IIFT SAMPLE QUESTION PAPERS
IIFT SAMPLE QUESTION PAPERS
Section 1- Mathematical Aptitude questions (50 questions)
Direction for Question 1 to 50: Read the information carefully and answer the questions:
1. If the sum of the roots of the quadratic equation px2 + qx + r = 0 is equal to the sum of the squares of their reciprocals, which are the correct statements.
a. r/p, p/q and q/r are in A. P.
b. p/ r, q/p and r/q are in G. P.
c. p/r, q/p and r/q are in H. P.
d. p/r, q/p and r/q are in A. P.
Ans: a and c are correct.
2. The area of an isosceles triangle is 12 sq. cm and if the length of one of the equal sides is 5 cm long, mark all the options which can give the length of the base.
a. 4 cm
b. 6 cm
c. 8 cm
d. 9 cm
Ans: b and c are correct.
3. A trader forms a mixture of cement and sand weighing 40 kgs. In this mixture, cement and sand are in the ratio of 4 : 1 in weight terms.And then , when he adds more sand to the mixture, the new ratio becomes 4 : 3. Given this,which are the correct statements.
a. The second mixture formed is one and a half times heavier than the original mixture.
b. In order to arrive at the second mixture, the trader added a quantity of sand weighing 16 kg.
c. if the original mixture had been in the ratio of 8 : 3, the weight of the sand in the original mixture would have been 12 kg.
d. If the trader sells 7 kg of the second mixture formed by him, and then he added 11 kg of a new mixture of cement and sand in the ratio 7 : 4 to the residual, then now the new ratio of cement to sand becomes 7 : 5.
Ans: b and d are correct.
4.Joshi has purchased a shop in a city by paying an amount of Rs. 20,000. Then he decorates the shop for which he spends Rs. 8,000 in the first month and Rs.2,000 in the next month. However, at the beginning of the third month, he gets a offer from Wadhwa and sells the shop to him and make a profit of 20 percent. Later Wadhwa decides that he will be better off by doing business in another location and decides to sell the shop back to Joshi. Given this,which are the correct statements.
a. If Wadhawa loses a total of Rs. 7,200 then his loss is not more than 20%.
b. If Joshi had originally purchased the shop at Rs. 14,000, then if he sells the shop to Wadhwa at the same price, he could have a profit of 50%.
c. If Joshi had sold the shop to Wadhwa at a profit of 40%, his monetary gain could be Rs.12,000.
d. If Joshi had sold the shop to Wadhwa at a profit of 40%, and Wadhwa sold the shop back to him at a loss of 40%, then Joshi would have acquired the shop with an investment of Rs. 13,200.
Ans: all the 4 options are correct.
5. In a pizza stall, Ajay and Mohan, became the lucky customers,they were given the option of drawing tickets from a pot in which there were x number of tickets for the knife-throwing show and y number of tickets for the talking-doll show. Both Ajay and Mohan were excited about the knife-throwing show, start drawing tickets from the pot until they get one for that show, replacing any drawn ticket for the talking-doll show in the pot. Ajay draws the ticket first, followed by Mohan. Given this condition ,which are the correct statements.
a. If the probability of Ajay first getting a ticket for the knife-throwing show is four times that for Mohan,then ratio between x and y is 3 : 1
b. If the probability of Ajay first getting a ticket for the knife-throwing show is five times that for Mohan, then ratio between y and x is 1 : 4
c. If the probability of Ajay first getting a ticket for the knife-throwing show is two times that for Mohan, then ratio between x and y is 1 : 1
d. If the probability of Mohan first getting a ticket for the knife-throwing show is six times that for Ajay, then ratio between x and y is 5 : 1
Ans: a, b and c are correct
6. Madan is going from Mumbai to Dehi in order to join a new job . He has a glass memento of right circular conic shape and he does not want it to break. So, he purchased a cubic metal box from the market spending Rs. 500. The cone is exactly fitted in the metal box in such a way that while the edges of the base of the cone are touching the edges of all the sides of the cube, the vertex of it touches the opposite face of the box. After inserting the memento in the box, he packed the metal box from outside with paper costing Rs. 1.5 per sq cm. Given that the volume of the glass memento is 718 ⅔ cc,which are the correct statements.
a. Madan had incurred total expenditure of Rs. 2,264 on the metal box.
b. Madan had incurred an expenditure of Rs. 1,754 on packing the metal box.
c. The area of any one side of the metal box is 196 sq. cm
d. The volume of the metal box is 2,644 cc.
