Quantitative Aptitude — UPSC Prelims Previous Year Questions

Q: In a tournament 14 teams play league matches. If each team plays against every other team once only then how many matches are played?

Q: A question paper had ten questions. Each question could only be answered as True (T) or False (F). Each candidate answered all the questions. Yet, no two candidates wrote the answers in an identical sequence. How many different sequences of answers are possible?

Q: Running at a speed of 60 km per hour, a train passed through a 1.5 km long tunnel in two minutes. What is the length of the train?

Q: A person X has four notes of Rupee 1, 2, 5 and 10 denomination. The number of different sums of money she can form from them is

Q: 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?

Q: A person travelled 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 ?

Q: How many numbers from 0 to 999 are NOT divisible by either 5 or 7?

Q: Each person's performance compared with all other persons is to be done to rank them subjectively. How many comparisons are needed in total, if there are 11 persons?

Q: Three men start together to travel the same way around a circular track of 11 km. Their speeds are 4, 5.5 and 8 kmph respectively. When will they meet at the starting point for the first time?

Q: 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 was the basket 1⁄4th full?

Q: The diameters of two circular coins are in the ratio of 1 : 3. The smaller coin is made to roll around the bigger coin till it returns to the position from where the process of rolling started. How many times did the smaller coin roll around the bigger coin?

Q: The difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2·50. What is the difference between their rates?

Q: When ten persons shake hands with one another, in how many ways is it possible?

Q: A candidate attempted 12 questions and secured full marks in all of them. If he obtained 60% marks in the test and all questions carried equal marks, then what is the total number of questions in the test?

Q: 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?

Q: A person has 4 coins each of different denomination. What is the number of different sums of money the person can form (using one or more coins at a time)?

Q: How many numbers lie between 300 and 500 in which 4 comes only one time?

Q: How many three-digit numbers can be generated from 1, 2, 3, 4, 5, 6, 7, 8, 9 such that the digits are in ascending order?

Q: There are four persons A, B, C, D; and A has some coins. A gave half of the coins to B and 4 more besides. B gave half of the coins to C and 4 more besides. C gave half of the coins to D and 4 more besides. Both B and D end up with same number of coins. How many coins did A have originally?

Q: While adding the first few continuous natural numbers, a candidate missed one of the numbers and wrote the answer as 177. What was the number missed?

Q: Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?

Q: 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

Q: How many times are an hour hand and a minute hand of a clock at right angles during their motion from 1.00 p.m. to 10.00 p.m.?

Q: There are 240 balls and n number of boxes B1, B2, B3, … , Bn. The balls are to be placed in the boxes such that B1 should contain 4 balls more than B2, B2 should contain 4 balls more than B3, and so on. Which one of the following cannot be the possible value of n?

Q: In a carrom 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 : 1. The total number of students that participated in the competition is 30. 2. The number of games in which both players were girls is 78. Which of the statements given above is/are correct ?

Q: What is the number of terms in the series 117, 120, 123, 126, ..., 333?

Q: 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?

Q: Carpenter A can make a chair in 6 hours, carpenter B in 7 hours and carpenter C in 8 hours. If each carpenter works for 8 hours per day, how many chairs will be made in 21 days?

Q: A person purchases 100 pens at a discount of 10%. The net amount of money spent by the person to purchase the pens is Rs 600. The selling expenses incurred by the person are 15% on the net cost price. What should be the selling price for 100 pens in order to earn a profit of 25%?

Q: A schoolteacher has to select the maximum possible number of different groups of 3 students out of a total of 6 students. In how many groups any particular student will be included?

Q: In an examination, 70% of the students passed in the Paper I, and 60% of the students passed in the Paper II. 15% of the students failed in both the papers while 270 students passed in both the papers. What is the total number of students?

Q: March 1, 2008 was Saturday. Which day was it on March 1, 2002?

Q: In how many different ways can all of 5 identical balls be placed in the cells shown above such that each row contains at least 1 ball?

