June 2017: Mathematical Sciences, Chemical Sciences and Earth Sciences Posted on June 28, 2017Author Christy VarghesePosted in Question Paper1 Reply 1. If NET14 and NET15 are 5 digit numbers such that their sum = 157229, then N + E + T would be 15 21 25 72 2. A tight fitting band is wrapped around the Equator. Another circular band whose length is 15 m more lies at a certain height over the first band. A group of human beings attempt to pass under the longer band. Can they walk under it? (Earth’s circumference is roughly 40,000 km. The height of the human beings is between 1 and 2 m). Yes No Cannot be determined Only those with height less than 1.7m 3. A cylindrical cake is to be cut into 16 equal pieces. What is the minimum number of cuts required to do so? 9 3 8 5 4. If P+ 1/Q = 1 and Q + 1/R = 1 then what is PQR? -1 2 -2 Cannot be calculated 5. A, B and C are three distinct digits. If they are added as below, A B C + A B C + A B C C C C Find out the value of A, B and C A = 3, B = 4, C = 5 A = 2, B = 3, C = 1 A = 5, B = 1, C = 3 A = 1, B = 8, C = 5 6. N is a two digit number such that a product of its digits when added to their sum = N. The unit digit of N would be: 1 7 8 9 7. If equal weights of 22 carat gold (alloy of 22 parts gold and 2 parts copper by weight) and 24 carat gold (pure gold) are mixed to form an alloy, what will be the weight proportion of copper in the alloy? 1/2 1/8 1/12 1/24 8. A 4m x 4m floor needs to be covered by tiles of size 2m x 1m. Two diagonally opposite corners of size 1m x 1m should be left uncovered. How many tiles are required to complete the job without breaking the tiles or overlapping them? 6 7 8 Impossible to cover 9. A shopkeeper sells the file and a notebook for Rs.27 to the first customer, a notebook and a pen for Rs.31 to the second customer and a pen and file for Rs.29 to the third customer. The price of the items are rounded in rupees. Which of the following inferences is correct? The pen is the costliest of the three. The file is the costliest of the three. The notebook is the costliest of the three. The shopkeeper sold the different items to different customers at different rates. 10. Pre-PhD exam score of 10 students are plotted against their M.Sc. m arks. Which of the following is true? Two students have scored better in Pre-PhD than their M.Sc. exam. All those students who scored 50% in Pre-PhD score more percentage of marks in their M.Sc. exam. Two students score the same percentage of marks in their Pre-PhD and M.Sc. exams. The student who sored maximum in M.Sc. is the only student to get maximum in Pre-PhD exam. 11. What is the reminder when 3^{256} is divided by 5? 1 2 3 4 12. If 42 → 26, 71 → 78, 33 →16 then 62 → 68 54 38 39 13. The diagram shows a cubic block of marbles (1 x 1 x 1 m^{3}) having a planar fracture. What is the maximum number of slabs sized 20 x 20 x 5 cm^{3} that can be cut from this block avoiding the fracture? 200 300 400 500 14. A tall metal cylinder is filled end-to-end with n snugly fitting spherical wax balls of diameter d. If the balls melt completely, the volume fraction occupied by the melted wax is Independent of both d and n Dependent on both d and n Independent of d, but dependent on n Dependent on d, but independent of n. 15. With reference to the right angle triangle shown what is the value of sin (A)cos(B) + cos(A)sin(B) -1/2 1 +1/2 -1 16. Walking from my home, at a speed of 5 km/h I am 8 minutes late in reaching my office. If I walk at a speed of 8 km/h I reach 5 minutes late. How far is my office from the house? 2 km 1/3 km 2/3 km 1/2 km 17. Some fishermen caught some fish. No one caught more than 20 fish. a_{1} number of fishermen caught at least 1 fish among them, a_{2} number of fishermen caught at least 2 fish among them, and so on and a_{20} number of fisher men caught exactly 20 fishes among them. How many fishes were caught? a1 + a2 + a3 + … + a20 a1 + 2a2 + 3a3 + … + 20a20 20(a1 + a2 + a3 + … + a20) 20(a1 + 2a2 + 3a3 + … + 20a20) 18. If the product of 3 consecutive positive integers is equal to their sum, then what would be the sum of their squares? 9 14 16 24 19. L is the tallest and eldest of a group of 5 people K, L, M, N and P. M is elder tot N and shorter than K. M and P are of same age and P is taller than K. N and K are of same height and K is younger to P. Which of the following inferences is certain? P is taller than M N is the youngest N is elder to P N is elder to K. 20. Consider a square of side a. Fit the largest possible circle inside it and the largest possible square inside the circle. What is the side length of the innermost square? . a/(π√2) a/2 a/(2√2) a/√2 Loading … Question 1 of 20

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