Correct Answer: Cartographer

Solution : The correct choice is the first option.

A cartographer is an individual who engages in the practice or art of making maps. Therefore, "cartographer" is the appropriate one-word substitute for the underlined group of words.

Correct Answer: Sodium thiosulphate

Solution : The correct option is Sodium thiosulphate.

Sodium thiosulfate is used in photography as a fixing agent, especially in traditional film and darkroom processes. It is used to fix or stabilise the developed image on photographic paper by removing unexposed silver halide.

Correct Answer: # = AOO, % = PAM

Solution : Given:
# : CLQ :: NDK : %

Let's check the options –
First option: # = AJS, % = MAM
AJS : CLQ→A + 2 = C; J + 2 = L; S – 2 = Q 
NDK : MAM→N – 1 = M; D – 3 = A; K + 2 = M
Second option: # = AOO, % = PAM
AOO : CLQ→A + 2 = C; O – 3 = L; O + 2 = Q 
NDK : PAM→N + 2 = P; D – 3 = A; K + 2 = M
Third option: # = EIT, % = QBN
EIT : CLQ→E – 2 = C; I + 3 = L; T – 3 = Q 
NDK : QBN→N + 3 = Q; D – 2 = B; K + 3 = N
Fourth option: # = DIS, % = PBN
DIS : CLQ→D – 1 = C; I + 3 = L; S – 2 = Q 
NDK : PBN→N + 2 = P; D – 2 = B; K + 3 = N 

So, a similar pattern in both pairs can be observed only in the second option. Hence, the second option is correct.

Correct Answer: 105°

Solution :
KI = IT and EK = ET
$\angle$ KET = 150°
In $\triangle$ KEI and $\triangle$ TEI,
KI = IT [Given]
EK = ET [Given]
EI = EI [Common]
So, $\triangle$ KEI $\cong$ $\triangle$ TEI,
⇒ $\angle$ KEI = $\angle$ TEI
Now,
$\angle$ KET + $\angle$ KEI + $\angle$ TEI = 360°
⇒ 150° + 2 × $\angle$ TEI = 360°
⇒ 2 $\angle$ TEI = 210°
⇒ $\angle$ TEI = 105°
Hence, the correct answer is 105°.

Correct Answer: FKQDWE

Solution : Given:
SLAIN is written as PKCNU and DENT is written as VPGF.

Follow the pattern to obtain the required code –

Thus, SLAIN is coded as PKCNU.
And, DENT is written as VPGF.

Thus, DENT is coded as VPGF.
Similarly, follow the same pattern for CUBOID –

So, CUBOID is coded as FKQDWE. Hence, the first option is correct.

Correct Answer: Abridgement

Solution : The correct choice is the fourth option.

Abridgement is a term used to describe a version of a larger work that has been condensed. This involves shortening the original work by omitting details while still preserving the essential content and narrative.

The meanings of the other options are as follows:

• Summary: It is a brief statement or account that covers the main points of a piece of writing, a speech, a film, etc., but omits the less important details.
• Precis: It is a concise summary of a text or speech. It focuses on the key points and the structure of the original work.
• Shorts: In the context of films, it means a shortened version of a story, but this isn't a standard literary term like the others.

Correct Answer: 48

Solution : Given: The ratio of the triangle's sides
$=\frac{1}{2} : \frac{1}{3} : \frac{1}{4}$.
$=\frac{1}{2} × 12 : \frac{1}{3} × 12 : \frac{1}{4} × 12$
$=6: 4: 3$
The perimeter of the triangle is $104$ cm.
$\therefore$ The longest length of the triangle = $\frac{104}{6+4+3}×6= 48$ cm
Hence, the correct answer is 48.

Correct Answer: exchange

Solution : The correct choice is the third option.

The word exchange is appropriate in this context as it implies a mutual or reciprocal action of giving and receiving greetings.

People at the marketplace take time from their busy schedules not just to offer greetings but also to receive greetings from friends or neighbours, creating a sense of interaction and connection.

Therefore, the use of exchange in this sentence conveys the idea of a two-way communication of greetings between individuals in the social setting of the marketplace.

Correct Answer: $\frac{1}{2}\left(5+\frac{1}{5}\right)$

Solution : Given: $\sec \theta+\tan \theta=5$ ..... equation1
$\sec^{2}\theta - \tan^{2}\theta =1$
⇒ $(\sec \theta+\tan \theta)(\sec \theta-\tan \theta)=1$
⇒ $\sec \theta-\tan \theta=\frac{1}{5}$......equation2
Adding equation1 and equation2
$2\sec\theta = 5 + \frac{1}{5}$
⇒ $\sec\theta=\frac{1}{2}\left(5+\frac{1}{5}\right)$
Hence, the correct answer is $\frac{1}{2}\left(5+\frac{1}{5}\right)$.

Correct Answer: the postman would be

Solution : The fourth option contains the error.

Would is used to express a past event and is the past tense of will, which is used to predict a future event. Since we are talking about a future event, we should use will instead of would.

Therefore, the correct sentence is: "I am sure that the postman will be coming shortly to deliver the letter."