CSAT › Quantitative Aptitude – UPSC Prelims PYQs
174 questions · 1995–2010 · answers as per the UPSC key · page 3 of 4
Solve the given equations: x² + y² = 34 x⁴ − y⁴ = 544 The values of x and y are
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A worker reaches his factory 3 minutes late if his speed from his house to the factory is 5 km/hr. If he walks at a speed of 6 km/hr, then he reaches the factory 7 minutes early. The distance of the factory from his house is
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A conveyer belt delivers baggage at the rate of 3 tons in 5 minutes, and a second conveyer belt delivers baggage at the rate of 1 ton in 2 minutes. How much time will it take to get 33 tons of baggage delivered using both the conveyer belts?
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Water is filled in a container in such a manner that its volume doubles after every five minutes. If it takes 30 minutes for the container to be full, in how much time will it be one-fourth full?
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A city has a population of 3,00,000 out of which 1,80,000 are males. 50% of the population is literate. If 70% of the males are literate, the number of literate females is
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In a survey, it was found that 80% of those surveyed owned a car while 60% of those surveyed owned a mobile phone. If 55% owned both a car and a mobile phone, what per cent of those surveyed owned a car or a mobile phone or both?
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In 1930, a person’s age was 8 times that of his son. In 1938, the father’s age became ten times that of his son’s age in 1930. The ages of the son and father in 1940 were, respectively.
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A circle of 1 m radius is drawn inside a square as shown in the figure given above. What is the area of the shaded portion in m²?
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In the above figure, ABCD is a cyclic quadrilateral, AB = BC and angle BAC = 70°, then angle ADC is
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A person travels from X to Y at a speed of 40 kmph and returns by increasing his speed by 50%. What is his average speed for both the trips?
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A rectangular water tank measures 15 m × 6 m at top and is 10 m deep. It is full of water. If water is drawn out lowering the level by 1 metre, how much of water has been drawn out?
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An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?
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The monthly income of Komal and Asha are in the ratio of 4 : 3. Their monthly expenses are in the ratio of 3 : 2. However, both save Rs. 600 per month. What is their total monthly income?
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If X = –2, then X³ – X² – X – 1 is equal to
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In the given figure, all line segments of the shaded portion are of the same length and at right angles to each other. The same can be cut out of a board of side 10 cm. What is the area of the shaded portion?
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In a class there are 18 boys who are over 160 cm tall. If these boys constitute three fourths of the boys and the total number of boys is two third of the number of students in the class, then what is the number of girls in the class?
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A rectangular piece of iron sheet measuring 50 cm by 100 cm is rolled into a cylinder of height 50 cm. If the cost of painting the cylinder is Rs. 50 per square metre, then what will be the cost of painting the outer surface of the cylinder?
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In an examination, every candidate took Physics or Mathematics or both. 65.8% took Physics and 59.2% took Mathematics. The total number of candidates was 2000. How many candidates took both Physics and Mathematics?
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A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blind-folded (without replacing any of it) to be assured of picking at least one ball of each colour?
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Which one of the following has a greater perimeter than the rest?
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In the given figure, angle QOP = 30° and angle ORP = 20°, angle QOR is equal to
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A club has 108 members. Two-thirds of them are men and the rest are women. All members are married except for 9 women members. How many married women are there in the club?
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What is the maximum number of pieces of 5 cm × 5 cm × 10 cm cake that can be cut from a big cake of 5 cm × 30 cm × 30 cm size?
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In the sequence of numbers 5, 8, 13, X, 34, 55, 89, ……… the value of ‘X’ is
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The average speed of a train in the onward journey is 25% more than that of the return journey. The train halts for one hour on reaching the destination. The total time taken for the complete to-and-fro journey is 17 hours covering a distance of 800 km. The speed of the train in the onward journey is
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In a town 25% families own a phone and 15% own a car. 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard: I. 10% families own both a car and a phone. II. 35% families own either a car or a phone. III. 40,000 families live in the town.
Which of the above statements are correct?
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A man is standing on the 8 m long shadow of a 6 m long pole. If the length of his shadow is 2.4 m, what is the height of the man?
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If the angles of a triangle are in the ratio of 4 : 3 : 2, then the triangle
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The surface area of a spherical dome-shaped roof of a cylindrical water tank shown in the figure is The original figure is not available for this question.
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If X + 2Y = 2X + Y, then X² / Y² is equal to
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A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is the same for both bowl and cylinder, then the volume of the beverage in the cylindrical vessel will be
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At a given time, two players are standing on a play-field. The cartesian coordinates of their locations are (20, 60) and (-40, -20) units. What is the distance between the players?
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The area of an ellipse is twice that of a circle. The major diameter of the ellipse is twice that of the minor diameter. The radius of the circle is
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Amar, Akbar and Anthony are friends, being looked after by a matron Farah. Amar weighs 50% more than Akbar and Anthony weigh 25% less than Amar. Farah weighs a third of the combined weight of the three boys. All four together weigh 232 kg. The correct arrangement of the persons in the ascending order of their weights is
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LMNOP is a semi-circle with centre at R and diameter LP; LSR and RQP are also semi-circles with centres at T and U and diameters LR = RP = 1⁄2 LP. The ratio of perimeters of LMNOP and LSRQP is
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A man purchases two clocks A and B at a total cost of Rs 650. He sells A with 20% profit and B at a loss of 25% and gets the same selling price for both the clocks. What are the purchasing prices of A and B respectively?
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If 15 pumps of equal capacity can fill a tank in 7 days, then how many extra pumps will be required to fill the tank in 5 days?
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Out of the three annual examinations, each with a total of 500 marks, a student secured average marks of 45 % and 55 % in the first and second annual examinations. To have an overall average of 60 %, how many marks does the student need to secure in the third annual examination?
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A square pond has 2 m sides and is 1 m deep. If it is to be enlarged, the depth remaining the same, into a circular pond with the diagonal of the square as diameter as shown in the figure, then what would be the volume of earth to be removed?
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One local and another express train were proceeding in the same direction on parallel tracks at 29 km/hour and 65 km/hour respectively. The driver of the former noticed that it took exactly 16 seconds for the faster train to pass by him. What is the length of the faster train?
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In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is nine years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?
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There are 50 students admitted to a nursery class. Some students can speak only English and some can speak only Hindi. Ten students can speak both English and Hindi. If the number of students who can speak English is 21, then how many students can speak only Hindi and how many can speak only English?
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An accurate clock shows the time as 3 : 00. After the hour hand has moved 135°, the time would be
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A rectangular plot of lawn shown in the figure has dimensions x and y and is surrounded by a gravel pathway of width 2 m. What is the total area of the pathway? The original figure is not available for this question.
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The average monthly income of a person in a certain family of 5 is Rs. 1000. What will be the monthly average income of a person in the same family if the income of one person increased by Rs. 12,000 per year?
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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
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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?
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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
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When three coins are tossed together the probability that all coins have the same face up is
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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