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Prove that the product of three consecutive positive integer is divisible by 6.

Let the three consecutive positive integers be n, n+1, and n+2 When a number is divided by 3, the remainder obtained are either 0, 1, or 2... View Article

In a right triangle ABC in which ∠B = 90^o, a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the tangent to the circle at P bisects BC.

The tangents PQ and BQ are drawn from an external point Q. PQ = BQ eq.1 (the length of the tangent drawn from an external point to the circle... View Article

Abscissa of a point is positive in which quadrant?

Abscissa of a point is positive in I and IV quadrants.... View Article

Write four solutions for each of the following equations: (i) 2x + y = 7 (ii) πx + y = 9 (iii) x = 4y

(i) 2x + y = 7 Substitute x = 0 in the above equation 2(0) + y = 7 y = 7 Therefore, (0,7) is a solution for the given equation Let y = 0 2x... View Article

What is the value of x, if sin 2x = sin 60^o cos 30^o – cos 60^o sin 30^o?

To determine the value of x, the below formula is used: sin (A-B) = sinA . cosB - cosA. sinB Substituting the values of A and B where A =... View Article

For a line x = t meets the ellipse x²+y²/9 = 1 in real and distinct points if and only if?

For a line x = t meets the ellipse x<sup>2</sup>+y<sup>2</sup>/9 = 1 in real and distinct points when |t| < 1.... View Article

who was the author of the novel anandamath

Anandamath is a Bengali novel written by Bankim Chandra Chatterjee.... View Article

Why were the linguistic states created? What are their advantages?

Linguistic states were created to ensure that people who speak the same language lived in the same state. Some states were purposefully created... View Article

Explain the concept of word processing

Word Processing includes creating editing, saving and printing of documents using computer. Word processor is a software tool that helps to type... View Article

Expand the idea health is wealth

The saying health is wealth explains that health is most important than money or asset. It says health is everything, and there is no substitute... View Article

Write a short note on ‘Democracy’

Democracy is a Greek word that means people and their rules. India is a democratic country where the government is elected by the people of... View Article

Explain the accommodation of social diversity.

Accommodation of social diversity in democracy helps the citizens to lead a peaceful and a harmonious life. This happens when various types of... View Article

Why was the right of the property removed from fundamental rights?

Right to property was removed from the fundamental rights because of the 44th Amendment Act of 1978. The main motive of this removal was to... View Article

What was the slogan given by Subhash Chandra Bose

The slogan given by Subhash Chandra Bose is 'Give me blood, I shall give you freedom'.... View Article

What do you mean by occupation?

Occupation refers to the profession that is followed by a person. Teaching, medicine, engineering, writer are a few examples of different occupation.... View Article

Discuss the meaning of domestic territory

When domestic territory is defined in terms of economics, it means the economic territory that refers to the geographical territory which is... View Article

Hardware and software are complementary to each other. Explain

Hardware refers to the visible devices which are assembled to build a computer system. Software refers to the computer programs that are loaded... View Article

Who was a ‘Gramini’?

The Gramini was the officer appointed by the king to look after the administration of villages.... View Article

nobody will get the right…. you are sleeping and are hungry, and you may have butter, cheeses and polony in the fridge. What’s the first thing you will open.

I will open my eyes since I will be sleeping.... View Article

Describe any three features of Himalayan mountains.

1) Himalayan mountains are spread over 2,400 km from west to east direction. 2) The Himalayan ranges are endowed with wide and unique varieties... View Article

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