Correct Answer: 900

Solution : Given:
529 : 576 :: 841 : ?

Like, (23)² = 529; (24)² = 576 (23 and 24 are the consecutive numbers.)
Similarly, 841 = (29)²; the next number to 29 will be 30. So, (30)² = 900

So, 900 is the required answer. Hence, the fourth option is correct.

Correct Answer: themselves

Solution : The third option is correct.

In the sentence, the word "themselves" is necessary to complete the thought. It refers to individuals who have experienced rejection. The subject is likely plural, as the only options given are plural pronouns. So, the most appropriate reflexive pronoun for a plural subject is "themselves".

Therefore, the correct answer is themselves.

Correct Answer: $x$ - $y$

Solution : If the lengths of the parallel sides of a trapezium are $x$ cm and $y$ cm and its height is h cm then, the area of the trapezium = $\frac{1}{2}(x+y) × {h}$. 
${x}^2-{y}^2 = ({x}+{y})({x} - {y})$ 
The area of the trapezium = $\frac{1}{2}({x}^2- {y}^2)$ = $\frac{1}{2}({x}+{y})({x} - {y})$ 
⇒  $\frac{1}{2}({x}+{y}){h}$ = $\frac{1}{2}({x}+{y})({x} - {y})$ 
⇒ $h = x – y$
$\therefore$ The distance between the parallel sides (in cm) is $x – y$.
Hence, the correct answer is $x$ - $y$.

Correct Answer: B. R. Ambedkar

Solution : The correct option is B. R. Ambedkar.

Dr. B. R. Ambedkar, a prominent Indian jurist, social reformer, and political leader, is credited as the architect of the Indian Constitution. As the head of the drafting committee of the Constituent Assembly of India, responsible for creating the Constitution after India gained independence, his legal acumen, profound grasp of social matters, and dedication to justice were pivotal in shaping this important document.

Correct Answer: Chess

Solution : The correct answer is Chess.

Born on November 30, 1990, Sven Magnus Carlsen is a chess grandmaster from Norway. He holds the titles of five-time World Chess Champion, four-time World Rapid Chess Champion, and six-time World Blitz Chess Champion, and he is considered one of the finest players in chess history.

Correct Answer: inspired

Solution : The correct choice is the fourth option.

The word inspired fits well in the context of the sentence, conveying that the story had a positive impact or influence on the speaker, leading them to create imaginative or fancy names for themselves. Inspired in this context suggests motivation, creativity, or a positive prompting.

Therefore, the complete sentence is: "The story inspired me to make up fancy names for myself."

Correct Answer: CR

Solution : Given:
OD, LA, IX, FU,?

Subtract 3 from the place value of the first and second letter, to get the required missing term in the series –
OD→O – 3 = L; D – 3 = A→LA
LA→L – 3 = I; A – 3 = X→IX
IX→I – 3 = F; X – 3 = U→FU
FU→F – 3 = C; U – 3 = R→CR

So, the required missing term in the series is CR. Hence, the third option is correct. 

Correct Answer: Centenarian

Solution : The first option is correct.

Centenarian means a person who is 100 years old or older. It is a noun and can be used to describe someone who has reached the age of 100 or more.

Therefore, the correct answer is centenarian.

Correct Answer: 48

Solution : Given: 25 × 7 ÷ 175 – 196 ÷ 14 × 2 + 625 ÷ 25 × 3
= $25 × \frac{7}{ 175} - \frac{196}{14} × 2 + \frac{625}{ 25} ×3$
= 1 – 14 × 2 + 25 × 3
= 1 – 28 + 75
= 48
Hence, the correct answer is 48.

Correct Answer: 1888

Solution : The correct option is 1888.

Durand Cup was first founded in India in 1888, more precisely in the city of Shimla. The competition bears Sir Mortimer Durand's name, who founded it and served as the British Indian government's Foreign Secretary at the time. With a long history, the Durand Cup has been closely linked to the Indian football community. Numerous football teams and clubs have participated in the competition over the years, which has helped to develop and promote football in India.