Correct Answer: to the bed

Solution : The error lies in the second option.

The correct preposition to use in this context is to bed rather than to the bed. 

The expression to bed is idiomatic when referring to going to sleep or lying down, and it doesn't require the article the.

Therefore, the correct sentence is," He went to bed with a slight fever".

Correct Answer: $49 \sqrt{3}$ cm²

Solution : Height of an equilateral triangle = $\frac{\sqrt{3}}{2} \times Side$
Area of an equilateral triangle = $\frac{\sqrt{3}}{4} \times Side^2$
So, each side of the triangle = $\frac{7\sqrt{3}}{\frac{\sqrt{3}}{2}}$ = 14 cm
Area of an equilateral triangle = $\frac{\sqrt{3}}{4} \times 14^2$ = $49\sqrt{3}$ cm²
∴ The area of this equilateral triangle is $49\sqrt{3}$ cm².
Hence, the correct answer is $49\sqrt{3}$ cm².

Correct Answer: 200000

Solution : Given: A mask manufacturing company manufactured an ‘$x$’ number of masks in 2018. It increased its manufacturing capacity by 30% in 2019 and further increased its manufacturing by 15% in 2020.
Mask manufactured in 2019 = $x × \frac{130}{100}$ = $\frac{13x}{10}$
Mask manufactured in 2020 = $\frac{13x}{10} × \frac{115}{100}$
Mask manufactured in 2021 = $\frac{13x}{10}×\frac{115}{100}×\frac{100-40}{100}$ = $\frac{13x}{10}×\frac{23}{20}×\frac{3}{5}$
According to the question,
⇒ $\frac{13x}{10}×\frac{23}{20}×\frac{3}{5} = 179400$
⇒ $x = \frac{179400×10×20×5}{13×23×3}$
$\therefore x = 200000$
Hence, the correct answer is 200000.

Correct Answer: 1

Solution : Given: $xy = -6$ and $x^3+ y^3= 19$ ($x$ and $y$ are integers)
We know the algebraic identity, $(x+y)^3=x^3 + y^3+3xy(x+y)$.
Substitute the given values in the above formula,
⇒ $(x+y)^3=19+3\times(-6)\times(x+y)$
⇒ $(x+y)^3=19-18\times(x+y)$
Let $(x+y)=u$.
⇒ $u^3+18u–19=0$
⇒ $u^3–u^2+u^2–u+19u–19=0$
⇒ $u^2(u–1)+u(u–1)+19(u–1)=0$
⇒ $(u–1)(u^2+u+19)=0$
⇒ $u-1=0$
⇒ $u=1$
⇒ $\frac{1}{x^{–1}}+\frac{1}{y^{–1}}=x+y=1$
Hence, the correct answer is 1.

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.