Correct Answer: idols

Solution : The correct choice is the first option.

Idols: Objects of adoration or worship, often referring to religious or celebrity figures.

The meanings of the other options are as follows:

• Idoles: Not a recognised English word.
• Ideals: Standards or principles that represent a perfect state, often used as a model to aspire to.
• Idles: Not engaged in work, activity, or purpose; inactive or doing nothing.

Therefore, the correct sentence is: They saw the beautiful idols of the gods in the temples.

Correct Answer: Article 21

Solution : The correct answer is Article 21.

The KA Najeeb vs. Union of India case is primarily concerned with a breach of Article 21 of the Indian Constitution. Article 21 of the Indian Constitution provides the right to life and personal liberty, and the courts have construed it to cover a variety of human rights and individual liberties.

Correct Answer: 2

Solution : Given: $(x-2)(x-p) = x^2-ax+6$
⇒ $x^2-px-2x+2p=x^2-ax+6$
⇒ $x^2-(p+2)x+2p=x^2-ax+6$
By comparing both sides of the equation,
$p+2=a$
⇒ $a-p=2$
Hence, the correct answer is 2.

Correct Answer: $\frac{80}{9}$

Solution : Time taken by A alone to do the work = 15
Work done by A alone in a day = $\frac{1}{15}$
Work done by A in the first and last two days = $\frac{4}{15}$
Work done by B in 16 days = 1 – $\frac{4}{15}$ = $\frac{11}{15}$
Work done by B alone in a day = $\frac{11}{15×16}$ = $\frac{11}{240}$
Work done by A and B together in a day
= $\frac{1}{15}$+$\frac{11}{240}$
= $\frac{27}{240}$
= $\frac{9}{80}$
$\therefore$ Time taken by A and B together to do the work = $\frac{80}{9}$ days
Hence, the correct answer is $\frac{80}{9}$.

Correct Answer: (3)

Solution : The third option is the correct choice for the sentence.

In this context, avoid noticing is the appropriate phrase because it conveys the idea that we cannot refrain from observing or paying attention to the building while travelling.

The other options, avoid to look and avoid to noticing, are grammatically incorrect and do not fit the context of the sentence.

Therefore, the correct sentence is: "You can’t avoid noticing the building while travelling."

Correct Answer: Only conclusion III follows

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

Let's analyse the conclusions –
Conclusion (I): No Ruth is Jack – From the Venn diagram, it is evident that there is no direct relation between Ruth and Jack. So, no definite relation can be drawn. Therefore, this conclusion does not follow.
Conclusion (II): Some Ben is Jack – From the Venn diagram, it is evident that there is a negative relation between Ben and Jack. So, this conclusion does not follow.
Conclusion (III): No Ben is Tim – From the Venn diagram, it is evident that all Tim is Jack and no Jack is Ben. So, it can be concluded that no Ben is Tim.

So, the only conclusion III follows. Hence, the second option is correct.

Correct Answer: banks financing pro-environmental projects

Solution : The correct answer is banks financing pro-environmental projects.

"Green banking" refers to banks sponsoring pro-environmental projects and efforts that have a good influence on the environment and contribute to long-term sustainability. Renewable energy, energy efficiency, sustainable agriculture, clean technology, and other environmentally beneficial areas can all be included in these initiatives. Banks play an active role in encouraging environmental protection, and sustainable development by giving financial assistance to such programmes.

Correct Answer: lying

Solution : The correct choice is the third option.

Explanation:

The correct verb form to be used here is the present participle form, which is lying. Thus, to lie should be replaced with lying i.e. gerund form of the verb, to make the sentence grammatically accurate.

Therefore, the correct sentence is: I found my bag lying where I had left it.

Correct Answer: Shahbaz is known to Rahul since childhood.

Solution : The correct choice is the second option.

Passive voice is the voice in which the object experiences an action rather than the object experiencing an action rather than the person that performs the action. Hence, the object in the active sentence becomes the subject in the passive voice.

The structure of the passive voice in the case of the simple present tense is: "Singular object + is + past participle form of the verb + prepositional phrase."

Therefore, the right answer is: "Shahbaz is known to Rahul since childhood."

Correct Answer: $4$

Solution : Given:
$\frac{11-13x}{x}+\frac{11-13y}{y}+\frac{11-13z}{z}=5$
$⇒\frac{11}{x}-\frac{13x}{x}+\frac{11}{y}-\frac{13y}{y}+\frac{11}{z}-\frac{13z}{z}=5$
$⇒\frac{11}{x}+\frac{11}{x}+\frac{11}{x}-39=5$
$⇒11(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})=44$
$\therefore\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{44}{11}=4$
Hence, the correct answer is $4$.