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Kerala State Board New Syllabus Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations.

Kerala Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations

we have studied linear equations in one and two variables and quadratic equations in one variable. We have seen that the equation x² + 1 = 0 has no real solution since the root of a negative number does not exist in a real number. So, we need to extend the real number system to a larger number system to accommodate such numbers.

I. Complex Numbers
A number of the form a + ib, where a and b are real numbers and i = √-1.
Usually, a complex number is denoted by z, a is the real part of z denoted by Re(z) and b is the imaginary part of z denoted by Im(z).

II. Algebra of Complex Numbers

Addition: Let z₁ = a + ib and z₂ = c + id be two complex numbers. Then the sum z₁ + z₂ is obtained by adding the real and imaginary parts.

1. z₁ + z₂ = z₂ + z₁, commutative.
2. z₁ + (z₂ + z₃) = (z₁ + z₂) + z₃, associative.
3. 0 + i0 is the identity element.
4. -z is the inverse of z.

Multiplication: Let z₁ = a + ib and z₂ = c + id be two complex numbers.
Then the product z₁z₂ is defined as follows:
z₁z₂ = (ac – bd) + i(ad + bc).

1. z₁z₂ = z₂z₁, commutative.
2. z₁(z₂z₃) = (z₁z₂)z₃, associative.
3. 1 + i0 is the identity element.
4. \(\frac{1}{z}\) is the inverse of z.
5. z₁(z₂ + z₃) = z₁z₂ + z₁z₃, distributive law.

Power of ‘i’: i³ = -i, i⁴ = 1
In general i^4k = 1, i^4k+1 = i, i^4k+2 = -1, i^4k+3 = -i

Identities:

The Modulus and Conjugate of a complex number:
Consider a complex number z = a + ib . Then, the conjugate of z is denoted by \(\bar{z}\), defined as \(\bar{z}\) = a – ib and the modulus of z is denoted by |z|, defined as \(\sqrt{a^{2}+b^{2}}\).

Properties:

III. Representation of Complex Number

Argand Plane:

A complex number z = a + ib which corresponds to the ordered pair (a, b) can be represented geometrically as the unique point P(a, b) in the XY-plane, where the real part is taken along the x-axis and the imaginary part along the y-axis. Such a plane is called the Argand Plane or Complex plane.

Polar Form:

Let the point P represent the non-zero complex number z = x + iy. Let the directed line segment OP be of length ‘r’ and be the angle which OP makes with the positive direction of the x-axis. Then, P is determined by the unique ordered pair of a real number (r, θ) called polar coordinate of the point P, where x = r cos θ, y = r sin θ and therefore the polar form of z can be represented as z = r(cos θ + i sin θ).
The principle argument of z is value ‘θ’ such that -x ≤ θ ≤ π, denoted by arg z.
To find the principle argument, we find tan α = |\(\frac{y}{x}\)|, 0 ≤ α ≤ \(\frac{\pi}{2}\)

The quadrant on which ‘P’ lies	arg z =
I	α
II	π – α
III	α – π
IV	-α
Positive real axis	0
Negative real axis	π
Positive imaginary axis	\(\frac{\pi}{2}\)
Negative imaginary axis	\(-\frac{\pi}{2}\)

Kerala State Board New Syllabus Plus One Maths Notes Chapter 4 Principle of Mathematical Induction.

Kerala Plus One Maths Notes Chapter 4 Principle of Mathematical Induction

Induction means the generalization from a particular case or facts. In contrast to deductive reasoning, inductive depends on working with each case and developing a conjecture by observing incidences till we have observed each and every case. In algebra or in another discipline of mathematics, there are certain results or statements that are formulated in terms of n, where n is a positive integer. To such statements, the well-suited principle that is based on the specific technique is known as the principle of mathematical induction.

The Principle of Mathematical Induction:
Suppose there is a statement P(n) involving the natural number n such that

1. The statement is true for n = 1, i.e; P(1) is true, and

2. If the statement is true for n = k (where k is some positive integer), then the statement is also true for n = k + 1, i.e; the truth of P(k) implies the truth of P(k+1). Then, P(n) is true for all natural numbers n.

Students can Download Chapter 4 Poverty Notes, Plus One Economics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Economics Notes Chapter 4 Poverty

Poverty and Poverty Line
Poverty is a multi-dimensional concept. It is defined as a situation in which a section of society is unable to fulfill even the basic necessities of life or deprived of basic necessities of life. Poverty is measured on the basis of the poverty line. One way is to determine it by the monetary value (per capita expenditure) of the minimum calorie intake that was estimated at 2,400 calories for a rural person and 2,100 for a person in the urban area.

Causes of Poverty
Important causes of poverty in India are:

• Low income
• Lack of assets
• Unemployment
• Inequality
• Exploitation
• Population explosion
• Undesirable economic growth
• Inflation
• Absence of industrialisation.

Poverty Eradication Programmes
Poverty eradication programmes in India are classified as follows:

Self-employment Programmes
Integrated Rural Development Programme (IRDP): The IRDP was introduced in 2nd October 1980. This programme has been renamed as
Swarnajayanthi Grama Swarojgar Yojana (SGSY) from 1st April 1999. The SGSY is a very holistic programme compared to IRDP. SGSY is developed by merging various programmes such as TRYSEM (Training of Rural Youth for Self-employment), DWCRA (Development of Women and Children in Rural Areas), GKY (Ganga Kalyan Yojana), MSW (Million Well Scheme), and SITRA (Supply of Improved Tool Kits to Rural Artisans). It forms SHG’s (Self-Help Groups) of poor people and formulates self-employment programmes under their leadership. It includes development of infrastructure, technology, credit and marketing managements, etc. Unlike other programmes, the priority of the employment programme can be fixed by the beneficiaries.

Wage Employment Programmes
1. National Rural Emptoyment Programme (NREP): NREP was the new name given to Food for Work Programme. It was launched in 1980 as a centrally sponsored scheme with state and central governments sharing equal amounts. The aim of this programmer the development of community assets like drinking water wells, irrigation wells, rural roads, schools, etc.

2. The Rural Landless Employment Guarantee Programme (RLEGP): This programme was launched on 15th August 1983 to supplement NREP. This is a centrally sponsored scheme with 100 percent fund by the union government.

3. Jawahar Rozgar Yojana (JRY) and Nehru Rozgar Yojana (NRY): NREP and the RLEGP were merged and renamed into a single rural employment programme known as Jawahar Rozgar Yojana. JRY came into effect from 1st April 1999. The aim of the programme was to provide gainful employment for unemployed rural areas. The urban version of JRY is known as Nehru Rozgar Yojana (NRY).

4. The Million Well Scheme (MWS) was to provide open irrigation well, free of cost, to poor small and marginal farmers belonging to SC/ST category.

5. Indira Awas Yojana (IAY) was introduced for providing houses, free of cost to SC/ST families. Now this facility is extended to other poor families too.

6. Pradan Manthri Gramodaya Yojana: Gramin Awas (PMRY)
The PMRY: GAwas launched on 1st April, 2000. The programme aims at providing the housing needs of the rural people.

7. National Rural Employment Guarantee Programme (NREGP) 2005: In August 2005, the Parliament has passed a new Act known as National Rural Employment Guarantee Act 2005. The act provides guaranteed wage employment to every household whose adult volunteer is to do unskilled manual work for a minimum of 100 days in a year. Thj act came into force from 2nd February 2006 and implemented in India’s 200 most backward districts. Later on it was extended to all over the country in two phases. The programme was later on renamed as Mahatma Gandhi National Rural Employment Guarantee Programme (MGNREGP) or commonly called Employment Assurance Scheme.

