Let the integers be x, x+1, x+2, x+3, x+4.\n\nMean = (5x + 10) / 5 = 12\n\n5x + 10 = 60\n\n5x = 50\n\nx = 10.

Total sum = 5 * 18 = 90. New sum = 4 * 16 = 64. Excluded number = 90 - 64 = 26.

Total of five numbers = 5 * 18 = 90. Total of four numbers = 4 * 16 = 64. Removed number = 90 - 64 = 26.

Total of five numbers = 5 * 20 = 100. Total of remaining four = 4 * 18 = 72. Excluded number = 100 - 72 = 28.

Total of five numbers = 5 * 20 = 100. Total of four numbers = 4 * 18 = 72. Number removed = 100 - 72 = 28.

Total sum = 5 * 50 = 250. New total = 250 + 10 = 260. New average = 260 / 5 = 52.

Let the integers be x, x+1, x+2. Average = (x + (x+1) + (x+2))/3 = 15. Solving gives x = 14, largest integer = 16.

Let the integers be x, x+1, x+2. Average = (x + (x+1) + (x+2)) / 3 = 15. Solving gives x = 14.

Let the integers be x, x+1, x+2. (x + (x + 1) + (x + 2)) / 3 = 20. Therefore, 3x + 3 = 60, so x = 19.

Let the integers be x, x+1, x+2. The average is (x + (x + 1) + (x + 2)) / 3 = 20. Solving gives x = 18.

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.

The Battle of Panipat in 1526 marked the beginning of the Mughal Empire in India.

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.