Correct Answer: 55, 22, 99, 33

Solution : Given:
REST

Number representations of each letter:
R → 10, 55, 98
E → 02, 22, 43, 85, 56, 68
S → 41, 23, 14, 69, 99
T → 31, 33, 76, 96

First option: 55, 43, 23, 69
T cannot be represented as 69. Hence, it's incorrect.

Second option: 98, 56, 31, 77
S cannot be represented as 31; T cannot be represented as 77. Hence, it's incorrect.

Third option: 10, 02, 69, 88
T cannot be represented as 88. Hence, it's incorrect.

Fourth option: 55, 22, 99, 33
All the letters of the word REST can be represented through this option. Hence, it's correct.

Hence, the fourth option is correct.

Correct Answer: public and private sector industries

Solution : The correct answer is public and private sector industries.

Government agencies and capital-contributing private citizens jointly own joint-sector businesses. In the joint sector, public and private sectors work together to launch new businesses. A mixed economy is expanded upon by the joint sector. The entities that have received investments from the public and private sectors, along with those in which the state actively participates in direction and control, would be considered members of the joint sector.

Correct Answer: Frantick

Solution : The correct choice is the second option.

The misspelt word is frantick, which should be spelt as frantic. The incorrect spelling contains an extra letter "k".

Correct Answer: Cornwallis .

Solution : Correct Answer is Cornwallis .

In India, he envisioned the emergence of a class of hereditary landlords. The East India Company, led by Governor-General Lord Cornwallis, implemented The Permanent Settlement of Bengal in 1793. Essentially, the company and the zamindars had an agreement to fix the land revenue.The Zamindari System was another name for this system.  

Correct Answer: intervention

Solution : The first option is the correct answer for the sentence because 'intervention' means 'involvement' which contextually fits in the sentence and makes the explanation of the sentence as 'our nation could face a crisis if got into another war'.

'Intention' means a plan for an action; 'perfection' means excellence or flawlessness; and 'invention' means to create something new; all of which do not fit in with the context of the sentence.

Therefore, the complete statement should be "Our nation's intervention into another war could pull us into the crisis."

Correct Answer: $1:4$

Solution : Given: A certain distance is covered by a cyclist at a certain speed. If a jogger covers half the distance in double the time.
We know the formula, $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$
Let the cyclist travel at $x$ km/h and the distance to be covered takes $y$ hours.
So, the cyclist covered $xy$ km.
Jogger's distance travelled is $\frac{xy}{2}$ km.
The time is $2y$ hours.
The ratio of the speed of the jogger to that of the cyclist is $\frac{xy}{2\times 2y}:x$ or $1:4$
Hence, the correct answer is $1:4$

Correct Answer: up

Solution : The fourth option is the correct answer: up.

The phrasal verb "back up" means to support someone and this is the only sentence that fits the sentence appropriately. 

Therefore, the answer is "Do your best and we'll back you up."

Correct Answer: CBDA

Solution : The correct choice will be the second option.

C. Mechanical production of goods leads to uniformity of design.
B. However, uniformity does not imply a lack of taste.
D. In fact, popular taste has improved because standardised goods of better design are now accessible.
A. Expert designers standardise basic designs, leaving scope for the satisfaction of individual taste.

Therefore, the correct answer will be CBDA.

Correct Answer: 220 sec

Solution : P beats Q by 120 metres or 30 sec, which means Q covers 120 m in 30 sec.
Speed of Q = $\frac{120}{30}=4$ m/s
Time taken to cover 1000 m = $\frac{1000}{4} = 250$ sec
P beats Q by 30 seconds, which means P reached 30 seconds early.
Time taken by P to complete the race = 250 – 30 = 220 sec.
Hence, the correct answer is 220 sec.

Correct Answer: Carbon dating

Solution : The correct option is Carbon dating.

The process of using radiation to establish the age of prehistoric items is known as "radiocarbon dating" or "carbon dating." This approach estimates the age of organic materials by using the decay of radioactive carbon isotopes. It specifically examines the decay of carbon-14 (14C) to determine how long the substance has been in a live body.