Social Security Programmes: There are not many programmes for the social security of the poor. However, there are some centrally sponsored schemes. They are as follows:

• Old-age pension for the elderly who are without support.
• Financial support in the event of the death of the breadwinner.
• Support for women of poor households on pregnancy.

Food Security Programmes: It is essential to ensure food security to the masses. As we know, though there js sufficient production of food grains, millions of people are starving in the country. The problem is mainly of distribution. To overcome these several measures are taken by the government. They are as follows:

1. Public distribution system (PDS): Foodgrains are made available at cheaper prices and distributed through Fair Price Shops, ration shops, Maveli Stores, Neethi Stores etc.

2. Targeted Public Distribution System (TPDS): The TPDS initiated in June 1997 aims at ensuring the availability of food grains to BPL families.

3. Integrated Child Development Schemes (ICDS): A nutrition programme meant for children below 6 years of age, pregnant and lactating women.

4. Mid-day Meal at School: Mid-day Meal at School is in operation in several states. The programme was launched in all India level on 15th August 1995.

5. Annapurna Scheme: This programme was commenced from 2000-01. Poor old people who are not getting old-age pensions are covered under this scheme.

6. Antyodaya Anna Yojana: This scheme is launched for the poorest of the poor. Under this scheme, food grains are made available to very poor families at a highly subsidised price.

Students can Download Chapter 3 Liberalisation, Privatisation and Globalisation – An Appraisal Notes, Plus One Economics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Economics Notes Chapter 3 Liberalisation, Privatisation and Globalisation – An Appraisal

Background of the economic reforms
India introduced economic reforms in 1991. It was due to several reasons. Important among them are:

• Policies such as MRTP and FEMA prevented large scale domestic and foreign investments.
• Reserving certain sectors exclusively for the public sector prevented private investment less attractive for such sectors.
• Gulf war and subsequent events created a severe foreign exchange crisis in our country.
• Import bill of petroleum products increased alarmingly leading to BoP deficit.
• Political instability.

Liberalisation
Liberalization implies liberating trade from unwanted government controls and restrictions. Indian economy prior to the nineties was following a restrictive policy and excessive government interferences in all economic activities. This interference created the license-permit-raj as indicated earlier. This has led to extensive corruption, red-tapism, undue delay, and inefficiency. Most of the policies such as the licensing system, FERA, MRTP hindered economic growth, and industrialisation. The aim of the liberalization policy was very comprehensive, promoting economic growth by reducing factors hindering it and makes the economy very competitive at international standards.

Liberalisation policies included reforms in the following sectors.

• Industrial sector reforms
• Financial sector reforms
• Tax reforms
• Foreign exchange reforms

Privatisation
Privatisation refers to any process that reduces the participation of the state/public sector in the economic activities of a country. In other words, the conversion of ownership or management of a government-owned enterprise into a private enterprise is known as privatization or denationalization. India started privatization as part of the Structural Adjustment Programme (SAP). The process of privatisation can take place either by the withdrawal of government ownership and management of public sector companies or by the outright sale of public sector companies (disinvestment).

Aims of disinvestment:

1. Better performance of public sector units (PSUs) through better management techniques
2. Enforcing financial discipline and improving financial performance
3. Enhancing the ability of companies to raise financial resources from the market
4. Raising revenue of the government from sale of equity
5. A strong impetus to the flow of FOI (Foreign Direct Investment)

Globalisation
Globalisation is a complex phenomenon. The term globalisation indicates the opening up of domestic economy for the world market, or integration of an economy with global economy. It involves creation of network and activities transcending economic, social and geographical boundaries. It attempts to establish links in such a way that the happening in India can be influenced by events happening miles away. Integration of economies is possible through interlinking domestic market with world market through foreign trade. Therefore, it is treated as a very complex phenomenon.

Outsourcing
Outsourcing is an important feature of globalisation. It is practice where a company hires regular service from external sources mostly from other countries which previously provided internally or within the country.

World Trade Organisation (WTO)
WTO was founded in 1995 replacing GATT. GATT was established in 1948. Following are the aims of WTO.

• Provides equal opportunities to all participating nations in international trade.
• To ensure optimum utilization of world resources and protect the environment.
• Remove of tariffs (tax) and non-tariffs (quota). This leads to the removal of restrictions on trade thereby facilitating free-entry and free exit of goods
• To encourage multi-lateral trade (more than two nations) rather than bilateral trade (two countries).
• Extension of a trade by including trade in services like banking, insurance communication.
• To include Trade-Related Intellectual Property Rights (TRIPs), commonly known as Patent Rights and Trade-Related Investment Measures (TRIMs) within the span of international trade.

Students can Download Chapter 2 Indian Economy 1950-1990 Notes, Plus One Economics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Economics Notes Chapter 2 Indian Economy 1950-1990

The Goals of Five Year Plans
A plan should have some clearly specified goals. The goals of the five-year plans are growth, modernization, self-reliance, and equity. This does not mean that all the plans have given equal importance to all these goals. Let us now learn about the goals of planning in some detail.

1. Growth: It refers to an increase in the country’s capacity to produce the output of goods and services within the country. It implies either a larger stock of productive capital, or a larger size of supporting services like transport and banking, or an increase in the efficiency of productive capital and services. A good indicator of economic growth, in the language of economics, is a steady increase in the Gross Domestic Product (GDP).

2. Modernization: To increase the production of goods and services the producers have to adopt new technology Adoption of new technology is called modernization.

3. Self-reliance: A nation can promote economic growth and modernization by using its own resources or by using resources imported from other nations. The first seven five-year plans gave importance to self-reliance which means avoiding imports of those goods which could be produced in India itself. This policy was considered a necessity in order to reduce our dependence on foreign countries, especially for food. It is understandable that people who were recently freed from foreign domination should give importance to self-reliance.

4. Equity: Now growth, modernization, and self-reliance, by themselves, may not improve the kind of life which people are living. A country can have high growth; the most modem technology developed in the country itself.

Agriculture
Land reforms and the green revolution were the two important changes in India’s agricultural sector during the initial periods of independence.

Land Reforms: The purpose of land reforms is twofold. On the one hand, it aims to make rational use of the scarce land resource by enforcing conditions on holding land. Secondly, it aims at the redistribution of land in favour of landless farmers.
Land reform consists of the following measures:

1. Abolition of intermediaries like Zamindars
2. Tenancy reforms, ie. regulation of rent, the security of tenure, etc.
3. Ceiling of landholding
4. Distribution of land among landless by acquiring surplus land from big landlords
5. Consolidation of holding and prevention of subdivision and fragmentation
6. Organization of cooperative farming

The policy decisions and legislative initiatives of the government on land reforms were very progressive. As a result of it, tillers were able to undertake the permanent improvement of their land and this contributed to growth in agriculture. However, the implementation of land reforms was not free from limitations. Some loopholes in the law were conveniently exploited by the landlords and transferred surplus land in the name of their relatives or binamies. But states like Kerala and West Bengal implemented the land reform measures in a relatively successful way.

