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UPSC Mathematics Optional for IAS and IFoS

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CSAT Model Test Series Practice Set – 4

CSAT Model Test Series Practice Set - 4 1

1. Two trains leave New Delhi at the same time. One travels north at 60 kmph and the other travels south at 40 kmph. After how many hours will the trains be 150 km apart?
(a)1.5  (b)8.5
(c)0.75  (d) 7.5

2. Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X?
(a) 8%   (b) 9%
(c) 10%  (d) 12%

3. A person traveled a distance of 50 km in 8 hours. He covered a part of the distance on foot at the rate of 4 km per hour and a part on a bicycle at the rate of 10 km per hour. How much distance did he travel on foot?
(a) 10 km  (b) 20 km
(c) 30 km  (d) 40 km

4. There is a family of 6 persons A, B, C, D, E and F. There are two married couples in the family. The family members are lawyer, teacher, salesman, engineer, accountant and doctor. D, the salesman is married to the lady teacher. The doctor is married to the lawyer. F, the accountant is the son of B and brother of E. C, the lawyer is the daughter-in-law of A. E is the unmarried engineer. A is the grandmother of F. how is E related to F?
(a) Brother  (b) Sister
(c) Father   (d) Can’t be determined

5. In an examination, there are three subjects A, B and C. A student has to pass in each subject. 20% students failed in A, 22% students failed in B and 16% failed in C. The total number of students passing the whole examination lies between
(a) 42% and 84%  (b) 42% and 78%
(c) 58% and 78%  (d) 78% and 84%

6. Half of the villagers of a certain village have their own houses. one-fifth of the villagers cultivate paddy. one-third of the villagers are literate. Four-fifth of the villagers are below twenty five. Then, which one of the following is certainly true?
(a) All the villagers who have their own houses are literate.
(b) Some villagers under twenty five are literate.
(c) A quarter of the villagers who have their own houses cultivate paddy.
(d) Half of the villagers who cultivate paddy are literate.

7. A man fills a basket with eggs in such a way that the number of eggs added on each successive day is the same as the number already present in the basket. This way the basket gets completely filled in 24 days. After how many days the basket was 1/4th full?
(a) 6  (b) 12
(c) 17  (d) 22

8. A candidate attempted 12 questions and secured full marks in all of them. If he obtained 60% in the test and all questions carried equal marks, then what is the number of questions in the test?
(a) 36  (b) 30
(c) 25  (d) 20

9. In how many ways can four children be made to stand in a line such that two of them, A and B are always together?
(a) 6   (b) 12
(c) 18  (d) 24

10. In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?
(a) 9    (b) 12
(c) 14  (d) 18

PASSAGE: But man is not destined to vanish. He can be killed, but he cannot be destroyed, because his soul is deathless and his spirit is irrepressible. Therefore, though the situation seems dark in the context of the confrontation between the superpowers, the silver lining is provided by amazing phenomenon that the very nations which have spent incalculable resources and energy for the production of deadly weapons are desperately trying to find out how they might never be used. They threaten each other, intimidate each other and go to the brink, but before the total hour arrives they withdraw from the brink.

11. The main point from the author’s view is that
(a) Man’s soul and spirit cannot be destroyed by superpowers.
(b) Man’s destiny is not fully clear or visible.
(c) Man’s soul and spirit are immortal.
(d) Human society will survive despite the serious threat of total annihilation.

12. The phrase ‘Go to the brink’ in the passage means
(a) Retreating from extreme-danger.
(b) Declare war on each other.
(c) Advancing to the stage of war buy not engaging in it.
(d) Negotiate for peace.

13. In the author’s opinion
(a) Huge stockpiles of destructive weapons have so far saved mankind from a catastrophe.
(b) Superpowers have at last realized the need for abandoning the production of lethal weapons.
(c) Mankind is heading towards complete destruction
(d) Nations is possession of huge stockpiles of lethal weapons are trying hard to avoid actual conflict.

14. ‘Irrepressible’ in the second line means.
(a) Incompatible  (b) Strong
(c) Oppressive  (d) Unrestrainable

15. A suitable title for the above passage is
(a) Destruction of mankind is inevitable.
(b) Man’s desire to survive inhibits use of deadly weapons.
(c) Mounting cost of modern weapons.
(d) Threats and intimidation between super powers.

Passage: The Indian telecommunication industry is the world’s fastest growing industry with 811.59 million mobile phone subscribers as of March 2011. It is also the second largest telecommunication network in the world in terms of number of wireless connections. As the fastest growing telecommunications industry in the world, it is projected that India will have 1.159 billion mobile subscribers by 2013. Furthermore, projections by several leading global consultancies indicate that the total number of subscribers in India will exceed the total subscriber count for wireless connections in China by 2013.

The industry is expected to reach a size of 344,921 crore (US$76.57 billion) by 2012 at a growth rate of over 26 per cent, and generate employment opportunities for about 10 million people during the same period. According to analysts, the sector would create direct employment for 2.8 million people and for 7 million indirectly. In 2008-09 the overall telecom equipments revenue in India stood at 136,833 crore (US$30.38 billion) during the fiscal, as against 115,382 crore (US$25.61 billion) a year before. A large population, low telephony penetration levels, and a rise in consumer spending power have helped make India the fastest-growing telecom market in the world.

The market’s first operator was the state- owned Bharat Sanchar Nigam Limited (BSNL), created by corporatization of the Indian Telecommunication Service, a government unit formerly responsible for provision of telephony services. Subsequently, after the telecommunication policies were revised to allow private operators, companies such as Bharti Airtel, Reliance Communications, Tata lndicorn, Idea Cellular, Aircel and Loop Mobile have entered the market (Bharti Airtel currently being the largest telecom company in India). In the fiscal year 2008-09, rural India outpaced urban India in mobile growth rate. The total number of telephones in the country stands at 846.32 million, while the overall tele-density has increased to 70.89% as of March 31st, 2011. Mobile telephony experiences growths at rates such as 20.21 million subscribers a month, which were added in March 2011. Telecom in the real sense means the transfer of information between two distant points in space.

