CSAT – UPSC Prelims PYQs

In the given figure, if QRS is an equilateral triangle and QTS is an isosceles triangle and x = 47°, then the value (in degrees) of y will be

In the series POQ, SRT, VUW, ?, the blank space refers to

There are three drawers in a table. One contains two gold coins, another two silver coins, and the third, a silver coin and a gold coin. One of the drawers is pulled out and a coin is taken out. It turns out to be a silver coin. What is the probability of drawing a gold coin, if one of the other two drawers is pulled out next and one of the coins in it is drawn at random?

P is 300 km eastward of O and Q is 400 km north of O. R is exactly in the middle of Q and P. The distance between Q and R is

When three coins are tossed together the probability that all coins have the same face up is

The number of students in two sections, A and B, having different heights is shown in the following table: Height (in metres) Number of students with that height in Section A Section B 1.55

3

2

1.60

7

3

1.62

12

14

1.65

15

14

1.68

8

9

1.71

6

5

1.75

3

4

The ratio of the number of students of a particular height in Section A to that in Section B is the maximum for the height of

The following table shows the per cent change in the number of sales (in rupees) at different retail stores in a given neighbourhood market in the period 1993 to 1995: Retail Store — Percent Change 1993 to 1994 — 1994 to 1995 Anshu: +10, -10 Borna: -20, +9 Calpo: +5, +12 Dilip: -7, -15 Elegant: +17, -8 If the sales at Anshu store amounted to Rs. 8 lakhs in 1993, then the number of sales (in lakhs of rupees) at that store in 1995 was

If the number representing volume and surface area of a cube are equal, then the length of the edge of the cube in terms of the unit of measurement will be

The length, breadth and height of a room are l, b and h respectively. The perimeter of the ceiling expressed as a percentage of the total area of the four walls is

Seven persons P, Q, R, S, T, U and V participate in and finish all the events of a series of swimming races. There are no ties at the finish of any of the events. V always finishes somewhere ahead of P. P always finishes somewhere ahead of Q. Either R finishes first and T finishes last or S finishes first and U or Q finishes last. If in a particular race V finished fifth, then which one of the following would be true?

Consider the following:

I. Saxena, David, Jain and Kumar were District Collectors at places P, Q, R and S respectively in 1970. II. In 1972 they were transferred. Saxena and Jain interchanged places. Kumar and David also interchanged places. III. One year later in 1973 they were again transferred such that David and Jain interchanged places and Saxena and Kumar were also interchanged. What should be the next round of transfers so that all the four persons could have been posted at all the four places?

In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujarati. In that group none can speak any other language. If 2 persons in the group can speak two languages and one person can speak all the three languages, then how many persons are there in the group?

Examine the following statements regarding a set of balls: I. All balls are black. II. All balls are white. III. Only some balls are black. IV. No balls are black. Assuming that the balls can only be black or white, which two statements given above can both be true, but cannot both be false?

Choose the correct answer from the codes given below:

A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is

A survey was conducted on a sample of 1000 persons with reference to their knowledge of English, French and German. The results of the survey are presented in the given Venn diagram. The ratio of the number of persons who do not know any of the three languages to those who know all the three languages is

Consider the figures given below:

(In the given sequence of figures, the figure that would logically appear at Sl. No. V is) The original figure is not available for this question.

The number of times in a day the Hour hand and the Minute hand of a clock at right angles is

Examine the following statements:

I. George attends Music classes on Monday. II. He attends Mathematics classes on Wednesday. III. His Literature classes are not on Friday. IV. He attends History classes on the day following the day of his Mathematics classes. V. On Tuesday, he attends his Sports classes. If he attends just one subject in a day and his Sunday is free, then he is also free on

Consider the following figures: (i) a rectangle 4 cm × 9 cm (ii) a square of side 6 cm

(iii) a right-angled triangle with base 8 cm and height 9 cm

Which one of the following conclusions can be drawn from these figures?

In an accurate clock, over a period of 2 hours 20 minutes, the minute hand will move over

Two important characteristics of a hypothesis are that it should be testable and that it should be stated in a manner that it can be refuted.

Which one of the following hypotheses fulfils these characteristics?

If the price of a television set is increased by 25%, then by what percentage should the new price be reduced to bring the price back to the original level?

The given pie charts show the proportion of literates and illiterates in a country, in the year 1970 and 1990 and also the proportion of males (M) and females (F) among the literates.