Q: There are 6 different letters and 6 correspondingly addressed envelopes. If the letters are randomly put in the envelopes, what is the probability that exactly 5 letters go into the correctly addressed envelopes?

Q: There are two identical red, two identical black and two identical white balls. In how many different ways can the balls be placed in the cells (each cell to contain one ball) shown above such that balls of the same colour do not occupy any two consecutive cells?

Q: (Each small circle represents a different station) Refer to the figure showing a network between station A and station B. What is the maximum number of different paths that exist between station A and station B?

Q: In how many maximum different ways can 3 identical balls be placed in 12 squares (each ball is placed in the exact centre of a square) shown in the figure above such that they do not lie along the same straight line?

Q: In the figure shown above, what is the maximum number of different ways in which 8 identical balls can be placed in small triangles 1, 2, 3 and 4 such that each triangle contains at least one ball?

Q: Amit has five friends: 3 girls and 2 boys. Amit’s wife also has five friends: 3 boys and 2 girls. In how many maximum different ways can they invite 2 boys and 2 girls such that two of them are Amit’s friends and two are his wife’s friends?

Q: Five balls of different colours are to be placed in three different boxes such that any box contains at least one ball. What is the maximum number of different ways in which this can be done?

Q: All six letters of the name SACHIN are arranged to form different words without repeating any letter in any one word. The words so formed are then arranged as a dictionary. What will be the position of the word SACHIN in that sequence?

Q: Three dice (each having six faces with each face showing one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one die shows the number 2?

Q: Groups, each containing 3 boys, are to be formed out of 5 boys – A, B, C, D and E – such that no one group contains both C and D together. What is the maximum number of different groups?

Q: Each of the 3 persons is to be given some identical items such that the product of the numbers of items received by each of the three persons is equal to 30. In how many maximum different ways can this distribution be done?

Q: Six equidistant vertical lines are drawn on a board. Six equidistant horizontal lines are also drawn on the board cutting the six vertical lines and the distance between any two consecutive horizontal lines is equal to that between any two consecutive vertical lines. What is the maximum number of squares thus formed?

Q: A person has to completely put each of three liquids – 403 litres of petrol, 465 litres of diesel and 496 litres of mobile oil – in bottles of equal size without mixing any of the three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required?

Q: A and B can complete work together in 5 days. If A works at twice his speed and B at half of his speed, this work can be finished in 4 days. How many days would it take for A alone to complete the job?

Q: If all the numbers from 501 to 700 are written, what is the total number of times the digit 6 appears?

Q: Amit starts from a point A, walks to another point B and then returns from B to A by his car, taking a total time of 6 hours 45 minutes. If he had driven both ways in his car, he would have taken 2 hours less. How long would it take for him to walk both ways?

Q: A watch showed a time of fourteen minutes past nine (9 hrs 14 minutes). The positions of the hour-hand and the minute-hand of the watch are exactly interchanged. The new time shown by the watch is closest to which one of the following?

Q: Each of 8 identical balls is to be placed in the squares shown in the figure given above in a horizontal direction such that one horizontal row contains 6 balls and the other horizontal row contains 2 balls. In how many maximum different ways can this be done?

Q: In a tournament each of the participants was to play one match against each of the other participants. 3 players fell ill after each of them had played three matches and had to leave the tournament. What was the total number of participants at the beginning, if the total number of matches played was 75 ?

Q: A box contains 5 sets of balls while there are 3 balls in each set. Each set of balls has one colour which is different from every other set. What is the least number of balls that must be removed from the box in order to claim with certainty that a pair of balls of the same colour has been removed?

Q: 3 digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8 and 9 without repeating any digit. What is the probability that their product is odd?

Q: In a question paper, there are four multiple-choice questions. Each question has five choices with only one choice for its correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

Q: There are three parallel straight lines. Two points A and B are marked on the first line, points C and D are marked on the second line, and points E and F are marked on the third line. Each of these six points can move to any position on its respective straight line. Consider the following statements: 1. The minimum number of triangles that can be formed by joining these points is zero. 2. The maximum number of triangles that can be formed by joining these points is twenty. Which of the statements given above is/are correct?