The popular meaning of telecom always involves electrical signals and as a result, people often exclude postal or any other raw telecommunication methods from its meaning. Therefore, the history of Indian telecom can be started with the introduction of telegraph. I ‘he Indian postal and telecom sectors saw a slow and uneasy start. In 1850, the first experimental electric telegraph line was started between Kolkata and Diamond Harbor. In 1851, it was opened for the use of the British East India Company.

The Posts and Telegraphs department occupied a small corner of the Public Works Department, at that time. Subsequently, the construction of 4,000 miles (6,400 km) of telegraph lines connecting Kolkata (then Calcutta) and Peshawbetween Kolkata and Diamond Harbor. In 1851, it was opened for the use of the British East India Company. The Posts and Telegraphs department occupied a small corner of the Public Works Department, at that time. Subsequently, the construction of 4,000 miles (6,400 km) of telegraph lines connecting Kolkata (then Calcutta) and Peshawar in the north along with Agra, Mumbai (then Bombay) through Sindwa Ghats, and Chennai (then Madras) in the south, as well as Ootacamund and Bangalore was started in November 1853. Dr. William O’Shaughnessy, who pioneered the telegraph and telephone in India, belonged to the Public Works Department, and worked towards the development of telecom throughout this period. A separate department was opened in 1854 when telegraph facilities were opened to the public.

In 1880, two telephone companies namely The Oriental Telephone Company Ltd. and The Anglo- Indian Telephone Company Ltd. approached the Government of India to establish telephone exchanges in India. The permission was refused on the grounds that the establishment of telephones was a Government monopoly and that the Government itself would undertake the work. In 1881, the Government later reversed its earlier decision and a license was granted to the Oriental Telephone Company Limited of England for opening telephone exchanges at Calcutta, Bombay, Madras and Ahmadabad and the first formal telephone service was established in the country. On 28th January 1882, Major E. Baring, Member of the Governor General of India’s Council declared open the Telephone Exchanges in Calcutta, Bombay and Madras. The exchange in Calcutta, named the “Central Exchange”, was opened at third floor of the building at 7, Council House Street, with a total of 93 subscribers. Later that year, Bombay also witnessed the opening of a telephone exchange.

16. “The permission was refused on the grounds that the establishment of telephones was a Government monopoly and that the Government itself would undertake the work”. what does the phrase “On the grounds that” mean in the above sentence?
(a) On the playing ground where permission is required
(b) On the basis that
(c) Refused
(d) According to procedure

17. Which of the following statements from the passage is false?
(a) In 2008-09 the overall telecom equipments revenue in India stood at 136,833 crore.
(b) India is the second largest telecommunication network in the world in terms of number of wired connections.
(c) The market’s first operator was the state owned Bharat Sanchar Nigam Limited.
(d) Mobile telephony experiences growths at rates such as 20.21 million subscribers a month, which were added in March 2011.

18. Which of the following statements from the passage is true?
(a) (a) The exchange in Calcutta was named the “Calcutta Exchange”
(b) India will have 1,159,000,000 mobile subscribers by 2013.
(c) Bharti Airtel is the smallest telecom company in India
(d) Reliance Communications is the largest telecom company in India

19. From the passage which of the following features of a market enables a favourable environment for the growth of the telecom industry?
(a) Large population
(b) Increase in consumer spending power
(c) Low telephony penetration levels
(d) All of the above

20. The posts and Telegraphs department was originally a part of which department?
(a) Communications Department
(b) Telecommunications Department
(c) Public Works Department
(d) No Department

Directions: Study the following information carefully and answer accordingly: There are 200 students in graduation. Out of these 165 are supposed to study at least one of the subjects from among Physics, Chemistry and Mathematics. 110 students study Physics, 80 students study Chemistry and 90 students Mathematics. 40 student study Physics and Chemistry but not Mathematics, 35 students study Physics and Mathematics but not Chemsistry and 20 students study Chemistry and Mathematics but not Physics.

21. How many students study all three subjects?
(a) 10  (b) 12
(c) 15  (d) Can’t be determined

22. What is the percentage of those students who study all the three subjects with respect to those admitted in graduation?
(a) 5.40%  (b) 6.06%
(c) 4%    (d) None of these

Directions: The following questions are accompanied by three statements (I),(II) and (III). You have to determine which statements (s) is/are sufficient/necessary to answer the questions.

23. To find the number which of the following statement (s) is/are sufficient/necessary?
I. The ratio between a two-digit number and the sum of the digits of that number is 5 : 2
II. The digit in ten’s place is 4 less than the digit in unit’s place.
III. The sum of the squares of the two digits is 26.
(a) Only I  (b) Only I and II
(c) Any two (d) All I, II and III

24. A cuboid has six sides of different colours. The red side is opposite to black. the blue side is adjacent to white. The brown side is adjacent to blue. The red side is face down. Which one of the following would be the opposite to brown?
(a) Yellow  (b) Black
(c) White  (d) Blue

25. In a carom board game competition, m boys and n girls (m > n > 1) of a school participate in which every student has to play exactly one game with every other student. Out of the total games played, it was found that in 221 games one player was a boy and the other player was a girl.
Consider the following statements:
I. The total number of students that participated in the competition is 30.
II. The number of games in which both players were girls is 78.
Which of the statements given above is/are correct?
(a) only I  (b) only II
(c) Both I and II  (d) Neither I nor II

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