Ans: a and c are correct.
7. Ranjan goes to a countryside lake for a boat ride. He is standing at the ferry counter, and he looked at the opposite bank and observed a tall tower on a hill downstream, the angle of elevation being 45°. The boat takes him directly to the opposite bank, from where the angle of elevation to the top of the tower becomes 60°and while exploring the site, he gets to know that the combined height of the tower and the hill is 300 m . If the speed of the boat by which Ranjan travelled was 2 km/hr in still waters,which are the correct statements.
a. It took Ranjan 3 √6 minutes to cross the lake by the boat.
b. The breadth of the lake is 100√ 6m.
c. It took A. Ranjan 4 √3 minutes to cross the lake by the boat.
d. If the combined height of the hill and the tower was 450 m and the speed of the boat was 1 km/hr (the angles of elevation remaining unchanged), the time taken by Ranjan to cross the lake by boat would have been 9 √6 minutes.
Ans: a ,b and d are correct.
8.Sunil goes to city in Europe , where he enjoys walking along the streets . He observed that there are 6 parallel roads running East – West and 5 parallel roads running North-South in the city. He wanted to observe the landmarks in the city, he prefers to take different routes every time he goes out. He also observed that the distance between every consecutive pair of roads was equal. Given this,which are the correct statements.
a. The number of shortest possible routes that Sunil can take to travel from one corner of the city to the other diagonal end is 126.
b. The total number of possible routes that Sunil can take to travel from one corner of the city to the other diagonal end is 196.
c. The number of rectangles that can be formed with their sides along the roads is 150.
d. If the number of parallel roads running East-West and North – South increase by one each, the number of shortest possible routes that Sunil can take to travel from one corner of the city to the other diagonal end would go up by 336.
Ans: a , c and d are correct.
9. Laxman and Bharat decide to go from Agra to Delhi for watching a cricket match and board two different trains for that purpose. While Laxman takes the first train that leaves for Delhi, Bharat decides to wait for some time and take a faster train. On the way, Laxman sitting by the window seat noticed that the train boarded by Bharat crossed him in 12 seconds. Now the faster train can travel 180 km in three hours, while the slower train takes twice as much time to do it. Given this,which are the correct statements.
a. If the faster train has taken 30 seconds to cross the entire length of the slower train, the difference between the lengths of the two trains is 50 m.
b. If the faster train had been running twice as much faster, it would have taken 10 seconds to overtake the slower train.
c. Had the faster train taken 24 seconds to cross the entire length of the slower train, the length of the slower train would have been 100 m.
d. If the slower train had been running at one and a half times of its current speed, the faster train would have taken 24 seconds to overtake Laxman.
Ans: a , c and d are correct.
10. A contractor takes up an assignment that 20 men can complete in 10 days. The same assignment could be finished by 15 women in 20 days. The contractor decides to employ 10 men and 10 women for the project. Given this,which are the correct statements.
a. If the wage rate for men and women are Rs. 50 and Rs. 45 respectively, the total wage bill for the project will be Rs. 11,400.
b. If the wage rate for men and women are Rs. 45 and Rs. 40 respectively, the total wage bill for the project will be Rs. 10,200.
c. If the wage rate for men and women are equal at Rs. 40, the total wage bill for the project will be Rs. 9,100.
d. If the contractor decides to employ 20 men and 30 women for the project and the wage rate for men and women are Rs. 40 and Rs. 35 respectively, the total wage bill for the project will be Rs. 9,250.
Ans: a , b and d are correct.
11. In the right-angled triangle QPR given below, PS is the altitude to the hypotenuse. The figure is followed by three possible inferences.
I. Triangle PQS and Triangle RPS are similar.
II Triangle PSQ and Triangle RSP are congruent.
III Triangle PSQ and Triangle RPQ are similar.
Which is the Correct option
a. I and II are correct
b. I and III are incorrect
c. Only III is correct
d. All three are correct
Ans: b is correct.
