Which of the following is a rational number?
\((\sqrt{2}+\sqrt{5})^2\)
2 +\(\sqrt{5}\)
2 -\(\sqrt{5}\)
\(\left(\sqrt{2}+\frac{1}{\sqrt{8}}\right)^2\)
The Vijayanagara empire was founded in the:
India secured the _____ rank on Global Innovation Index 2020.
Study the following information carefully and answer the question that follows.
The following are the eligibility criteria for becoming a member of a library.
(i) The applicant should be able to pay a one-time membership fee of ₹10,000 and contribute two books worth ₹500.
(ii) The one-time membership fee is relaxed up to 50% if the applicant donates books worth ₹5,000 in total.
(iii) For school students, membership fee is relaxed till the age of 18 years.
(iv) Serving school teachers are required to pay only ₹2,000 if they help 20 students to become members of the library.
(v) Only for serving Defence personnel and their wards, the membership of the library is free of cost.
Data/information about an individual is given. You have to decide, based on the information provided, under which criterion/criteria is the individual eligible, if so, to get a membership. Please note that an individual can be eligible under more than one criteria. You are not to assume anything other than the information provided in each question.
Mr. A is 30-years-old and the son of a retired army officer. He is ready to pay a membership fee of ₹10,000 and contribute two books worth ₹500.
Eligible only under (v)
Not eligible
Eligible only under (i)
Eligible only under (ii) and (v)
In the following Venn diagram, the rectangle represents engineers, the circle represents the people who live in urban areas and the triangle represents the people who are in government jobs. Which letter represents engineers who live in urban areas and are in government jobs?
A vehicle before overhauling requires \( \frac{5}{6} \) h service time every 90 days, while after overhauling it requires \( \frac{5}{6} \) h service time every 120 days. What fraction of the pre-overhauling services time is saved in the latter case?
\( \frac{1}{4} \)
\( \frac{1}{6} \)
\( \frac{1}{3} \)
\( \frac{1}{2} \)