Q: A mixed doubles tennis game is to be played between two teams (each team consists of one male and one female). There are 4 married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played?

Q: How many numbers are there in all 6000 to 6999 (both 6000 and 6999 included) having at least one of their digits repeated?

Q: Each of 2 women and 3 men is to occupy one chair out of 8 chairs, each of which is numbered from 1 to 8. First, women are to occupy any two chairs from those numbered 1 to 4; and then 3 men would occupy any three chairs out of the remaining 6 chairs. What is the maximum number of different ways in which this can be done?

Q: Left pan of a faulty balance weighs 100 gram more than its right pan. A shopkeeper keeps the weight measure in the left pan while buying goods but keeps it in the right pan while selling his goods. He uses only 1 kg weight measure. If he sells his goods at the listed cost price, what is his gain?

Q: On a railway route between two places A and B, there are 10 stations on the way. If 4 new stations are to be added, how many types of new tickets will be required if each ticket is issued for a one-way journey?

Q: Aryan runs at a speed of 40 metre/minute. Rahul follows him after an interval of 5 minutes and runs at a speed of 50 metre/minute. Rahul’s dog runs at a speed of 60 metre/minute and starts along with Rahul. The dog reaches Aryan and then comes back to Rahul, and continues to do so till Rahul reaches Aryan. What is the total distance covered by the dog?

Q: A big rectangular plot of area 4320 m² is divided into 3 square-shaped smaller plots by fencing parallel to the smaller side of the plot. However some area of land was still left as a square could not be formed. So, 3 more square-shaped plots were formed by fencing parallel to longer side of the original plot such that no area of the plot was left surplus. What are the dimensions of the original plot?

Q: 2 men and 1 woman board a bus in which 5 seats are vacant. One of these five seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies but a man can not sit on the seat reserved for ladies. In how many different ways can the five seats be occupied by these three passengers?

Q: A square is divided into 9 identical smaller squares. Six identical balls are to be placed in these smaller squares such that each of the three rows gets at least one ball (one ball in one square only). In how many different ways can this be done?

Q: There are 6 persons – A, B, C, D, E and F. They are to be seated in a row such that B never sits anywhere ahead of A. In how many different ways can this be done?

Q: 300 persons are participating in a meeting, out of which 120 are foreigners and the rest are Indians. Out of the Indians there are 110 men who are not judges; 160 are men judges, and 35 are women judges. There are no foreign judges. How many Indian women attended the meeting?

Q: There are 6 persons: A, B, C, D, E and F. (i) A has 3 items more than C (ii) D has 2 items less than B (iii) E has 6 items less than F (iv) C has 2 items more than E (v) F has 3 items more than D Which one of the following figures CANNOT be equal to the total number of items possessed by all the 6 persons?

Q: Ten identical particles are moving randomly inside a closed box. What is the probability that at any given point of time all ten particles will be lying in the same half of the box?

Q: An equilateral triangular plate is to be cut into a number of identical small equilateral triangular plates. Which one of the following can be a possible value of n?

Q: There are 10 identical coins and each one of them has ‘H’ engraved on one face and ‘T’ engraved on the other face. These 10 coins are lying on a table and each one of them has the ‘H’ face as the upper face. In one attempt, exactly four (neither more nor less) coins can be turned upside down. What is the minimum number of attempts in which the ‘T’ faces of all the 10 coins can be brought to be the upper faces?

Q: Two cars X and Y start from two places A and B respectively which are 700 km apart at 9 a.m. Both the cars run at an average speed of 60 km/hr. Car X stops at 10 a.m. and again starts at 11 a.m. while the other car Y continues to run without stopping. When do the two cars cross each other?

Q: In a question of a test paper, there are five items each under List-A and List-B. The examinees are required to match each item under List-A with its corresponding correct item under List-B. Further, it is given that 1. no examinee has given the correct answer 2. answers of no two examinees are identical What is the maximum number of examinees who took this test?