Which one of the following statements can be said to be beyond any doubt?

If A = x² − y², B = 20 and x + y = 10, then

Six roads lead to a country. They may be indicated by letters X, Y, Z and digits 1, 2, 3. When there is storm, Y is blocked. When there are floods X, 1 and 2 will be affected. When road 1 is blocked, Z also is blocked. At a time when there are floods and a storm also blows, which road(s) can be used?

Which one of the following Venn diagrams correctly illustrates the relationship among the classes: Carrot, Food, Vegetable?

When the frequency distribution is normal

In the given figure, the triangle represents girls, the square represents sportspersons and the circle represents coaches. The portion in the figure which represents girls who are sportspersons but not coaches is the one labelled

The next pair of letters in the series AZ, CX, FU, ...... is

Mouse is to cat as fly is to

The average of X1, X2 and X3 is 14. Twice the sum of X2 and X3 is 30. What is the value of X1?

A rectangle has a perimeter of 50 metres. If its length is 13 metres more than its breadth, then its area is

Two packs of cards are thoroughly mixed and shuffled and two cards are drawn at random, one after the other. What is the probability that both of them are Jacks?

A man starts walking in the north-easterly direction from a particular point. After walking a distance of 500 metres, he turns southward and walks a distance of 400 metres. At the end of this walk he is situated

Examine the following statements: I. All children are inquisitive. II. Some children are inquisitive. III. No children are inquisitive. IV. Some children are not inquisitive.

Among these statements, the two statements which cannot both be true simultaneously but can both be false would be

Consider the series given below: 4/12/95, 1/1/96, 29/1/96, 26/2/96... The next term of the series is

In track meets both 100 yards and 100 metres are used as distances. By how many metres is 100 metres longer than 100 yards?

Examine the following statements: I watch TV only if I am bored.

I am never bored when I have my brother’s company. Whenever I go to the theatre, I take my brother along.

Which one of the following conclusions is valid in the context of the above statements?

In the given diagram, circle A represents teachers who can teach Physics, circle B represents teachers who can teach Chemistry and circle C represents those who can teach Mathematics. Among the regions marked p, q, r, s, t, u and v, the one which represents teachers who can teach Physics and Mathematics but not Chemistry, is

Seven men, A, B, C, D, E, F and G are standing in a queue in that order. Each one is wearing a cap of a different colour like violet, indigo, blue, green, yellow, orange and red. D is able to see in front of him green and blue but not violet. E can see violet and yellow, but not red. G can see caps of all colours other than orange. If E is wearing an indigo-coloured cap, then the colour of the cap worn by F is

A person travelled from one place to another at an average speed of 40 kilometres/hour and back to the original place at an average speed of 50 kilometres/hour. What is his average speed in kilometres/hour during the entire roundtrip?

The value of (a – m)(b – m) … (y – m)(z – m) is

A rectangular sump of dimensions 6 m × 5 m × 4 m is to be built by using bricks to make the outer dimension 6.2 m × 5.2 m × 4.2 m. Approximately how many bricks of size 20 cm × 10 cm × 5 cm are required to build the sump for storing water?

Consider the figure given below: PQRS is a square of side 1 unit and Q, S are the centres of the two circles. The area of the shaded portion is

A thief running at 8 km/hr is chased by a policeman whose speed is 10 km/hr. If the thief is 100 metres ahead of the policeman, then the time required for the policeman to catch the thief will be

A student has 60% chance of passing in English and 54% chance of passing in both English and Mathematics. What is the percentage probability that he will fail in Mathematics?

One of the drawers is opened at random and a coin is drawn. It is found to be a silver coin. What is the probability that the other coin in the drawer is a gold coin?

In the Cartesian plane four points P, Q, R, S have coordinates (1, 1), (4, 2), (4, 4) and (1, 4). The area of the quadrilateral PQRS is

Consider the table given below providing details of traffic volume per hour for four locations (showing total traffic volume, % of heavy vehicles, average noise level in dB(A) and noise-pollution level in dB(A)). When the total traffic volume is the same, the factor(s) which affect(s) the noise-pollution level is/are

X and Y are two variables whose values at any time are related to each other as shown in Fig. (i). X is known to vary periodically with reference to time as shown in Fig. (ii).

Which of the following curves depicts correctly the dependence of Y on time?