Total of three numbers = 3 * 15 = 45.\n\nNew total = 45 + 5 = 50.\n\nNew average = 50 / 3 = 16.67.

Total of three numbers = 3 * 15 = 45. New total after increasing one number by 5 = 45 + 5 = 50. New average = 50 / 3 = 16.67.

Let the three numbers be x, y, z.  (x + y + z) / 3 = 30 => x + y + z = 90. After removing one number, (x + y) / 2 = 25 => x + y = 50. Therefore, removed number = 90 - 50 = 40.

The sum of the three numbers is 3 * 30 = 90. If one number is increased by 10, the new sum is 90 + 10 = 100. The new average = 100 / 3 = 33.33.

The sum of the three numbers is 3 * 40 = 120. Increasing the first number by 10 gives a new sum of 120 + 10 = 130. The new average is 130 / 3 = 43.33, which rounds to 42.

Let the numbers be x and x+10. (x + (x + 10)) / 2 = 30. Solving gives x = 25, so numbers are 25 and 35.

Mean = (20 + x) / 2 = 30.\n\n20 + x = 60\n\nx = 60 - 20 = 40.

Let the other number be x. (40 + x) / 2 = 36. Solving gives x = 32.

Total score of 5 students = 5 * 80 = 400. New total score for 6 students = 6 * 82 = 492. Score of new student = 492 - 400 = 92.

New average = (72 * 5 + 80) / 6 = (360 + 80) / 6 = 440 / 6 = 73.33, which rounds to 74.

The average speed of gas molecules is given by the formula v_avg = (8kT/πm)^(1/2), where k is the Boltzmann constant, T is the temperature, and m is the mass of a gas molecule.

The average speed of gas molecules is given by the expression v_avg = √(8RT/πM), where R is the universal gas constant, T is the temperature, and M is the molar mass of the gas.

The average speed of gas molecules is given by the formula v_avg = sqrt(8kT/πm), where k is the Boltzmann constant, T is the temperature, and m is the mass of a molecule.

The Ayushman Bharat scheme aims to provide health insurance coverage to economically vulnerable families.

Refraction is the bending of light as it passes from one medium to another due to a change in speed.

The Berlin Conference of 1884-85 is significant for dividing Africa among European powers, leading to arbitrary borders that disregarded ethnic and cultural divisions.

The Berlin Conference regulated European colonization and trade in Africa, leading to the 'Scramble for Africa'.

The Beti Bachao Beti Padhao scheme, launched in 2015, aims to prevent gender discrimination and promote the education of girls.

The Beti Bachao Beti Padhao scheme aims to prevent female foeticide and promote education for girls.

The Bhakti movement emphasized personal devotion to God, transcending caste and ritualistic practices.

The Bhakti movement emphasized personal devotion to God and sought to transcend caste divisions, promoting a sense of unity among diverse communities.

The Bill of Rights is significant because it enumerated specific rights and protections for individuals, ensuring fundamental liberties such as freedom of speech and religion.

To convert from passive to active voice, identify the subject performing the action. Here, 'the students' is the subject who reads 'the book'.

The word 'interesting' suggests that the book captured the reader's attention.

The Booker Prize is awarded annually for the best original novel written in the English language and published in the UK.

The Booker Prize is awarded for the best original novel written in the English language.

The Brihadeeswarar Temple, built in the 11th century, is a prime example of Chola architecture, showcasing the grandeur of Dravidian style.

The British East India Company primarily governed India through indirect rule, utilizing local princes and zamindars to maintain control.

According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced by the object.

According to Archimedes' principle, the buoyant force on a submerged object is equal to the weight of the fluid displaced by the object.