The Green Revolution: Planners and policymakers of independent India gave top priority to the development of agriculture. In the 1960s the new technology in agriculture was tried in seven districts and was called the Intensive Agricultural Districts Programme (IADP). Later, the High Yielding Varieties Programme (HYVP) “was extended to the entire country, which is popularly known as Green Revolution or modem agricultural technology, seed fertilizer water technology. Norman Borlaug, an American Biologist was known as the father of the green revolution. Prof. M.S. Swaminathan is known as the father of the green revolution in India.
Features of the green revolution are:

1. Use of high yielding variety (HYV) seeds
2. Use of chemical fertilizers and pesticides
3. Use of modem farm implements like power tillers, tractors, water pump sets, etc.
4. Better irrigation facilities
5. Easy availability of credit to farmers at lower interest rates

Industry and Trade
Economic growth and development depend upon industry and trade. The industry provides employment. In order to promote the industrial sector government introduced industrial policies.

Industrial Policy Resolution 1956 (IPR-1956)
To mould the economy into a socialist pattern, where the state ‘holds the commanding heights’ the Industrial Policy Resolution of 1956 (IPR1956) was adopted. This resolution classified industries into three categories:

1. Industries exclusively owned by the state.
2. Industries in which the private sector could supplement the efforts of the state.
3. Remaining industries were to be in the private sector. But they will be kept under state control through a system of licenses.

Small Scale Industries
Small scale industries are crucial for economic development. A small scale industry is defined with the reference to the maximum investment allowed to set up a unit. This limit of investment has changed over a period of time. In 1950 a small-scale industry unit was one which invests a maximum of rupees five lakhs, in 1966 it was raised to rupees 7.5 lakhs, in 1990 it was raised to rupees 60 lakhs and from 2000 it has been fixed at rupees one crore.
Small scale industries have the following advantages:

1. Less capital investment
2. Labour intensive technology – generates more employment opportunities
3. Less dependence on imports
4. Less pollution-environment friendly
5. Rural development

Import Substitution
The practice of replacing imports with the products made within the country is known as import substitution. The government allowed a policy of protection in order to protect domestic industries.

Students can Download Chapter 1 Indian Economy on the Eve of Independence Notes, Plus One Economics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Economics Notes Chapter 1 Indian Economy on the Eve of Independence

Low level of economic development under the colonial rule:
The British rule started in India in 1757 and came to an end in 1947. The Indian economy underwent rapid changes under British rule. The economic policies pursued by the colonial government in India were concerned more with the protection and promotion of the economic interests of their home country than the development of the Indian economy. The twin objectives of British rule in India were

1. To use India as a supplier of raw materials for British Industries.
2. To convert India into a market for the finished products produced in Britain.

Agricultural Sector:
Agricultural Sector was the backbone of the Indian economy.
During the British colonial rule India remained fundamentally an agrarian economy. Around eighty percent of India’s population lived in villages. Agriculture was stagnant and it was the main source of livelihood of the population. People depended directly or indirectly on agriculture and its productivity was very slow. The agricultural sector stagnated during British rule.
Major reasons for agricultural stagnation were:

1. The exploitative land settlement system followed by British rulers
2. Use of low level of technology
3. Rural indebtedness
4. Low agricultural productivity
5. Use of limited chemical fertilizer
6. Inadequate irrigation facilities

Industrial Sector:
India’s industrial sector could not make progress during British rule. Their aim was to collect raw materials from India and sell their final products in India.

By the second half of the nineteenth century, modem industry began to take root in India. Initially, cotton industries in Maharashtra and Gujarat (Bombay presidency) and the jute industry in Bengal were established. Then industries of fertilizers, rayon, rubber, cement, sugar, pepper, etc., were established in some regions of the country. The setting up of Tata Iron and Steel Company (TISCO) in 1907 was a landmark in the industrialization of India. Jemshedji Tata established TISCO in Jamshedpur in Bihar. During the British rule hardly any capital goods industries were established in the country.

Foreign Trade:
Though India exported value-added products before the British period, we started exporting primary products during their rule. Consequently, India became an exporter of primary products such as raw silk, cotton, wool, sugar, indigo, jute, etc. and an importer of finished consumer goods like cotton, silk and woollen clothes and capital goods like light machinery produced in the factories of Britain.
The most important characteristic of India’s foreign trade, throughout the colonial period was the generation of a large export surplus.

Demographic Condition:
Various details about the population of British India were first collected through a census in 1881. Through Suffering from certain limitations, it revealed the unevenness in India’s population growth. Subsequently, every ten years such census operations were carried out. Before 1921, India was in the first stage of demographic transition. The second stage of transition began after 1921.

Occupational Structure:
Occupational structure refers to the distribution of working persons across different industries and sectors. Broadly we divide occupations into three types. Agriculture, animal husbandry, forestry, fisheries, etc., are collectively known as ‘primary’ activities. Manufacturing industries, both small and large scale, are known as ‘secondary’ activities. Transport, communication, banking, financial services, etc., are ‘tertiary’ activities.

Infrastructure:
Infrastructural facilities developed in India during the British period. Infrastructure means some kind of permanent installation, which are used over a long period of time for the supply of basic inputs like railway lines, roads, dams, canal systems, power stations, pipelines, hospitals, educational institutions like schools, colleges, etc. Basic infrastructure facilities such as railways, ports, water transport, and telegraph did develop during the British rule. The real intention behind such a development was to serve the various colonial interests of Britain.

Students can Download Chapter 10 Respiration in Plants Notes, Plus One Botany Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Botany Notes Chapter 10 Respiration in Plants

How are respiration and photosynthesis-related?
Green plants and cyanobacteria can prepare their own food by the process of photosynthesis, they trap light energy and convert it into chemical energy that is stored in the bonds of carbohydrates (Macromolecules) like glucose, sucrose, and starch.
By Cellular respiration, food materials undergo breakdown that release energy and the trapping of this energy for the synthesis of ATP.

ATP is called the energy currency of the cell why?
ATP is broken down whenever (and wherever) energy needs to be utilised. Hence, ATP acts as the energy currency of the cell.

Seat of photosynthesis and respiration
Photosynthesis takes place within the chloroplasts whereas the breakdown of complex molecules to yield energy takes place in the cytoplasm and in the mitochondria (also only in eukaryotes).
The compounds that are oxidized during respiration are known as respiratory substrates.
Eg. Proteins, fats, and even organic acids.

Do Plants Breathe?
Plants require O₂ for respiration and give out CO₂ and H₂O as end products and release energy most of which is given out as heat.

Respiration is least important to plants than animals
Roots, stems, and leaves respire at rates far lower than animals When cells photosynthesize O₂ is released within the cell.
But some cells live where oxygen may or may not be available.
All living organisms retain the enzymatic machinery to partially oxidise glucose without the help of oxygen. This breakdown of glucose to pyruvic acid is called glycolysis.

Glycolysis
The term glycolysis -(Greek words, glycols for sugar, and lysis for splitting).
The scheme of glycolysis was given by Gustav Embden, Otto Meyerhof, and J. Parnas, Hence glycolysis is called an EMP pathway.
In anaerobic organisms, it is the only process in respiration.
Glycolysis occurs in the cytoplasm of the cell and is present in all living organisms.
In this process, Glucose undergoes partial oxidation to form two molecules of pyruvic acid.

Steps lead to end products of glycolysis

1. Glucose and fructose are phosphorylated to give rise to glucose-6-phosphate by the activity of the enzyme hexokinase.

2. This phosphorylated form of glucose then isomerises to produce fructose-6-phosphate.

3. In this pathway, ATP is utilised at two steps: first in the conversion of glucose into glucose 6-phosphate and second in the conversion of fructose 6-phosphate to fructose 1,6 diphosphate).

4. The fructose 1,6-diphosphate is split into dihydroxyacetone phosphate and 3 phosphoglyceraldehydes (PGAL). In this step NADH +H+ is formed from NAD+.

