Correct Answer: Kiran

Solution : Given:
(I) Six students Prateek, Sameer, Kabir, Ziya, Joseph, and Kiran are sitting around a circular table facing the centre (not necessarily in the same order). Prateek is an immediate neighbour of both Sameer and Kabir.

(II) Ziya is sitting second to the right of Sameer. Kiran is sitting third to the left of Kabir. Joseph is an immediate neighbour of both Ziya and Kabir.
 

So, Kiran and Joseph are the immediate neighbours of Ziya. Hence, the fourth option is correct. 
 

Correct Answer: Rs. 600

Solution : Let the initial cost of the radio be $x$.
According to the question,
$x+\frac{20x}{100}+60=x+\frac{30x}{100}$
⇒ $60=\frac{30x}{100}-\frac{20x}{100}$
⇒ $60=\frac{10x}{100}$
⇒ $x=600$
Hence, the correct answer is Rs. 600.

Correct Answer: 22 km

Solution :

In the above figure, O is the starting point and T is the finishing point.
A's distance from his initial place in the horizontal direction is (OP + QR).
OP + QR = 7 + 15 = 22 km

So, A is 22 km from the starting point in the horizontal direction. Hence, the second option is correct. 

Correct Answer: 2 km

Solution : Firstly, we will draw the diagram as per the given instructions –

In the above figure, O is the starting point and E is the finishing point. So, OE is M's distance from the starting point to the final point.
OE = CD – AB
OE = 7 – 5 = 2 km

So, M's distance from the starting point to the final point is 2 km. Hence, the second option is correct. 

Correct Answer: Connoiseur

Solution : The correct choice is the third option.

In this case, the misspelt word is "connoiseur", which should be spelt as connoisseur, which refers to an expert judge in matters of taste, someone who has expert knowledge and keen discrimination in a particular field, often related to art, food, or culture.

The meanings of the other options are as follows:

• Diarrhoea: This refers to a condition characterised by frequent and liquid bowel movements.
• Pseudonym: This refers to a fictitious name used by an author or a pen name used by individuals to conceal their real identity.
• Perseverance: This refers to the persistence and determination to continue doing something despite challenges or difficulties.

Correct Answer: Brazil

Solution : The correct answer is Brazil.

Situated along the Atlantic shore, Copacabana Beach extends from Posto Dois to Posto Seis and stands as a vibrant centrepiece in Rio de Janeiro, Brazil. Renowned globally, it's celebrated for its lively atmosphere and spans a 4-kilometre coastline.

Correct Answer: 20, 00, 65, 40

Solution : Given:
CAGE

Number representations of each letter –
C→02, 11, 20, 31, 43
A→00, 14, 23, 34, 42
G→56, 65, 77, 87, 97
E→04, 13, 24, 33, 40

First option: 95, 82, 31,14; C, A, G, and E cannot be represented as 95, 82, 31, and 14 respectively.
Second option: 20, 00, 65, 40; All the letters of the word CAGE can be represented through this option.
Third option: 14, 20, 41, 86; C, A, G, and E cannot be represented as 14, 20, 41 and 86 respectively.
Fourth option: 00, 21, 41, 95; C, A, G, and E cannot be represented as 00, 21, 41, and 95 respectively.

So, CAGE can be represented by using the codes 20, 00, 65, 40. Hence, the second option is correct.

Correct Answer: $62$

Solution : Given: $x^2-8x+1=0$
Dividing both sides by $x$, we get,
$⇒x-8+\frac{1}{x}=0$
$⇒x+\frac{1}{x}=8$
Squaring both sides, we get,
$⇒(x+\frac{1}{x})^2=8^2$
$⇒x^2+\frac{1}{x^2}+2=64$
$\therefore x^2+\frac{1}{x^2}=64-2=62$
Hence, the correct answer is $62$.

Correct Answer: (2)

Solution : The error lies in the second part of the sentence.

The word hanged is incorrect in this context. Both hung and hanged are the past participle forms of the verb hang. The correct verb form to use when suspending or attaching something, like a lamp, is hung.

Hanged is typically used when referring to the act of executing someone by hanging them from a noose, not for hanging objects on a wall.

Therefore, the correct sentence is: The servant hung the lamp on the wall.

Correct Answer: 24 hours

Solution : The correct option is 24 hours.

An orbital period for a geostationary satellite is equal to one sidereal day, which is the length of time it takes for the Earth to complete one rotation of its axis. It takes the Earth around 23 hours, 56 minutes, and 4 seconds to complete one revolution. In other words, a geostationary satellite orbits the planet once in the same amount of time as it takes the planet to rotate once.