Q: A and B start from the same point and in the same direction at 7 a.m. to walk around a rectangular field 400 m × 300 m. A and B walk at the rate of 3 km/hr and 2.5 km/hr respectively. How many times shall they cross each other if they continue to walk till 1 and 2.30 p.m.?

Q: Nine different letters are to be dropped in three different letter boxes. In how many different ways can this be done?

Q: How many three-digit even numbers are there such that 9 comes as a succeeding digit in any number only when 7 is the preceding digit, and 7 is the preceding digit only when 9 is the succeeding digit?

Q: In how many different ways can six players be arranged in a line such that two of them, Ajit and Mukherjee, are never together?

Q: 50 men or 80 women can finish a job in 50 days. A contractor deploys 40 men and 48 women for this work, but after every duration of 10 days, 5 men and 8 women are removed till the work is completed. The work is completed in

Q: Three students are picked at random from a school having a total of 1000 students. The probability that these three students will have identical date and month of their birth is

Q: Three flags, each of different colour, are available for a military exercise. Using these flags, different codes can be generated by waving i) a single flag of different colours, or ii) any two flags in a different sequence of colours, or iii) three flags in a different sequence of colours. The maximum number of codes that can be generated is

Q: A car travels the first one-third of a certain distance with a speed of 10 km/hr, the next one-third distance with a speed of 20 km/hr and the last one-third distance with a speed of 60 km/hr. The average speed of the car for the whole journey is

Q: ‘A’ walks around a circular field at the rate of one round per hour while ‘B’ runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at

Q: A two-member committee comprising of one male and one female member is to be constituted out of five males and three females. Amongst the females, Ms. A refuses to be a member of the committee in which Mr. B is taken as the member. In how many different ways can the committee be constituted?

Q: Total time taken by a person in going to a place by walking and returning on cycle is 5 hours 45 minutes. He would have gained 2 hours by cycling both ways. The time taken by him to walk both ways is

Q: ‘A’ and ‘B’ are two fixed points in a field. A cyclist C moves such that ACB is always a right angle. In this context, which one of the following statements is correct?

Q: A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 seconds, yellow for 5 seconds and red for 30 seconds. At a randomly chosen time, the probability that the light will not be green is

Q: A trader fixed the price of an article in such a way that by giving a rebate of 10 % on the price fixed he made a profit of 15 %. If the cost of the article is Rs 72, the price fixed on it is

Q: Consider the volumes of the following: 1. A parallelepiped of length 5 cm, breadth 3 cm and height 4 cm 2. A cube of each side 4 cm 3. A cylinder of radius 3 cm and length 3 cm 4. A sphere of radius 3 cm The volumes of these in the decreasing order is

Q: A train of length 150 metres, moving at a speed of 90 km/hr can cross a 200-metre bridge in

Q: The age of a man is three times the sum of the ages of his two sons. Five years hence, his age will be double the sum of the ages of his sons. The father’s present age is

Q: The length of the longest pole that can be placed in a room 12 m long and 9 m wide and 8 m high is

Q: In a company 60 % of the employees are men. Of these, 40 % are drawing more than Rs 50,000 per year. If 36 % of the total employees of the company draw more than Rs 50,000 per year, what is the percentage among women who are drawing less than Rs 50,000 per year?

Q: A bus is moving at 30 km/h, and a car is coming from behind at 50 km/h. How far apart are they if it takes 15 minutes for the car to catch up with the bus?

Q: Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels 2 km/hr faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour?

Q: Amit started a business by investing Rs 30,000. Rahul joined the business after some time and invested Rs 20,000. At the end of the year, profit was divided in the ratio of 2 : 1. After how many months did Rahul join the business?

Q: The time in the wall clock is 3.25; the acute angle between the hours hand and the minutes hand is

Q: Solve the given equations: x² + y² = 34 x⁴ − y⁴ = 544 The values of x and y are

Q: 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

Q: 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?

Q: 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?

Q: 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

Q: 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?

Q: 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.

Q: In the above figure, ABCD is a cyclic quadrilateral, AB = BC and angle BAC = 70°, then angle ADC is

Q: 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?