5. 3-phosphoglyceraldehyde (PGAL) is converted to 1,3 bisphosphoglycerate (DPGA).

6. The conversion of DPGA to 3-phosphoglyceric acid (PGA), is also an energy-yielding process; this energy is trapped by the formation of ATP.

7. 3-phosphoglyceric acid (PGA) is converted into 2 phosphoglycerates.

8. 2 phosphoglycerates are converted into 2 phosphoenol pyruvic acid. ATP is synthesized during the conversion of PEP to pyruvic acid.

9. 2 phosphoenol pyruvic acid undergoes dephosphorylation to form 2 molecule of pyruvic acid

The fate of pyruvic acid
It involves

1. Lactic acid fermentation
2. Alcoholic fermentation
3. Aaerobic respiration.

Fermentation takes place under anaerobic conditions in many prokaryotes and unicellular eukaryotes.

The complete oxidation of glucose to CO₂ and H₂O occurs in organisms that adopt Krebs’ cycle which is also called as aerobic respiration. This requires an O₂ supply.

Fermentation
In fermentation, glucose undergoes incomplete oxidation and forms CO₂ and ethanol
The enzymes, pyruvic acid decarboxylase, and alcohol dehydrogenase catalyze these reactions.
Fermentation occurs in the presence of yeast
Yeasts poison themselves to death when the concentration of alcohol reaches about 13 percent. Some organisms like bacteria produce lactic acid from pyruvic acid.

The lactic acid in eukaryotic cell
In animal muscle cells during exercise, when oxygen is inadequate for cellular respiration, pyruvic acid is reduced to lactic acid by lactate dehydrogenase.
The reducing agent is NADH+H* which is re oxidised to NAD+ in both the processes.
In both lactic acid and alcohol fermentation, less than seven percent of the energy in glucose is released.
In eukaryotes second step after glycolysis take place within the mitochondria and this requires O₂.
It is aerobic respiration leads to complete oxidation of carbohydrate in the presence of oxygen and releases CO₂, water and a large amount of energy.
This type of respiration is most common in higher organisms.

Aerobic Respiration
The second step of Aerobic respiration takes place within the mitochondria.
The product of glycolysis- pyruvate is transported from the cytoplasm into the mitochondria.

First step of oxidation of pyruvic acid
In the mitochondrial matrix, pyruvate undergoes oxidative decarboxylation by pyruvic dehydrogenase. The reactions require the participation of several coenzymes, including NAD+ and Coenzyme A.

During this process, two molecules of NADH are produced from the metabolism of two molecules of pyruvic acid.
The acetyl CoA then enters a cyclic pathway, tricarboxylic acid cycle(Krebs’ cycle) after the scientist Hans Krebs who first elucidated it.

Tricarboxylic Acid Cycle
The TCA cycle starts with the condensation of acetyl group with oxaloacetic acid (OAA) and water to yield citric acid.
The reaction is catalysed by the enzyme citrate synthase and a molecule of CoA is released.
It is followed by two successive steps of decarboxylation, leading to the formation of alpha-ketoglutaric acid and then succinyl-CoA. In the remaining steps, Succinic acid is oxidised to OAA.

Which step of the Krebs cycle substrate-level phosphorylation occurs?
During the conversion of succinyl-CoA to succinic acid, a molecule of GTP is synthesised. This is substrate-level phosphorylation.

At three sites in the cycle where NAD+ is reduced to NADH + H+ and one site where FAD+ is reduced to FADH₂.

In the mitochondrial matrix, pyruvate is broken down to release.
8 molecules of NADH + H+
2 molecules of FADH₂
2 molecules of GTP and
3 molecules of CO₂

Electron Transport System (ETS) and Oxidative Phosphorylation

The metabolic pathway through which the electron passes from one carrier to another is called the electron transport system (ETS).
It is present in the inner mitochondrial membrane.
Reduced coenzyme like NADH(complex) in the mitochondrial matrix is oxidised and release 2 electrons and 2protons
Electrons and protons are transferred to FMN, it reduced to FMNH2
It breaks and releases protons and electrons .protons go to intermembrane space but electrons reach ubiquinone.
Ubiquinone also receives reducing equivalents via FADH2 (complex II).
The reduced ubiquinone is then oxidised with the transfer of electrons to cytochrome c via cytochrome bc1 complex (complex III).

Electron Transport System (ETS)
Cytochrome c acts as a mobile carrier for the transfer of electrons between complex III and IV.
Complex IV refers to cytochrome c oxidase complex containing cytochromes a and a3.

Oxidation of one molecule of NADH gives rise to 3 molecules of ATP, while that of one molecule of FADH2 produces 2 molecules of ATP.
Oxygen acts as the final hydrogen acceptor.

Oxidative phosphorylation in mitochondria
In ETS the energy of oxidation-reduction is utilised for the production of proton gradient required for phosphorylation. This process is called oxidative phosphorylation.

Chemiosmosis (proposed by peter Mitchel)
The energy released during the electron transport system is utilised in synthesizing ATP with the help of ATP synthase (complex V) called chemiosmosis.

F1 – F0/exosomes
This complex consists of two major components, F1 and Fo.
The F1 headpiece is a site for synthesis of ATP from ADP and inorganic phosphate.
F0 is an integral membrane protein complex act as a channel through which protons cross the inner membrane.
For each ATP produced, 2H+ passes through F0 from the intermembrane space to the matrix down the electrochemical proton gradient.

The Respiratory Balance Sheet
How many ATP molecules are produced in Aerobic respiration?
In aerobic respiration, the number of ATP molecules produced or utilized in glycolysis, TCA cycle and ETS gives the net gain of 36 ATP molecules
Fermentation accounts for only a partial breakdown of glucose whereas in aerobic respiration it is completely degraded to CO₂ and H₂O.

How many ATP molecules are produced in Fermentation?
In fermentation there is a net gain of only two molecules of ATP for each molecule of glucose degraded NADH is oxidized to NAD+ rather slowly in fermentation.

Amphibolic Pathway
It involves two processes anabolism and catabolism.
For example, fats is broken down into glycerol and fatty acids. Then fatty acids degraded to acetyl CoA and enter the pathway.
Glycerol enters the pathway after being converted to PGAL.
The proteins are degraded by proteases and the individual amino acids enter the pathway at some stage within the Krebs’cycle as pyruvate or acetyl CoA.

Is it true both catabolism and anabolism occur in fat metabolism?
Fatty acids( substrate) are broken down to acetyl CoA before entering the respiratory pathway. But when the organism needs to synthesize fatty acids, acetyl CoA withdrawn from the respiratory pathway for it.
Hence, the respiratory pathway involves the breakdown and synthesis of fatty acids, i.e catabolism, and anabolism respectively. Hence it is considered as an amphibolic pathway.

Respiratory Quotient
Definition: The ratio of the volume of CO₂ evolved to the volume of O2 consumed in respiration is called the respiratory quotient (RQ) or respiratory ratio.

Respiratory quotient of some respiratory substrates
1. Carbohydrates: When carbohydrates are completely oxidised, the RQ is 1, because equal amounts of CO₂ and O₂ are evolved and consumed, respectively

2. Fats: If fats are used in respiration, the RQ is less than 1.

3. Proteins: When proteins are respiratory substrates the ratio is 0.9.

4. Organic acids: When organic acids are respiratory substrates, the ratio is more than one.

Students can Download Chapter 9 Photosynthesis in Higher Plants Notes, Plus One Botany Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Botany Notes Chapter 9 Photosynthesis in Higher Plants

What Do We Know?
Role of light, CO₂, H₂O, and Chlorophyll
Actually, chlorophyll (green pigment of the leaf), light, and CO₂ are required for photosynthesis. A variegated leaf ora leaf that was partially covered with black paper, and one that was exposed to light. On testing these leaves for starch it was clear that photosynthesis occurred only in the green parts of the leaves in the presence of light.

