There are two ways of balancing Redox reactions:

• Oxidation number method
• Half equation method

Oxidation method: The steps to be followed-

1. Write the skeletal equation of reactants and products.
2. Indicate the oxidation number of all the elements involved in the reaction.
3. Calculate the increase or decrease in oxidation number per atom. Also, identify the oxidizing and reducing agents.

1. Multiply the formula of oxidizing agent and reducing agent by suitable integers, so as to equalize the total increase or decrease in oxidation number as calculated in step c.
2. Balance all atoms other than H and O.
3. Finally balance H and O atoms by adding water molecules using hit and trial method.
4. In case of Ionic reactions:

• For acidic medium
• First balance O atoms by adding water molecules to the deficient side.
• Balance H+ ions to the side deficient in H atoms.
• For Basic medium
• First balance oxygen atom by adding water molecules to the deficient side.
• Then to balance hydrogen, add water molecules equal to the number of deficiency of H atoms.
• Also add equal number of OH^- ions to opposite side of the equation.

Example: Permagnate ion reacts with bromide ion in basic medium to give manganese dioxide and Bromate ion .

Step1: the skeletal ionic equation is :

MnO₄^- (aq) +Br^- (aq) ---> MnO₂ +BrO₃^-

Step 2: assign oxidation numbers for Mn and Br

Step3: calculate the increase and decrease in oxidation number and make the change equal :

Step: 4 as the reaction occurs in basic medium, and the ionic charges are not equal on both sides, add 2OH^- ions on the right to make it equal.

Step5: finally count the hydrogen atoms and add appropriate number of water molecules on the left side to achieve balanced Redox reaction.

Half reaction method or Ion electron method

1. Write the skeletal equation and indicate the oxidation number of all the elements which occur in skeletal equation
2. Find out the species that are oxidized and reduced.
3. Split the skeletal equation into two half reactions: oxidation half reaction and reduction half reaction
4. Balance the two-half equation separately by rules described below:

• In each half reaction first balance the atoms of element that has undergone a change in oxidation number.
• Add electrons to whatever side is necessary to make up the difference in oxidation number in each half reaction.
• Balance the charge by adding H⁺ ions, if the reaction occurs in acidic medium .For basic medium, add OH^- ions if the reaction occurs in basic medium.
• Balance oxygen atoms by adding required number of water molecules to the side deficient in oxygen atoms
• In the acidic medium, H atoms are balanced by adding H ⁺ ions to the side deficient in H atoms.
• However, in the basic medium H atoms are balanced by adding water molecules equal to number to H atoms deficient.
• Add equal number of OH^- ions to opposite side of equation.
• The two half reactions are then multiplied by suitable integers .so that the total number of electrons gained in half reaction becomes equal to total number of electrons lost in another half reaction.
• Then the two half reactions are added up.
• To verify the balancing, check whether the total charge on either is equal or not.

Example: Let us consider the skeletal equation:

Fe²⁺ + Cr₂O₇^2- -->  Fe³⁺ +Cr³⁺

Step 1: Separate the equation in to two halves:

Oxidation half reaction: Fe² --> Fe³⁺

 Reduction half reaction: Cr₂O₇^2-  -->    Cr³⁺

Step 2: Balance the atoms other than hydrogen and oxygen in each half reaction individually. Here the oxidation half reaction is already balanced with respect to Fe atoms .For the reduction half reaction, we multiply the Cr³⁺ by 2 to balance Cr atoms.

Step 3: For reactions occurring in acidic medium, add water molecules to balance oxygen atoms and hydrogen ions are balanced by adding H atoms. Thus, we get:

Cr₂O₇^2- + 14 H⁺  +  6e^- --> 2 Cr³⁺ + 7H₂O

Step 4: Add electrons to one side of the half reaction to balance the charges .if needed make the number of electrons equal in two half reactions by multiplying one or both half reaction by suitable coefficient.

The oxidation half reaction is thus written again to balance the charge .Now in the reduction half reaction there are 12 positive charges on the left hand side and only 6 positive charge on right hand side .Therefore, we add six electrons to left hand side .

Cr₂O₇^2- + 14 H⁺  +  6e^- --> 2 Cr³⁺ + 7H₂O

To equalize the number of electrons in both reactions, we multiply oxidation half reaction by 6 and write as:

6Fe²⁺  -->  6Fe³⁺ +6e^-

Step 5: We add the two half reactions to achieve the overall reaction and cancel the electrons on each side .This give us net ionic equation:

6Fe²⁺  + Cr₂O₇^2- + 14 H_⁺ -->    2Cr³⁺+6Fe³⁺ +7H₂O

Step6: Verify that the equation contains the same type and number of atoms and the same charges on both sides of the equation. This last check reveals that the equation is fully balanced with respect to number atoms and the charges.

