Correct Answer: Neither conclusion I nor II follows

Solution : The possible Venn diagram according to the given statement is as follows –

Let's analyse the conclusions –
Conclusion I: Some cats are chairs – From the Venn diagram, it is evident that there is no direct relation between cats and chairs. So, no definite relation can be drawn. Thus, this conclusion does not follow.
Conclusion II: Some chairs are not paper – It is a possibility that the circle representing chairs is not completely overlapped by the circle representing papers. But this is not definite. Thus, this conclusion does not follow.

So, neither conclusion I nor II follows. Hence, the fourth option is correct.

Correct Answer: U

Solution : Given:
 (I) P scored the second-highest marks in the class. Marks scored by V were more than only one of the persons.
_ > P > _ > _ > _ > V > _   
(II) S's score was more than T but less than P. Three people got higher than T and three got lesser than T. Neither R nor Q received the lowest marks. Given that no two students have the same marks.
R/Q > P > S > T > R/Q > V > U

So, U scores the lowest marks. Hence, the second option is correct.

Correct Answer: T13S

Solution : Given:
K4N : P9N :: A5Z : B11D :: P6R : ?

Like, K4N : P9N –

And, A5Z : B11D –

Similarly, follow the same pattern for P6R –

Thus, P6R is coded as T13S. Hence, the first option is correct.

Correct Answer: OV3LA

Solution : Given:
PASTA is written as AP19AT.

Interchange the position of the first letter with the second letter and the fourth letter with the fifth letter and write the place value of the middle letter of PASTA, to obtain the required code –

Thus, PASTA is coded as AP19AT.
Similarly, follow the same pattern for VOCAL –

Thus, VOCAL is coded as OV3LA in the code language. Hence, the third option is correct.

Correct Answer: HP

Solution : Given:
DH, EJ, FL, GN, ?

In the above-given series, add 1 and 2 to the place values of the first and second letters of the letter clusters.
DH→D + 1 = E; H + 2 = J
EJ→E + 1 = F; J + 2 = L
FL→F + 1 = G; L + 2 = N
GN→G + 1 = H; N + 2 = P

So, HP is the missing term of the series. Hence, the fourth option is correct.

Correct Answer: 343

Solution : Given:
7 : 125 :: 8 : 216 :: 9 : ?

Subtract 2 from the first number, and then find the cube of the resultant, to get the second number –
Like, 7 : 125→7 – 2 = 5; (5)³ = 125
And, 8 : 216→8 – 2 = 6; (6)³ = 216
Similarly, follow the same pattern for, 9 : ?→9 – 2 = 7; (7)³ = 343

So, 343 is related to 9. Hence, the third option is correct.

Correct Answer: 300

Solution : Given: The ratio of P, Q, and R is 2 : 5 : 7 respectively.
Their sum is 840.
Let the required number be $2x$, $5x$ and $7x$ respectively.
According to the question,
⇒ $2x+5x+7x=840$
⇒ $14x=840$
⇒ $x=60$
The difference between P and R $=7x-2x=5x=5\times 60=300$
Hence, the correct answer is 300.

Correct Answer: 121

Solution : Given:
100, 105, 92, 113, 84, ?

In the above-given series, add and subtract alternately, the natural numbers with the difference of 8 to the numbers.
100 + 5 = 105;
105 – (5 + 8) = 105 – 13 = 92; 
92 + (13 + 8) = 92 + 21 = 113;
113 – (21 + 8) = 113 – 29 = 84;
84 + (29 + 8) = 84 + 37 = 121

So, 121 is the missing number. Hence, the third option is correct.

Correct Answer: Operating system

Solution :  The correct answer is the Operating system.

Booting is the initial process that initiates the operating system of a computer upon powering it up. This involves loading the operating system into the computer's primary memory, known as Random Access Memory (RAM).

Correct Answer: formed, they eventually becomes

Solution : The error lies in the first option.

• The part of the given sentence that has an error is becomes. The correct form should be become. 
• The subject mountains are plural, so the verb become should also be in the plural form to agree with the subject.

Therefore, the correct sentence should be: "No matter how mountains are formed, they eventually become too heavy and succumb to gravity."