Q: 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?

Q: 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?

Q: 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?

Q: If X = –2, then X³ – X² – X – 1 is equal to

Q: 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?

Q: 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?

Q: 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?

Q: 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?

Q: Which one of the following has a greater perimeter than the rest?

Q: In the given figure, angle QOP = 30° and angle ORP = 20°, angle QOR is equal to

Q: The distribution of 1,00,000 tourists who visited India during a particular year is shown in the given charts. Based on this, the number of Japanese tourists below the age of 39 who visited India in the year concerned is

Q: 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?

Q: In the sequence of numbers 5, 8, 13, X, 34, 55, 89, ……… the value of ‘X’ is

Q: 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

Q: 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?

Q: The yield versus fertilizer input is shown in the graph. Consider the following statements based on this graph: I. Yield rate is zero at B and C. II. There is no yield with no fertilizer input. III. The yield is minimum at D. IV. The yield is neither minimum nor maximum at C. Which of the above statements are correct?

Q: A company manufacturing air-conditioners has set a monthly target. The target and realised values are shown in the bar chart. Consider the following statements based on the chart: I. The targeted sales on a monthly basis have been achieved. II. The overall target value has been exceeded by 7.5%. III. The Sales Department deserves a pat on the back. Which of the above statements is/are correct?

Q: 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?

Q: If the angles of a triangle are in the ratio of 4 : 3 : 2, then the triangle

Q: The surface area of a spherical dome-shaped roof of a cylindrical water tank shown in the figure is

Q: If X + 2Y = 2X + Y, then X² / Y² is equal to

Q: 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

Q: In an office, the distribution of work hours is as shown in the following table: No. of Staff Members | No. of hours worked 5 | 0 – 19 12 | 20 – 24 25 | 25 – 29 40 | 30 – 34 15 | 35 – 39 8 | 40 – 45 Consider the following inferences drawn from the table: I. The average number of hours worked by a staff member is about 30. II. The percentage of those who worked 35 or more hours is less than 25. III. At least 5 staff members worked more than 44 hours. Which of these inferences is/are valid?

Q: In a factory, a quality-assurance test is conducted on various samples for a specific characteristic value of the product. The values and the number of samples are as given in the following table (table not reproduced here). Consider the following statements based on the table: I. The probability that X = 15 is 0.64. II. The probability that 13 < X = 17 is greater than 0.64. III. The probability that X = 15 is less than 0.22. Which of the above statements is/are NOT true?

Q: 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?

Q: 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

Q: 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

Q: 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

Q: 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?

Q: 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?

Q: 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?

Q: 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?

Q: 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?

Q: 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?

Q: 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?

Q: An accurate clock shows the time as 3 : 00. After the hour hand has moved 135°, the time would be

Q: 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?

Q: 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?

Q: 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

Q: 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?

Q: 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

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

Q: 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

Q: 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

Q: 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

Q: 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

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

Q: 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?

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

Q: 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?

Q: 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?

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

Q: When the frequency distribution is normal

Q: The following figure contains three squares with areas of 100, 16 and 49 lying side by side as shown. By how much should the area of the middle square be reduced in order that the total length PQ of the resulting three squares is 19?

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

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

Q: 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?

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

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

Q: 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?

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

Q: 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?

Q: 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

Q: 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

Q: 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?

Q: 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?

Q: 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

Q: 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?

Q: Out of a total of 120 musicians in a club, 5 % can play all the three instruments—guitar, violin and flute. It so happens that the number of musicians who can play any two and only two of the above instruments is 30. The number of musicians who can play the guitar alone is 40. What is the total number of those who can play violin alone or flute alone?

Q: A person earns Rs 2000 per month over and above his salary as additional charge allowance. However, 30 % of this additional income will be deducted as additional income tax at source. If the person would deposit Rs 1000 per month in a long-term saving fetching 12 % interest, his tax liability on the additional allowance would reduce to 10 %. What is the effective interest for this person for money invested in the long-term savings scheme?