An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.

Water equivalent is defined as the amount of water that can replaces any substance gaining the same variation in temperature, when provided with the same amount of energy as that of substance. It is written as W.

• The Port of Kolkata is a riverine port in the city of Kolkata, India, located around 203 kilometres (126 mi) from the sea. It is the oldest operating port in India, and was constructed by the British East India Company.
•  Kolkata is an Inland riverine port serving a large hinterland of Ganga Brahmaputra basin.
•  It is located along the banks of the Ganges.

Throughout different places, the Brahmaputra is known by different names: the Yarlung Tsangpo is Tibet, the Dihang or Siang in Arunachal Pradesh, and the Jamuna in Bangladesh.

Nanda Devi and Dhaulagiri are mountain peaks in the Himalaya mountain range.

Today, most countries in the world have a Constitution. While all democratic countries are likely to have a Constitution, it is not necessary that all countries that have a Constitution are democratic. There can be several purposes for drafting a constitution, they are: To provide a set of basic rules that allow for minimal coordination amongst members of society. To specify who has the power to make decisions in a society. It decides how the government will be constituted. To set some limits on what a government can impose on its citizens. These limits are fundamental in the sense that government may never trespass on them. To enable the government to fulfil the aspirations of a society and create conditions for a just society. Therefore, it can be understood that the constitution allows coordination and assurance. On the other hand, it can limit the powers of the government.

The ratio of the A.M and G.M. of two positive numbers a and b, is m: n. Show that

a:b=(m+ √(m²-n²)):(m-√(m²-n²))

Answer

Using this in the identity (a – b)² = (a + b)² – 4ab, we obtain

Adding (1) and (2), we obtain

It can be defined as the electrons which are there in degenerate orbitals have a parallel spin and tend to exchange their position.  The exchange energy is the energy released when two or more electrons with the same spin-exchange their positions in the degenerate orbitals of a subshell. Exchange energy is nothing but the energy released during this process. When the orbitals are half-filled or completely filled then the number of exchanges is maximum. Therefore, its stability is maximum.

Internal Rate of Return or IRR is a measure in capital budgeting parlance which is used for estimating the profit that can be obtained from the investments.

Internal rate of return is a type of discount rate that is instrumental in making the net present value of all the cash flows from any project equal to zero.

In simple words, it can be referred to as the compounded annual rate of return that can be earned on an investment or a project.

Simple meaning:

The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) ZERO. In other words, it is the expected compound annual rate of return that will be earned on a project or investment.

Internal Rate of Return or IRR is a measure in capital budgeting parlance which is used for estimating the profit that can be obtained from the investments.

Internal rate of return is a type of discount rate that is instrumental in making the net present value of all the cash flows from any project equal to zero.

In simple words, it can be referred to as the compounded annual rate of return that can be earned on an investment or a project.

Simple meaning:

The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) ... In other words, it is the expected compound annual rate of return that will be earned on a project or investment.

Internal Rate of Return or IRR is a measure in capital budgeting parlance which is used for estimating the profit that can be obtained from the investments.

Internal rate of return is a type of discount rate that is instrumental in making the net present value of all the cash flows from any project equal to zero.

In simple words, it can be referred to as the compounded annual rate of return that can be earned on an investment or a project.

They have been learning English for one year.

"Has been" and "have been" are both in the present perfect tense. "Has been" is used in the third-person singular and "have been" is used for first- and second-person singular and all plural uses. The present perfect tense refers to an action that began at some time in the past and is still in progress. For example, if I started studying art when I was 13 years old and I am still studying art, I would say "I have been studying art since I was 13 years old."

They................... (has been/had been/have been) learning English for one year.

have been

Accounting as a Source of Information:

 Accounting is regarded as the language of a business. It is used as a means of communication between a business organization and its shareholders. The accounting process is a source of information, it uses business data and processes it to generate relevant information

Accounting is regarded as the language of a business. It is used as a means of communication between a business organization and its shareholders. The accounting process is a source of information, it uses business data and processes it to generate relevant information.

• The accounting records business transaction which is the source of generating information.
• Proper accounting system makes information more reliable.
• Accounting ensures it is a reliable source of information.
• Accounting works as a management information system to the organization. It helps the management to manage the organization in a proper way.
• Accounting system generator various information in the form of different accounts. These documents have to be to true and fair.