12. Find the square root of the harmonic mean of the roots of the equation
(5 + √ 2 )x2 – (4 + √5 )x + 8 + 2√ 5 = 0 ?
a. ± 3
b. ± 4
d. None of these
Ans: d is correct
13. If a ¹ n p and tan a is the GM of sin a and cos a, find the square of the expression 2 – 4 sin4 a + 3 sin4 a – sin6 a.
d. None of these
Ans: a is correct
14. If one root is the square of the other root in the equation x^2+ px + q = 0, which is the correct relationship in the following options.
a. p3 – q (3p + 1) + q2 = 0
b. p3 – q (3p – 1) + q2 = 0
c. p3 + q (3p – 1) + q2 = 0
d. p3 – q (3p – 1) – q2 = 0
15. If a,b are the roots of the quadratic equation x2 + mx + 1 = 0 and c,d are the roots of the equation x2 + nx + 1 = 0, then calculate the value (a-c)(b-c)(a+d)(b+d)
a. n2 – m2.
b. m2 – n2.
c. 2 m2 – n2.
d. None of the above
16. A wire, if bent into a square, encloses an area of 484 cm^2. This wire is cut into two pieces; with the bigger piece having a length three-fourth of the original wire’s length. Now, if a circle and a square are formed with the bigger and the smaller piece respectively, determine the area to be enclosed by the two pieces?
b. 544.25 cm2
c. 376.75 cm2
17. Pavan builds an overhead tank in his house, which has three taps attached to it. While the first tap can fill the tank in 12 hours, the second one takes one and a half times more than the first one to fill it completely. A third tap is attached to the tank which empties it in 36 hours. Now one day, in order to fill the tank, Pavan opens the first tap and after two hours opens the second tap as well. However,at the end of the sixth hour, he realizes that the third tap has been kept open right from the beginning and promptly closes it. Determine the total time required to fill the tank?
a. 8 hours 48 minutes
b. 9 hours 12 minutes
c. 9 hours 36 minutes
d. 8 hours 30 minutes
18. Area ABC is 40 cm2. Length of BD is 1/4th of AB. The length of EC is 1/3rd of AC. Calculate the area of CDE.
19. a and b are two vectors and the angle between a and b is x. If (a + 3b). (7a – 5b) = 0 and (a – 4 b). (7a – 2b) = 0, then calculate the value of tan x is
d. None of the above
20. Three business entities X Ltd, Y Ltd. and Z Ltd, with 4, 3 and 5 employees respectively, merged into XYZ Ltd in order to jointly raise the capital for setting up a new modern production plant in Jaipur. After two years, on the question of management decisions on the new venture at Jaipur, the employees started adopting differing viewpoints and began to quarrel among themselves. Given the fact that there is not quarrel among the employees of the erstwhile X Ltd, Y Ltd and Z Ltd, then determine that what could be the maximum number of quarrels that can take place within XYZ Ltd?
21. Amit, Sumit and Pramit go to a seaside town to spend a vacation there and on the first day everybody decides to visit different tourist locations. After breakfast, each of them boards a different tourist vehicle from the nearest bus-depot.After three hours,Sumit who had gone to a famous beach, calls on the mobile of Pramit and claims that he has observed a shark in the waters. Pramit learns from the local guide that at that time of the year, only eight sea-creatures (including a shark) are observable and the probability of observing any creature is equal. However, Amit and Pramit later recall during their discussion that Sumit has a reputation for not telling the truth five out of six times.Then determine What is the probability that Sumit actually observed a shark in the waters?
21. Find the number of pairs of positive integers (a, b) where a and b are prime numbers and a2 – 2b2 = 1,
c . 2
22. In the game of picking the parcel, 4 players stand at the corners of a square and a parcel is kept at the center of the square. As soon as the signal goes up, a player has to run and pick up the parcel and proceed towards the diagonally opposite corner. The parcel changes hand, and the third player now runs with the parcel and taking a quarter-circular pat h lands at the spot vacated by the 1st player. He then places the parcel at the center and second player takes a quarter-circular path and passes the parcel to the player on his right returns of his spot. If the distance between opposite corners is 14 m, Calculate the total distance traveled by the parcel?
a. 36 m
23. Two commandos A and B are the equidistant from the target and the three are in a straight line. Another commando C stands equidistant from A and B such that the distance between him and either A or B is the same as the distance between A and B.Calculate the ratio of the distance AC and distance between C and the target?
24. Rajdhani express leaves Mumbai towards Delhi at 3.10 p. m. and travels uniformally at 120 kmph. August Kranti Express leaves Delhi towards Mumbai at 12.20 p. m. and travels uniformally at 80 kmph. Both trains cross at Baroda at 4.30 p.