Half leaf experiment and the importance of CO₂ in photosynthesis
In this, a part of a leaf is enclosed in a test tube containing some KOH soaked cotton (which absorbs CO₂), while the other half is exposed to air. The set up is then placed in light for some time. Then conducted the starch test, showed that the exposed part of the leaf tested positive for starch while the portion that was in the tube, tested negative. This showed that CO₂ is required for photosynthesis.

Early Experiments

Historical aspects of photosynthesis
1. Priestley
He observed that a candle burning in a closed space – a bell jar, soon gets extinguished. Similarly, a mouse would soon suffocate in a closed space.

He concluded that a burning candle or an animal that breathes the air, both damage the air. But when he placed a mint plant in the same bell jar, he found that the mouse stayed alive and the candle continued to burn.

2. Jan Ingenhousz
He showed that sunlight is essential to the plant process that purifies the air fouled by burning candles or breathing animals. In aquatic habitat, during bright sunlight, small bubbles were formed around the green parts while in the dark they did not. Later he identified these bubbles are oxygen. So the green part of the plants could release oxygen.

3. Julius von Sachs
Glucose is usually stored as starch. He found that the green parts in plants where glucose is made.

4. T.W Engelmann
By using a prism he split light into its spectral components and then illuminated a green alga, Cladophora, placed in a suspension of aerobic bacteria. The bacteria were used to detect the sites of O₂ evolution. He observed that the bacteria accumulated mainly in the region of blue and red light of the split spectrum.

An empirical equation for photosynthesis

[CH₂O] represent a carbohydrate (e.g., glucose, a six-carbon sugar).

Hydrogen donor in bacteria and green plants
Some organisms do not release O₂ during photosynthesis
When H₂S, instead is the hydrogen donor for purple and green sulphur bacteria, the ‘oxidation’ product is sulphur or sulphate depending on the organism and not O₂. In the green plants, the O₂ evolved from H₂O, not from carbon dioxide.

The modern equation for photosynthesis

C₆H₁₂O₆ represents glucose. The O₂ released is from water

Where Does Photosynthesis Take Place?
It takes place in the chloroplast of leaves that contain grana, the stroma lamellae, and the fluid stroma.

Where is the energy production site in chloroplast?
The energy-rich molecules like ATP and NADPH are synthesized in grana and stroma lamellae by light reactions.

Where is the Glucose production site in chloroplast?
In stroma by dark reactions, CO₂ fixation leading to the synthesis of glucose, which in turn forms starch

Structure of chloroplast

Diagrammatic representation of an electron micrograph of a section of chloroplast

How Many Pigments are Involved in Photosynthesis?
Chromatographic separation of the leaf pigments shows that different types of pigments in leaves i.e
Chlorophyll a (bright or blue-green in the chromatogram)
chlorophyll b (yellow-green)
xanthophylls (yellow)
carotenoids (yellow to yellow-orange)

a) Graph showing the absorption spectrum of chlorophyll a, b, and the carotenoids.

b) Graph showing the action spectrum of photosynthesis.

c) Graph showing action spectrum of photosynthesis superimposed on the absorption spectrum of chlorophyll a.

Wavelengths of light absorbed by pigments
Chlorophyll pigments absorb light, at specific wavelengths of blue and the red regions while carotenoids absorb the blue and green wavelength
Chlorophyll is the major pigment responsible for trapping light, other thylakoid pigments like chlorophyll b, xanthophylls, and carotenoids, which are called accessory pigments, also absorb light and transfer the energy to chlorophyll a. but also protect chlorophyll a from photo-oxidation.

What is Light Reaction?
It is the photochemical phase include

1. light absorption
2. water splitting
3. oxygen release
4. Formation of high-energy rich molecules ATP and NADPH.

The pigments are organised into two light-harvesting complexes(LHC)

1. Photosystem I (PS I)/P700
2. Photosystem II (PS II)/P680

Each photosystem has single chlorophyll a molecule forms the reaction centre, all the pigments except chlorophyll-a forming a light-harvesting system also called antennae.

In PS I the reaction centre, chlorophyll a has an absorption peak at 700 nm while in PS II it has absorption maxima at 680 nm, and is called P680.

The Electron Transport
How does electron flow in electron carriers that connect two photosystems?
Initially, excitation of chlorophyll molecule occurs due to light, then electrons are emitted from Ps II (uphill) that are accepted by electron acceptor, electron flows through electron carriers cytochromes, (downhill) and (Loss of electrons of PSII is compensated by electrons coming from water and loss of electrons of PS I is compensated by electrons coming from PS II).

PS I is also excited due to light and electrons are emitted (uphill), it transfers an electron to another accepter, and finally down the hill to NADP+ causing it to be reduced to NADPH + H+ is called the Z scheme.

Result of Z-scheme

1. production of ATP and NADPH
2. O₂ evolution

Splitting of Water
Photolysis
It is the splitting of water into H+, [O] and electrons in the presence of light and these electrons are available to PSII.
This process takes place on the inner side of the membrane of the thylakoid.
Oxygen released is one of the net products of photosynthesis.
2H₂O → 4H⁺ + O₂ + 4e^–

Cyclic and Non-cyclic Photo-phosphorylation
Phosphorylation
The process of which ATP from ADP and inorganic phosphate in the presence of light (in mitochondria and chloroplasts) is named phosphorylation.

Electron in a cyclic process
When only PS I is functional, the cyclic flow of electrons within the photosystem and the phosphorylation occurs in the stroma lamellae.
Cyclic photophosphorylation also occurs when only light of wavelengths beyond 680 nm are available for excitation i.e at 700 nm

Result of cyclic photophosphorylation
ATP is produced.

Where does the light-harvesting complex work for acyclic and noncyclic processes?
The membrane or lamellae of the grana have both PS I and PS II so a noncyclic process occurs,
The stroma lamellae membranes lack PS II as well as NADP reductase enzyme So a cyclic process occurs.

Chemiosmotic Hypothesis
It is the ATP synthesis linked to the development of a proton gradient across a membrane
In chloroplast, the proton accumulation is towards the inside of the membrane, i.e., in the lumen. In respiration, protons accumulate in the intermembrane space of the mitochondria when electrons move through the ETS.
The proton gradient develops due to,

a. Splitting of the water molecule takes place on the inner side of the membrane, the protons accumulate within the lumen of the thylakoids

b. As electrons move through the photosystems, protons are transported across the membrane moves into the lumen side of the membrane

c. The NADP reductase enzyme is located on the stromal side of the membrane. Along with electrons that come from the accepter of electrons of PS I, protons are necessary for the reduction of NADP+ to NADPH+ H+. These protons are also removed from the stroma.

In chloroplast, protons in the stroma decrease in number, while in the lumen there is an accumulation of protons. This creates a proton gradient across the thylakoid membrane The gradient is broken down due to the movement of protons across the membrane to the stroma through the transmembrane channel of the F₀ of the ATP.
ATPase have a channel that allows diffusion of protons back across the membrane; this releases enough energy to activate the ATPase enzyme that catalyses the formation of ATP.

