decision making will be based on norms and procedure. 

(ii) Every citizen has the right and means to examine the process of decision making. 

(iii) Democratic governments are accountable, legitimate and transparent governments. 

(iv) People have the right to choose their rulers. 

(v) Democracy gives its citizens the right to information about the government and its functioning. 

(vi)A democratic government is the people’s own government and it is run by the people. 

(vii) Any other relevant point

OR

(i) Democratic government is peoples own government. 

(ii) Countries from South Asia want democratic rights for people. 

(iii) Countries want to elect their representatives by themselves. 

(iv) Democracy provides dignity and freedom to its citizens. 

(v) Democracy accommodates social diversity. 

(vi) Democracy is based on the idea of discussion and negotiation.

(vi) Eg. India, Nepal, Bangladesh, Sri Lanka, Pakistan 

(vii) Any other relevant point

21157.

What is mean by Ribonucleic Acid

Answer»

Ribonucleic acid, or RNA, is named on the bases of ribose sugar group found in backbone. RNA is known to be involved in several important roles like transcribing genetic information from deoxyribonucleic acid (DNA) into proteins.

21158.

Viola plants represent the largest genus of cleistogamous flowers. Which of the following is NOT a requirement for Viola plants to assure propagation? A. flowering B. fertilisation C. bisexual flowers D. external pollinators

Answer»

D. external pollinators

21159.

In some species of flowering plants, fruits develop without the process of fertilisation. Which of these can be an identifying factor of such fruits? A. They are not developed from the ovary. B. They are always composite. C. They are always seedless. D. They are not juicy.

Answer»

C. They are always seedless. 

21160.

Define adaptive radiation.

Answer» The process of evolution which results in transformation of original species to many different varieties is called adaptive radiation.
21161.

Plants living in the water are called hydrophytes, Those living in theareas with water scarcity are called xerophytes; and the plants living insaline waters are called halophytes. Write the type of plant against thefollowing examples.a. Salvinia ________________b. Opuntia ________________c. Rhizophora ________________d. Mangifera ________________

Answer»

a. Hydrophyte,  

 b. Xerophyte, 

 c. Halophyte, 

 d. Mesophyte

21162.

Name the four types of chromosomal aberrations.

Answer» Deletion, duplication, inversion and translocation.
21163.

Plants living in the water are called hydrophytes, Those living in the areas with water scarcity are called xerophytes; and the plants living in saline waters are called halophytes. Write the type of plant against the following examples. a. Salvinia ____________________ b. Opuntia ____________________ c. Rhizophora ____________________ d. Mangifera ____________________

Answer»

a. Hydrophyte, 

b. Xerophyte,

 c. Halophyte,

 d. Mesophyte

21164.

In a pond, we see plants which are free-floating; rooted–submerged; rooted emergent; rooted with floating leaves; Write the type of plant against the following examples. a. Hydrilla ____________________ b. Typha ____________________c. Nymphaea ____________________ d. Lemna ____________________ e. Vallisnaria ________________

Answer»

a. submerged,

 b. Rooted emergent,

 c. Rooted with floating leaves,

 d. free – floating,

 e. Rooted Submerged

21165.

Number of individuals of a population in a habitat per unit area is called density and density is measured in different units. Write the unit of measurement against the following: a. Bacteria b. Grass c. Banyan d. Deer e. Fish

Answer»

 a. Nos. / Vol; 

b. Coverage / area;

 c. Biomass / area; 

d. Nos. / area;

 e. Wt. / area 

21166.

What is a tree line?

Answer»

When we go up the altitude, beyond a particular height no trees are found and the vegetation comprises only of shrubs and herbs. The altitude beyond which no tree is seen is known as tree line.

21167.

Number of individuals of a population in a habitat per unit area is called density and density is measured in different units. Write the unit of measurement against the following:a. Bacteriab. Grassc. Banyand. Deere. Fish

Answer»

a. Nos. / Vol;

 b. Coverage / area;

 c. Biomass / area

 d. Nos. / area;
e. Wt. / area

21168.

