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

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.

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

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 English, thus it is a fiction award.

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

In active voice, the subject 'my mother' performs the action of baking the cake, thus it becomes 'My mother baked the cake.'

The word 'tasty' suggests that the cake was delicious and enjoyable.

The correct word is 'quick' as it implies the mouse was fast enough to escape.

A cat lives in a house just as a fish lives in a tank.

The relationship is predatory; a cat hunts a mouse just as a dog is associated with a bone.

The most logical option is 'mat' as it is a common place for a cat to sit.

The word 'excited' describes the children's feelings about the circus.

The correct form is 'The committee has made its decision.' 'Committee' is a collective noun and is treated as singular.

The Constitution of India was adopted on 26th November 1949 and came into effect on 26th January 1950.

The Dadasaheb Phalke Award is the highest award in Indian cinema.

The Dandi March in 1930 was a key event in the Civil Disobedience Movement, led by Gandhi to protest against the salt tax.

The sentence is correct. 'Data' can be treated as a singular mass noun in modern usage, hence 'is' is appropriate.

The Directive Principles of State Policy are contained in Part IV of the Constitution.

The statement implies that waking up early is associated with seizing opportunities, hence waking up late may lead to missed chances.

Potential energy is the energy stored in an object due to its position or configuration.

Factoring gives (x-3)(x+3)=0, hence the roots are -3 and 3.

The rock edicts were issued by Emperor Ashoka, promoting Buddhism and moral governance.

The Fields Medal is awarded to mathematicians for outstanding achievements in mathematics.

The Fields Medal is awarded to mathematicians under 40 years of age for outstanding achievements in mathematics.

To convert to active voice, we say 'The gardener watered the flowers.' highlighting the gardener's action.

Drag is the force that opposes the motion of an object through a fluid, such as air or water.