Where are the ATP and NADPH Used?
It is used in the biosynthetic phase of photosynthesis. This process does not directly depend on the presence of light but is dependent on the products of the light reaction, i.e., ATP and NADPH.
Melvin Calvin studied the algal photosynthesis by using radioactive 14C led to the discovery that the first CO₂ fixation product was identified as 3-phosphoglyceric acid or PGA.

The Primary Acceptor of CO₂
The studies showed that the accepter molecule was a 5-carbon sugar -ribulose bisphosphate (RuBP) in the Calvin cycle.

The Calvin Cycle
It involves three stages:

1. carboxylation
2. reduction
3. regeneration

1. Carboxylation:
Carboxylation is the fixation of CO₂ into a stable compound catalysed by the enzyme RuBisCO that results in the formation of two molecules of 3-PGA.

2. Reduction: These are a series of reactions that lead to the formation of glucose.
The steps involve the utilization of 3 molecules of ATP for phosphorylation and two NADPH for reduction per CO₂ molecule fixed. For the fixation of six molecules of CO₂, 6 turns of the cycle are required and one molecule of glucose is generated

3. Regeneration: Regeneration of the CO₂ acceptor molecule require one ATP for phosphorylation to form RuBP.
Hence for every CO₂ molecule entering the Calvin cycle, 3 molecules of ATP and molecules of NADPH are required

The Calvin cycle proceeds in three stages:
1. carboxylation, during which CO₂ combines with ribulose- 1, 5- bisphosphate
2. reduction, during which carbohydrate is formed at the expenses of the photochemically made ATP and NADPH; and
3. regeneration during which the CO₂ acceptor ribulose- 1, 5-bisphosphate has formed again so that the cycle continues

The C₄ Pathway (Hatch and Slack Pathway)
Plants that are adapted to dry tropical regions have the C₄ pathway, C₄ plants have a special type of leaf anatomy. They tolerate higher temperatures. They lack a process called photorespiration and have greater productivity of biomass.

Special leaf anatomy-kranz anatomy
Large cells around the vascular bundles are centripetally arranged bundle sheath cells such anatomy is called ‘Kranz’ anatomy. Eg- maize or sorghum

Primary CO₂, accepter, first stable product and Enzyme of C₄ Pathway
The primary CO₂ acceptor is a 3-carbon molecule- phosphoenolpyruvate (PEP) present in the mesophyll cells. The enzyme responsible for this fixation is PEP carboxylase or PEPcase.
The first stable product C₄ acid OAA is formed in the mesophyll cells.

Diagrammatic representation of a Hatch arid Slack Pathway
OAA converted into 4-carbon compounds like malic acid or aspartic acid in the mesophyll cells .which are transported to the bundle sheath cells. In the bundle sheath cells, these C4 acids are broken down to release CO₂ and a 3-carbon molecule. The 3-carbon molecule is transported back to the mesophyll where it is converted to PEP again, thus, completing the cycle.
Thus the basic pathway that results in the formation of the sugars, the Calvin pathway, is common to the C₃ and C₄ plants.

Photorespiration
In C₃ plants, under high concentration of O₂ and low CO₂ concentration, RUBP binds with O₂ to form one molecule of PGA and phosphoglycolate and a large quantity of CO₂ is released.

Can you say photorespiration is a wasteful process?
This process utilise ATP but neither synthesis of sugars, nor of ATP. Hence photorespiration is a wasteful process.

The specialty of C₄ plants to avoid Photorespiration
In C₄ plants photorespiration does not occur because C₄ acid from the mesophyll is broken down in the bundle cells to release CO₂ – this results in increasing the intracellular concentration of CO₂. Here RuBisCO functions as a carboxylase minimizing the oxygenase activity, productivity, and yields are better in these plants.

Factors Affecting Photosynthesis
Photosynthesis is influenced by several factors, both internal (plant) and external. The plant factors include the number, size, age, and orientation of leaves, mesophyll cells and chloroplasts, internal CO₂ concentration, and the amount of chlorophyll. The external factors include the availability of sunlight, temperature, CO₂ concentration, and water.

Blackman s Law of Limiting Factors
If a chemical process is affected by more than one factor, then its rate will be determined by the factor which is nearest to its minimal value: it is the factor that directly affects the process if its quantity is changed.
For example, In the green leaf, the light and CO₂ conditions are optimum but the plant does not photosynthesize if the temperature is very low.

Light
The availability of light shows a direct relationship with CO₂ fixation rates at low light intensities At higher light intensities the rate does not show further increase because other factors are not in optimal amount. The intensity of light beyond a point causes the breakdown of chlorophyll and a decrease in photosynthesis.

Carbon dioxide Concentration
The concentration of CO₂ is very low in the atmosphere (between 0.03 and 0.04 percent). An increase in concentration up to 0.05 percent can cause an increase in CO₂ fixation rates. The C₃ and C₄ plants respond differently to CO₂ concentrations.

Graph of light Intensity on the rate of photosynthesis

C₄ plants show saturation at about 360µL^-1 while C₃ responds to increased CO₂ concentration and saturation is seen only beyond 450µL^-1 Thus, the current availability of CO₂ levels is limiting to the C₃ plants.

C₃ plants respond to higher CO₂ concentration by showing increased rates of photosynthesis leading to higher productivity The above concept is used for some greenhouse crops such as tomatoes and bell pepper.

Temperature
The dark reactions that take place in stoma are enzymatic and temperature controlled. C₄ plants respond to higher temperatures and show a higher rate of photosynthesis while C₃ plants have a much lower temperature optimum.

Water
Water stress causes the closure of stomata and it is difficult to receive CO₂ for photosynthesis. The stress condition also makes leaves wilt and reducing the surface area of the leaves and their metabolic activities.

Students can Download Chapter 8 Mineral Nutrition Notes, Plus One Botany Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Botany Notes Chapter 8 Mineral Nutrition

Methods to Study the Mineral Requirements of Plants
In 1860, Julius von Sachs a German botanist demonstrated that plants could be grown in a nutrient solution in the complete absence of soil.

Hydroponics and its Importance

• This technique of growing plants in a nutrient solution is known as hydroponics.
• The nutrient solutions must be aerated to obtain optimum growth.
• In this method, essential elements are used and their deficiency symptoms can be studied.
• Hydroponics is used in the commercial production of vegetables such as tomato, seedless cucumber, and lettuce.

 

Hydroponic plant production. Plants are grown in a tube or trough placed on a slight incline. A pump circulates a nutrient solution from a reservoir to the elevated end of the tube. The solution flows down the tube and returns to the reservoir due to gravity. Inset shows a plant whose roots are continuously bathed in the aerated nutrient solution. The arrows indicate the direction of the flow.

Essential Mineral Elements

Some minerals are not essential to plants

• More than sixty elements are found in different plants.
• Some plant species absorb selenium, some others gold, while some plants growing near nuclear test sites take up radioactive strontium.

Criteria for Essentiality
The criteria for the essentiality of an element are given below:

• The element must be supporting normal growth and production.
  In the absence of the element, the plants do not complete their life cycle or set the seeds.
• The requirement of the element must be specific and not replaceable by another element.
• The element must be directly involved in the metabolism of the plant.

Based upon the above criteria 17 elements are essential for plant growth and metabolism. They are
i. Macronutrients:
Carbon, hydrogen, oxygen, nitrogen, phosphorous, sulphur, potassium, calcium, and magnesium
They are present in plant tissues in large amounts(in excess of 10 m mole/ Kg of dry matter).

ii. Micronutrients:
Iron, manganese, copper, molybdenum, zinc, boron, chlorine, and nickel
They are needed in very small amounts (less than 10 m mole /Kg of dry matter).

