Correct Answer: 36.5%

Solution :  Total students in P and R = Students in P + Students in R
=  8000 + 15000 = 23000
Students in Mathematics in P and R =
=  30% of 8000 + 40% of 15000
=  0.3 × 8000 + 0.4 × 15000
=  2400 + 6000 = 8400
Required percentage = $\frac{\text{Students in Mathematics in P and R​}}{\text{Total students in P and R}}$×100%
= $\frac{\text{8400​}}{\text{23000}}$×100%
= 36.5%
Hence, the correct answer is 36.5%.

Correct Answer: To work fast

Solution : The second option is correct.

The given idiom, work against the clock, means to do it as fast as possible and try to finish it before a certain time.

Therefore, the correct answer is to work fast.

Correct Answer: 2.1-2.9

Solution : The correct answer is 2.1-2.9.

According to the 2011 Census, India's Total Fertility Rate (TFR)* was 2.4 per woman. The majority of Indian states now have fertility rates far below the replacement level of 2.1, and the nation is rapidly reaching the replacement level itself, according to recent research and surveys.

Correct Answer: India

Solution : The correct answer is India.

With its lush meadows and tropical woods, India is the only country in the world where one may witness both tigers and lions roaming freely. The country is home to both species, but they never come into contact in the wild because lions are restricted to Gir Forest National Park.

Correct Answer: mild sweet due to low sulphur content

Solution : The correct option is mild sweet due to low sulphur content.

Sweet crude oil is a type of oil that contains only 1% sulphur. The term "sweet" is used to describe its mild and pleasant smell, unlike sour crude, which has a higher sulphur content and a less pleasant odour. Refineries prefer sweet crude oil because it requires less processing to remove sulphur impurities, resulting in cleaner end products.

Correct Answer: and on many evenings he helps me with the

Solution : The correct choice is the second option.

Explanation: The sentence requires consistency in verb tense between the two clauses connected by "and". The initial part of the sentence, "he lights his pipe", is in the present tense. Therefore, to maintain consistency, the verb in the second clause should also be in the present tense.

So, the correct sentence would be: "He lights his pipe, and on many evenings he helps me with the dishes."

Correct Answer: Disclose

Solution : The correct choice is the fourth option.

Explanation: The hint here is to look for a word that has a similar meaning to reveal, which implies making something known or showing something that was previously hidden. Disclose fits this context perfectly, as it means to make information known or reveal something that was previously kept secret.

The meaning of the other options is as follows:

• Curb: This word means to restrain or control.
• Veil: This word means to cover or conceal.
• Darken: This word means to make something less bright or clear.

Therefore, the correct answer is disclose.

Correct Answer: gi

Solution : Given:
(I) life and love⇒ri ti gi
(II) life is tangible⇒mi pi ri
(III) love is pure⇒mi gi oi

By comparing all the three coded sentences, we find that –
In sentences I and II, life and ri are common.
In sentences I and III, love and gi are common.
In sentences II and III, is and mi are common.
The remaining word and codes in sentence 1 are and and ti; in sentence 2 are tangible and pi; in sentence 3 are pure and oi.
Finally, life⇒ri; love⇒gi; is⇒mi; and⇒ti; tangible⇒pi; pure⇒oi

So, the love is coded as gi. Hence, the first option is correct.

Correct Answer: 15

Solution : According to the question
 Prime numbers between 9 and 22:  are 11, 13, 17,19
Average of $n$ observations is given by $\frac{\text{Sum of all observations}}{n}$
⇒  Average = $\frac{(11 + 13 + 17 + 19)}{4}$ =  15
Hence, the correct answer is 15.

Correct Answer: (3)

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

A question tag is a very short clause at the end of a statement that changes the statement into a question. We have a negative statement in the sentence, followed by a negative question tag. It should be replaced with a positive question tag. So, have you? should replace, didn't you?

Therefore, the correct sentence is: You haven't responded to my invitation, have you?