The number of arrangements of 6 people at a round table is (6-1)! = 5! = 120.

The number of ways to choose 2 fruits from 5 is given by 5C2 = 10.

'Modern' is the antonym of 'ancient', referring to something contemporary.

'Natural' is the antonym of 'artificial', which refers to something made by human beings rather than occurring naturally.

'Rare' is the opposite of 'frequent', meaning not occurring often.

'Quiet' is the opposite of 'noisy'.

'Pessimistic' is the antonym of 'optimistic', which refers to a negative outlook.

'Fail' is the opposite of 'succeed'.

'Defeat' is the antonym of 'victory', indicating a loss in a competition.

A conjunction is a part of speech that connects words, phrases, or clauses.

An interjection is a part of speech that expresses strong emotion or surprise, such as 'wow!', 'ouch!', or 'hey!'.

A noun names a person, place, thing, or idea.

An adjective provides additional information about a noun.

A preposition shows the relationship between a noun (or pronoun) and other words in a sentence.

A preposition shows the relationship of a noun or pronoun to other words in a sentence.

'Gregarious' refers to being sociable and enjoying the company of others, so the synonym is 'sociable'.

'Vigilant' means keeping careful watch for possible danger or difficulties; hence, the synonym is 'alert'.

'Candid' means truthful and straightforward; thus, the synonym is 'honest'.

'Vigilant' means keeping careful watch for possible danger or difficulties; hence, the synonym is 'alert'.

'Vivid' means producing powerful feelings or strong, clear images.

According to the law of conservation of mass, the total mass of the products is equal to the total mass of the reactants, which is 10 g + 20 g = 30 g.

Concentration = mass/volume = 10 g / 0.5 L = 20 g/L.

Using the formula m1c1T1 + m2c2T2 = (m1 + m2)cT, we find T = (200*80 + 300*20) / (200 + 300) = 40°C.

Members from ruling party = 30% of 245 = 0.3 * 245 = 73.5, rounded to 74.

3x + 2 = 11 => 3x = 9 => x = 3.

Let the number be x. The equation is 5x - 3 = 12. Adding 3 to both sides gives 5x = 15. Dividing by 5 gives x = 3.

Using the identity a^2 + b^2 = (a + b)^2 - 2ab, we have 70 = 12^2 - 2ab. Thus, 70 = 144 - 2ab, leading to ab = 37.

a² + b² = (a + b)² - 2ab = 5² - 2*6 = 25 - 12 = 13.

Work done = mgh = 10 kg × 9.8 m/s² × 5 m = 490 J.

Using Ohm's law, I = V/R = 5V / 10Ω = 0.5 A.