In addition to the essential elements, sodium, silicon, cobalt, and selenium are required by higher plants. Essential elements are grouped into four broad categories on the basis of their diverse functions.
i. Essential elements as components of biomolecules (e.g., carbon, hydrogen, oxygen, and nitrogen).

ii. Essential elements that are components of energy-related chemical compounds (e.g, magnesium in chlorophyll and phosphorous in ATP).

iii. Essential elements that activate or inhibit enzymes, (Mg²⁺ is an activator for both ribulose bisphosphate carboxylase oxygenase and phosphoenolpyruvate carboxylase, both of which are critical enzymes in photosynthetic carbon fixation
Zn²⁺ is an activator of alcohol dehydrogenase and Mo of nitrogenase during nitrogen metabolism.

iv. Essential elements alter the osmotic potential of a cell.
Potassium plays an important role in the opening and closing of stomata.

Role of Macro- and Micro-nutrients
Essential elements participate in various metabolic processes in the plant cells. The various forms and functions of mineral elements are given below.

Nitrogen

• It is absorbed mainly as NO₃^– Some taken up as NO₂ or NH₄⁺
• Nitrogen is required in meristematic tissues and the metabolically active cells.
• It is one of the major constituents of proteins, nucleic acids, vitamins and hormones

Phosphorus

• It is absorbed in the form of phosphate ions (either as HPO₄^2- or H₂PO₄^–)
• Phosphorus is a constituent of cell membranes, certain proteins, all nucleic acids, and nucleotides.
• It is required for all phosphorylation reactions.

Potassium

• It is absorbed as a potassium ion (K⁺).
• It is required in abundant quantities for meristematic tissues, buds, leaves, and root tips.
• Potassium helps to maintain an anion-cation balance in cells
• It is involved in protein synthesis
• It is involved in the opening and closing of stomata and activation of enzymes
• It helps in the maintenance of the turgidity of cells.

Calcium

• It is absorbed in the form of calcium ions (Ca²⁺).
• Calcium is required by meristematic and differentiating tissues.
• It is important in the formation of calcium pectate in the middle lamella.
• It is also needed during the formation of the mitotic spindle.
• It activates certain enzymes and plays an important role in regulating metabolic activities.

Magnesium

• It is absorbed by plants in the form of divalent Mg²⁺
• It activates the enzymes of respiration, photosynthesis, and are involved in the synthesis of DNA and RNA.
• Magnesium is a constituent of the ring structure of chlorophyll
• It helps to maintain the ribosome structure.

Sulphur

• It is absorbed in the form of sulphate (SO₄^2-)ion.
• Sulphur is present in two amino acids – cysteine and methionine
• It is the main constituent of several coenzymes, vitamins (thiamine, biotin, Coenzyme A), and ferredoxin.

Iron

• It is absorbed in the form of ferric ions (Fe³⁺)
• It is an important constituent of proteins involved in the transfer of electrons like ferredoxin and cytochromes.
• It activates the catalase enzyme and is essential for the formation of chlorophyll.

Manganese

• It is absorbed in the form of manganous ions (Mn²⁺).
• It activates many enzymes involved in photosynthesis, respiration, and nitrogen metabolism.
• It is also involved in the splitting of water to liberate oxygen during photosynthesis.

Zinc

• Plants obtain zinc as Zn²⁺ ions.
• It activates various enzymes, especially carboxylases.
• It is also needed in the synthesis of auxin.

Copper

• It is absorbed as cupric ions (Cu²⁺).
• It is essential for the certain enzymes involved in redox reactions

Boron

• It is absorbed as BO₃^3- or B₄O₇^2-
• It is required for uptake and utilisation of Ca²⁺
• it helps in membrane functioning
• it helps pollen germination
• it helps cell elongation and cell differentiation
• it is involved in carbohydrate translocation.

Molybdenum

• Plants obtain it in the form of molybdate ions (MoO₂²⁺).
• It is a component of nitrogenase and nitrate reductase both of which participate in nitrogen metabolism.

Chlorine

• It is absorbed in the form of chloride anion (Cl^–).
• Along with Na⁺ and K⁺, it helps in determining the solute concentration and the anion cation balance in cells.
  It is essential for the water-splitting reaction in photosynthesis, a reaction that leads to oxygen evolution.

Deficiency Symptoms of Essential Elements
If the concentration of the essential element below the critical concentration plants shows certain morphological changes. These are indications of deficiency symptoms.

Mobility of element determines deficiency symptoms
Deficiency symptoms in older tissues
Deficiency symptoms also depend on the mobility of the element in the plant. It first appears in the older tissues.
For example, the deficiency symptoms of nitrogen, potassium, and magnesium are visible first in the senescent leaves.
In the older leaves, biomolecules containing these elements are broken down and available for mobilising to younger leaves.

Deficiency symptoms in younger tissues
Sometimes the deficiency symptoms appear first in the young tissues. If the elements are immobile, they are not transported from mature organs to younger organs.
For example, Elements like sulphur and calcium are structural components of the cell and hence are not easily released.

The deficiency symptoms are

1. Chlorosis
2. Necrosis
3. stunted plant growth
4. premature fall of leaves and buds
5. and inhibition of cell division.

Chlorosis is the loss of chlorophyll leading to yellowing in leaves. It is due to the deficiency of elements like N, K, Mg, S, Fe, Mn, Zn, and Mo.
Necrosis, or death of tissue, particularly leaf tissue. It is due to the deficiency of Ca, Mg, Cu, K.
Lack or low level of N, K, S, Mo causes inhibition of cell division.
Deficiency of elements like N, S, Mo delay flowering

Toxicity of Micronutrients
If the supply of micronutrients at a moderate decreased level shows deficiency symptoms but the moderate increase causes toxicity, i.e the excess of an element inhibits the uptake of another element.

Symptoms and other effects of Manganese toxicity

• Symptom of manganese toxicity is the appearance of brown spots surrounded by chlorotic veins.
• Manganese competes with iron and magnesium for uptake and for binding with enzymes.
• Manganese also inhibits calcium translocation in the shoot apex.
• Symptoms of manganese toxicity induce
• Deficiency symptoms of iron, magnesium, and calcium.

Mechanism of Absorption of Elements
The process of absorption occurs in two main phases-

1. Apoplast (passive). The passive movement of ions into the apoplast occurs through ion- channels and the transmembrane proteins.
2. Symplast(active) The inward movement of ions into the cells is called influx and the outward movement efflux. This movement occurs by using metabolic energy.

Translocation of Solutes

• Mineral salts are pulled up through the plant by the transpirational pull.
• Analysis of xylem sap shows the presence of mineral salts in it.
• Radioisotopic studies support the xylem transport of mineral elements.

Soil as a Reservoir of Essential Elements

• Soil consist of a variety of minerals, nitrogen-fixing bacteria, and other microbes holds water and supplies air to the roots, and acts as a matrix that stabilises the plant.
• If the amount of nutrients in the soil is decreased, it is supplied from outside as fertilizers in the form of macronutrients (N, P, K, S, etc.) and micronutrients (Cu, Zn, Fe, Mn, etc.)

Metabolism of Nitrogen
Nitrogen Cycle
Nitrogen is a constituent of amino acids, proteins, hormones, chlorophyll, and many vitamins.
Atmospheric nitrogen consists of two nitrogen atoms joined by a very strong triple covalent bond main nitrogen pools-atmospheric soil, and biomass.