Is it Possible to achieve ‘zero population growth rate? If yes, what kind of age pyramid is obtained?​

Answer»

Yes. An inverted bell-shaped age pyramid is obtained. The young of pre-reproductive age group individuals are less in number and both pre-reproductive and reproductive stages are in the same level

21169.

Embryo sacs of some apomictic species appear normal but contain diploid cells. Suggest a suitable explanation for the condition.

Answer»

It is true that many apomicts posses normal looking embryo sacs. The only possibility of the embryo sac possessing diploid cells is due to failure of meiotic division at the megaspore mother cell stage. Since, the megaspore mother cell has a diploid nucleus, if it undergoes mitosis instead of meiosis, all the resulting nuclei and cells will be diploid in nature.

21170.

Is it Possible to achieve ‘zero population growth rate? If yes, what kind of age pyramid is obtained?

Answer»

Yes. An inverted bell-shaped age pyramid is obtained. The young of pre-reproductive age group individuals are less in number and both pre-reproductive and reproductive stages are in the same level

21171.

Which of the following mouthparts of the cockroach is found in a pair and performs mastication ?A. B. C. D.

Answer» Correct Answer - C
21172.

Embryo sacs of some apomictic species appear normal but contain diploid cells. Suggest a suitable explanation for the condition.​

Answer»

It is true that many apomicts posses normal looking embryo sacs. The only possibility of the embryo sac possessing diploid cells is due to failure of meiotic division at the megaspore mother cell stage. Since the megaspore mother cell has a diploid nucleus, if it undergoes mitosis instead of meiosis, all the resulting nuclei and cells will be diploid in nature.

21173.

During ovulation, the ovum is released from the ovary directly into the,

Answer»

secondary oocyte

21174.

Wolffian duct is also known as,

Answer»

mesonephric duct

21175.

Wolffian is also known as,

Answer»

The Wolffian also known as an archinephric.

21176.

Read the following passage carefully and on the basis of your reading answer the questions given below it :Sardar Patel was a strict man. People call him the ‘Iron Man of India’. He was, no doubt, an iron man in the sense that he was an efficient administrator. But as a man to those who had the good fortune of coming into close contact with him, he was kind and gentle. At times, he even became emotional, when his personal friends and followers were concerned. However, it goes without saying that the Sardar had the great skill for organising affairs. He knew the art of selecting proper men for proper posts. Once he judged the man and found him correct, he trusted him fully and got him to do anything he wanted.1. What was the main quality of Sardar Patel?2. Why do people call him ‘The Iron Man of India’?3. When did he become emotional?4. How do you know that the Sardar Patel had the great skill of organising affairs?5. Explain the italicized words in the passage.6. Give a suitable title to the above passage.

Answer»

1. The main quality of Sardar Patel was his capacity of efficient administration.
2. People call Sardar Patel ‘The Iron Man of India’ because he was a strict man and had an efficiency of managing the affairs well.
3. Sardar Patel became emotional particularly when his personal friends and followers were concerned.
4. It is well-known that Sardar Patel was an excellent administrator and he knew the art of selecting proper men for proper posts.
5. Emotional – sentimental, full of strong feelings. Concerned – the matter related to someone.
6. Sardar Patel – The Iron Man of India.

21177.

What is the LCM of the polynomial x2 – 13x – 30, x2 – 8x – 105 and x2 + 9x + 14?1. (x +5)(x + 7)(x – 15)2. (x +7)(x + 2)(x – 15)3. (x +7)(x + 2)4. (x + 2)(x – 15)

Answer» Correct Answer - Option 2 : (x +7)(x + 2)(x – 15)

Concept used:

LCM is the least number which is divisible by every given number.

Calculation:

Our first polynomial is x2 – 13x – 30

⇒ x2 – 15x + 2x – 30

⇒ (x – 15)(x + 2)

Our second polynomial is x– 8x – 105

⇒ x– 15x + 7x – 105

⇒ (x – 15)(x + 7)

Our third polynomial is x2 + 9x + 14

⇒ x2 + 7x + 2x + 14

⇒ (x + 7)(x + 2)

LCM = (x + 7)(x + 2)(x – 15)

∴ The LCM of the required polynomial is (x + 7)(x + 2)(x – 15)

21178.

Find the HCF of 84 and 105?1. 222. 213. 234. 31

Answer» Correct Answer - Option 2 : 21

Calculation:

84 = 2 × 2 × 3 × 7

105 = 3 × 5 × 7

HCF = 3 × 7

⇒ 21

∴ The HCF of 84 and 105 is 21

21179.

Why does a gas not have a unique value of specific heat?

Answer»

This is because a gas can be heated under different conditions of pressure and volume. The amount of heat required to raise the temperature of unit mass through unit degree is different under different conditions of heating.

21180.

Give one argument in favour of the fact that frictional force is a non conservative force?

Answer»

The direction of the frictional force is opposite to the direction of motion. When a body is moved, say from A to B and then back to A, work is required to be done both during forward and backward motion. So, the net workidone in a round trip is not zero. Hence, the frictional force is a non-conservative force.

21181.

A particle is moving along a circular track of radius lm with uniform speed. What is the ratio of the distance covered and the displacement in half revolution?

Answer»

Distance covered by a particle = π × 1 = πm 

Displacement covered by a particle = 2 × 1 = 2m 

Ratio between distance and displacement

21182.

The dimensional formula of planck’s constant is ………(a) [M L2 T-1] (b) [M L2 T-3] (c) [M L T1] (d) [M L3T-3]

Answer»

Correct answer is  (a) [M L2 T-1

21183.

“ A healthy environment is a positive work environment”. Write any four ways by which a teacher can create healthy environment in her class.

Answer»

Four ways by which a teacher can create healthy environment in the class:

1. Paying adequate attention to the individual students needs 

2. Building a positive work climate 

3. Motivating students 

4. Being fair and treating all students equally 

21184.

Advertisements are everywhere, from columns of small __1__ advertisements for houses, jobs cars etc. in newspapers to big __2__ on walls and enormous advertisements on __3__ by the side of the road. The job of the advertising __4__ is to __5__ the products of the firms who employ them. They design eye- __6__ advertisements and make television __7__ to __8__ us to buy, buy, buy. 1. A) classical B) class C) classified D) classic 2. A) hostels B) posters C) commercials D) agencies 3. A) hoardings B) commercials C) hostels D) agencies 4. A) centers B) agencies C) commercials D) agents 5. A) produce B) stick C) classify D) publicize 6. A) persuading B) keeping C) holding D) catching 7. A) classicals B) agencies C) commercials D) documentaries 8. A) persuade B) refuse C) accept D) publicize

Answer»

1- C) classified

2- B) posters

3- A) hoardings

4- B) agencies

5- D) publicize

6- D) catching

7- C) commercials

8-A) persuade

21185.

Read the passage given below.I Research from the Publishers Association has shown that films based on books take 44% more at the box office revenue in the UK and 53% more worldwide than original screenplays. The report explores what impact a book has when adapted for film and TV.II. The report reads: “Published material is the basis of 52% of top UK films in the last 10 years, and accounts for an even higher share of revenue from these leading performers, at 61% of UK box office gross and 65% of worldwide gross.” The Hollywood adaptation of“My Cousin Rachel” was shown to have a significant impact on the sales of the Daphne Du Maurier thriller. The sales of the book in 2017 alone accounted for 23% of all sales since 1992.III. The research suggests that adapted films tend to perform better, because films can “leverage the popularity” of well-known books through an existing audience. Films adapted from books also tend to have a richer, more fully-developed story to draw on. In terms of TV adaptation, it was revealed that a quarter of dramas were based on literary sources and attracted a 56% larger share of the audience than those based on original scripts. Fourteen of the 35 high end series produced in the UK in the period between January and September 2017 were based on books, compared to seven based on true stories or historical events and five based on pre-existing films or TV stories.IV. In the case of the 2016 BBC broadcast of “The Night Manager”, research revealed that while the novel was in circulation for over 25 years, 82% of the copies it sold were in 2016 and 2017. Sales of the paperback edition remained strong in 2017 even after theseries went off the air.V. In conclusion, the report states that “there is a strong two-way relationship between publishing and the wider creative economy, wherein a successful adaptation often has spill-over effects and gives a substantial boost to the sales of the original book.” (338 words)Based on your understanding of the passage, answer the questions by choosing the correct option.(1) The purpose of the research by Publishers Association was to study the_____. Choose the correct option. A. variety in films and TV shows. B. impact of films on books. C. choice of books for film-making. D. connect between books and films.(2) Select the option that is true for the two statements given below. (1) The revenues generated at the box office have increased. (2) Majority of the top films in the UK are based on published material. A. (1) is the result of (2). B. (1) is the reason for (2). C. (1) is independent of (2). D. (1) contradicts (2).(3) Select the option that gives the correct meaning of the following statement. “The sales of the book in 2017 alone accounted for 23% of all sales since 1992.”A. There were 23% higher sales in 2017 than previous years. B. A major chunk of sales happened in 2017. C. The sales were limited to 23% in 2017. D. There were very few books sold in the previous years.(4) According to the research, the films based on books have greater success because____. A. people like to see the characters from the books on screen. B. the films get the advantage of the fame of the books. C. it takes less effort for people to watch films than read books. D. the films get a ready-made script from the books.(5) Select the option listing what the given sentence refers to. ‘Films adapted from books also tend to have a richer, more fully-developed story to draw on.’ (1) The plot and the storyline of such films are better. (2) The characters are likely to be more vivid. (3) The production of such films is meant for the rich and famous. (4) The settings and costumes are adapted from the book. (5) The making of such films require the author to write a sequel.A. (1), (3) and (4) B. (2), (3) and (5) C. (1), (2) and (5) D. (1), (2) and (4)(6) On what from the following were the maximum TV serials in UK in the year 2017 based? A. books. B. historical stories. C. original true stories. D. previous films.(7) This passage lists an example proving that TV dramas based on literary works have_______. Select the correct option. A. increased the immediate sales of the book B. increased the sales of the book during the first screening C. had no immediate impact on the sales of the book D. had very little impact on the sales of the book(8) Choose the correct option to answer the following: According to paragraph V, ‘there is a two-way relationship between books and the screen’. This is so because both A. revolve around the same stories. B. cater to an audience with the same taste. C. gain from each other’s popularity. D. belong to the creative field.

Answer»

(1) D. connect between books and films.

(2) A. (1) is the result of (2).

(3) B. A major chunk of sales took place in the year 2017.

(4) B. the films get advantage of the fame of books.

(5) D. (1), (2) and (4)

(6) A. books.

(7) A. increased the immediate sales of the book.

(8) C. gain from each other’s popularity.

(1) Impact of films on books.

(2) A. (1) is the result of (2).

(3) B. A major chunk of sales took place in the year 2017.

(4) B. the films get the advantage of the fame of books.

(5) D. (1), (2) and (5)

(6) A. books.

(7) A. increased the sales of the book during the first screening.

(8) C. gain from each other’s popularity.
21186.

What two skills should Sudha possess to work as an early child care professional?

Answer»

Two skills an early childhood professional needs to have are

  1. An interest in children and their development 
  2. Knowledge about the needs and capabilities of young children
  3. Capacity and motivation for interacting with children
21187.

Elements of Design are the tools of the Art. These are colour, texture, and line, shape or form. Colour is all around us in many forms. The identity of the product is most often attributed to colour. Everyone responds to colour and has definite preferences. Colour reflects the season, events and the spirit of people. The choice is affected by culture, tradition, climate, season, occasion or purely personal reason. Colour is an important part of Fashion. Designers carefully choose fabric colours to make a definite statement. Colour can be seen in fabrics in various design forms. Some fabrics may have one uniform solid colour, while the colour follows the yarn interlacing in others or may be colored in other patterns.1. Which word can be used for brightness of a colour? a) Valueb) Intensity c) Hue d) Complementary2. Colours are said to be contrasting if they are _____________.a) Different in lightness and darkness b) Light in value c) Dark in value d) Bright and intense3. Yellow-orange, red-orange, and yellow-green are examples of_______. a) Intermediate or Tertiary colour b) Secondary colour c) Primary colour d) Triadic colour4. Which of the following visual elements is concerned with the shade of a colour? a) Line b) Texture c) Value d) Size5. When white colour is added to any other colour it is called as_____________ of a colour. a) Shade b) Tone c) Tint d) Hue

Answer»

1. b) Intensity

2. a) Different in lightness and darkness

3. a) Intermediate or Tertiary colours

4. c) Value

5. c) Tint

21188.

Malnutrition is the underlying cause of at least 50 per cent of deaths of children under five years of age. The statistics for nutrition-related problems in our country reveal an alarming situation: Almost one-third of the infants born in India are low birth weight babies. Low birth weight may have adverse effects throughout their growing years and may have adverse implications even in adult life. Low birth weight may even lead to child mortality. There is widespread prevalence of growth retardation among preschoolers (from socio-economically disadvantaged families) and almost half the children suffer from mild and moderate under nutrition.A large proportion of children (and adults) suffers from micro-nutrient deficiencies in varying degrees of severity. The micro-nutrients of most concern are iron, zinc, vitamin A, iodine, folic acid, B12.1. Micro nutrient deficiencies are referred asa) Goitre b) Hidden Hunger c) Protein energy malnutrition d) Anemia2. Which of the following is immediate cause of under nutrition?a) Inadequate dietary intake b) Inadequate education c) Inadequate health services d) Poor sanitation and hygiene3. When the height of the child is less than adequate for age, this is termed asa) Underweight b) Stunting c) Wasting d) Protein energy malnutrition4. Which of the following is incorrect statementa) Enlarged thyroid known as goiter is the most common manifestation of iodine deficiency. b) Hemoglobin is required for carrying oxygen in the body. c) Due to Vitamin A deficiency growth of children are adversely affected. d) Protein deficiency is called as marasmu

Answer»

1. b) Hidden Hunger

2. a) Inadequate dietary intake

3. b) Stunting

4. d) Protein deficiency is called as marasmus

21189.

Read the given extract to attempt questions that follow:The tall girl with her weighed-down head. The paperseeming boy, with rat’s eyes. The stunted, unlucky heir Of twisted bones, reciting a father’s gnarled disease, His lesson, from his desk. At back of the dim class One unnoted, sweet and young. His eyes live in a dream…(i) The poet draws attention to the problem of while describing the boy as paper-seeming. A. malnutrition B. untidiness C. isolation 13 D. abandonment(ii) Which option has the underlined phrase that applies the poetic device used for ‘rat’s eyes’? A. He shut up like a clam when interrogated. B. She runs a as swift as a gazelle.C. He is considered the black sheep of the family. D. She ran away chattering with fear.(iii) Select the correct option to fill the blank. The tall girl’s head is weighed down due to the_____. A. effect of diseases B. need for concentration C. desire to remain unnoticed D. burdens of poverty(iv) The literal meaning of ‘reciting’ refers to delivering the lesson aloud. What does its figurativemeaning refer to? A. Showing extra interest in the lesson. B. Carrying his father’s disease. C. Resigning to his disease and condition. D. Voicing the poor conditions, he lives in.(v) How does the ‘unnoted’ pupil present a contrast to others? A. He appears to be in a world of dreams. B. He struggles with the fulfilment of dreams. C. He seems taller than most. D. He sits in the dimmest part of the classroom.

Answer»

(i) A. malnutrition 

(ii) C. He is considered the black sheep of the family. 

(iii) D. burdens of poverty 

(iv) B. Carrying his father’s disease 

(v) A. He appears to be in a world of dreams.

21190.

The Glycine content of a protein is 0.3% what is the minimum mass of protein [Molecular weight of Glycine = 75]

Answer»

0.3 g is present in 100 g.

1 g is present in 100/0.3 g.

75 g is present in 100/0.3 x 75 = 25000.

21191.

The problem was with the battery _______ a dead cell. A) that has B) which had C) who had D) in which has

Answer»

Correct option is B) which had

21192.

Neron, _______ was Emperor of Rome, from 45 to 68 A.D, is believed to have murdered both his mother and his wife. A) whom B) whose C) who D) that

Answer»

Correct option is C) who

21193.

The building where you can go and watch the latest blockbuster film is called a

Answer»

Correct answer is movie theatre or cinema

21194.

A place where you can go to see many different kinds of fish swimming is called an ___.

Answer»

Correct answer is aquarium

21195.

Concentrated nitric acid used in the laboratory work is `68%` nitric acid by mass in aqueous solution. What should be the molaritiy of such a sample of the acid if the density of solution is `1.504 g mL^(-1)`?

Answer» Correct Answer - `16.23M`
`68%` by mass that `68g` of `HNO_(3)` is present in `100g` of solution.
Volume of solution `=(Mass of solution )/(Density of solution )`
`=(100g)/(1.50gmL^(-1))=66.5cm^(3)=0.65L`
Molar mass, `Mw_(B)` of `HNO_(3)=1+14+48=63`
Molarity`=(W_(A))/(Mw_(B)xxV)`
`=(68g)/(63g mol^(-1)xx0.0665)=16.23M`
21196.

The osmotic pressure exerted by a solution prepared by dissolving 2.0 g of protein of molar mass 60 kg mol–1 in 200 mL of water at 27°C is _______ Pa. [integer value] (use R = 0.083 L bar mol–1 K –1 )

Answer»

π = iCRT

\(\frac{1\times2}{60000\times0.2}\times0.083\times300\)

= 0.00415 bar (\(\because\) 1 bar  = 105 Pa)

So, 0.00415 x 105 Pa = 415 Pa

21197.

Define the following terms `:` `a.` Mole fraction `b.` Molality `c.` Molarity `d. Mass percentage.

Answer» Refer `"` Overview `"` point 25, CHMapter
21198.

Suppose a solide solution is formed between two substances, one whose particles are very large and the other whose particles are very small. What kind of solide solution is this likely to be ?

Answer» Interstitial solide solution.
21199.

Define the term solution. How many types of solutions are formed ? Write briefly about eaCHM type with an example.

Answer» Correct Answer - Refer text.
21200.

In the figure, a very large plane sheet of positive charge is shown. P1and P2 are two points at distance l and 2l from the charge distribution. If σ is the surface charge density, then the magnitude of electric fields E1 and E2 at P1 and P2 respectively are:(A) E1 = σ/ε0, E2 = σ/2ε0(B) E1 = 2σ/ε0, E2 = σ/ε0(C) E1 = E2 = σ/2ε0(D) E1 = E2 = σ/ε0

Answer»

Correct option is (C) E1 = E2 = σ/2ε0

As the sheet is very large \(\vec E\) is independent of distance from it.

Thus E1 = E2 = \(\frac{\sigma}{2\varepsilon_0}\)