1. N₂ Fixation: The process of conversion of atmospheric nitrogen (N₂) to ammonia is termed nitrogen fixation.

2. Nitrification:

• Ammonia is converted into nitrate.
• Ammonia is first oxidized to nitrite by Nitrosomonas or Nitrococcus.
• The nitrite is further oxidized to nitrate with the help of the bacterium Nitrobacter

3. Ammonification: Decomposition of organic nitrogen of dead plants and animals into ammonia is called ammonification

4. Denitrification: It is the conversion of soil nitrate into molecular N₂ by Thiobacillus and pseudomonas

Formation of nitrogen oxides

• In nature, lightning and UV provide energy to convert nitrogen to nitrogen oxides (NO, NO₂, N₂O).
• Industrial combustions, forest fires, automobile exhausts, and power generating stations are also sources of atmospheric nitrogen oxides.

Biological Nitrogen Fixation
The nitrogen-fixing microbes are free-living or symbiotic. ‘Free-living nitrogen-fixing aerobic microbes are Azotobacter, Beijernickia Rhodospirillum Bacillus Anabaena Nostoc.

Development of root nodules in soyabean

Development of root nodule sin soyabean:

• Rhizobium bacteria contact susceptible root hair, divide near it.
• Upon successful infection of the root hair cause it to curl.
• Infected thread carries the bacteria to the inner cortex. The bacteria get modified into rod-shaped bacteroids and cause inner cortical and pericycle cells to divide. Division and growth of cortical and pericycle cells lead to nodule formation.
• A mature nodule is complete with vascular tissues continuous with those of the root.

Basic steps are given below

• Rhizobium bacteria attach the root hair.
• Root hair curls.
• Infected thread carries the bacteria to the inner cortex.

The bacteria get modified into rod-shaped bacteroids and cause inner cortical and pericycle cells to divide. Division and growth of cortical and pericycle cells lead to nodule formation, d) A mature nodule is complete with vascular tissues continuous with those of the root.

Overall equation for N2 fixation
N₂ + 8e^– + 8H⁺ +16ATP → 2NH₃ + H₂ + 16ADP + 16Pt

Fate of ammonia

• At first, ammonia protonated to form NH⁴⁺.
• This ammonium ion is used to synthesise amino acid in plants

There are two ways for the synthesis of amino acids in plants

1. Reductive animation
In this, ammonium ion reacts with alpha-ketoglutaric acid and forms glutamic acid.

2. Transamination
It involves the transfer of an amino group from one amino acid to the keto group of a keto acid.
Glutamic acid is the main amino acid from which the transfer of amino groups takes place and other amino acids are formed in the presence of transaminase.

Amides

• The important amides are asparagine and aspartate.
• Amide is formed when the hydroxyl group of one amino acid is replaced by an amino group.
• Since amide contains more nitrogen than amino acids. They are transported through xylem vessels.

Kerala State Board New Syllabus Plus One Maths Notes Chapter 3 Trigonometric Functions.

Kerala Plus One Maths Notes Chapter 3 Trigonometric Functions

I. Angles
The measure of an angle is the amount of rotation performed to get the terminal side from the initial side.

1. Degree measure: If a rotation from the initial side to terminal side is \(\left(\frac{1}{360}\right)^{t h}\) of a revolution, the angle is said to have a measure of one degree, written as 1°. 1° = 60′ and f = 60″.

2. Radian measure: An angle subtended at the center by an arc of length 1 unit in a unit circle is said to be of 1 radian. Radian measure is a real number corresponding to degree measure.

180° = π radians

Radian measure = \(\frac{\pi}{180}\) × Degree measure

Degree measure = \(\frac{180}{\pi}\) × Radian measure

l = rθ, where l = arc length, r = radius of the circle and θ = angle in radian measure.

II. Trigonometric Function
Consider a unit circle with centre at the origin of the coordinate axis.
Let P (a, b) be any point on the circle which makes an angle θ° with the x-axis. Let x be the corresponding radian measure of the angle θ°, i.e; x is the arc length corresponding to θ°.

From the ∆OMP’m the figure we get;
sin θ = sin x = \(\frac{b}{1}\) = b and cos θ = cos x = \(\frac{b}{1}\) = a
This means that for each real value of x we get corresponding unique ‘sin’ and ‘cosine’ value which is also real. Hence we can define the six trigonometric functions as follows.

1. f : R → [-1, 1] defined by f(x) = sin x

2. f : R → [-1, 1] defined by f(x) = cos x

3. f : R – {nπ, n ∈ Z} → R – (-1, 1) defined by f(x) = \(\frac{1}{\sin x}\) = cosec x

4. f : R – {(2n + 1) \(\frac{\pi}{2}\)} → R – (-1, 1) defined by f(x) = \(\frac{1}{\cos x}\) = sec x

5. f : R – {(2n + 1)π, n ∈ Z} → R defined by f(x) = \(\frac{\sin x}{\cos x}\) = tan x

6. f : R – {nπ, n ∈ Z} → R defined by f(x) = \(\frac{\cos x}{\sin x}\) = cot x

Sign of trigonometric functions in different quadrants;

For odd multiple of \(\frac{\pi}{2}\) trignometric functions changes as given below.
sin → cos
cos → sin
sec → cosec
cosec → sec
tan → cot
cot → tan

The value of trigonometric functions for some specific angles;

III. Compound Angle Formula

sin(x + y) = sin x cos y + cos x sin y

sin(x – y) = sin x cos y – cos x sin y

cos(x + y) = cos x cos y – sin x sin y

cos(x – y) = cos x cos y + sin x sin y

sin(x + y) sin(x – y) = sin² x – sin² y = cos² x – cos² y

cos(x + y) cos(x – y) = cos² x – sin² y

IV. Multiple Angle Formula

cos2x = cos² x – sin² x
= 1 – 2sin² x
= 2 cos² x – 1
= \(\frac{1-\tan ^{2} x}{1+\tan ^{2} x}\)

V. Sub-Multiple Angle Formula

VI. Sum Formula

VII. Product Formula

2 sin x cos y = sin(x + y) + sin(x – y)

2 cos x sin y = sin(x + y) – sin(x – y)

2 cos x cos y = cos(x + y) + cos(x – y)

2 sin x sin y = cos(x – y) – cos(x + y)

VIII. Solution of Trigonometric Equations

sin x = 0 gives x = nπ, where n ∈ Z

cos x = 0 gives x = (2n + 1)π, where n ∈ Z

tanx = 0 gives x = nπ, where n ∈ Z

sin x = sin y ⇒ x = nπ + (-1)ⁿ y, where n ∈ Z

cos x = cos y ⇒ x = 2nπ ± y, where n ∈ Z

tan x = tan y ⇒ x = nπ + y, where n ∈ Z

Principal solution is the solution which lies in the interval 0 ≤ x ≤ 2π.

IX. Sine and Cosine formulae

Let ABC be a triangle. By angle A we mean the angle between the sides AB and AC which lies between 0° and 180°. The angles B and C are similarly defined. The sides AB, BC, and CA opposite to the vertices C, A, and B will be denoted by c, a, and b, respectively.

Theorem 1 (sine formula): In any triangle, sides are proportional to the sines of the opposite angles. That is, in a triangle ABC
\(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\)

Theorem 2 (Cosine formulae): Let A, B and C be angles of a triangle and a, b and c be lengths of sides opposite to angles A, B, and C, respectively, then
a² = b² + c² – 2bc cos A
b² = c² + a² – 2ca cos B
c² = a² + b² – 2ab cos C

A convenient form of the cosine formulae, when angles are to be found are as follows: