Rashtriya Indian Military College Mathematics Exam Paper 2010

RASHTRIYA INDIAN MILITARY COLLEGE. DEHRADUN
Sainik School Previous Question Papers

ENTRANCE EXAMINATION - JUNE 2010
SUBJECT : MATHEMATICS

TIME: 1 Hr 30Mins MARKS: 200

Instructions:

1. Attempt all 30 questions; Write all your answer separately on the answer sheet provided at the Exam Centre.


2. Part 'A' contains20 questions, and each question in this part carries five marks.


3. Part 'B' contains10 questions and each question in this part carries ten marks.


4. USE OF CALCULATOR IS PROHIBITED.

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PART 'A' (20 X 5 Marks)



Q.1. Simplify: - -3/5 x (-10/9) x (21/-4) x (-6)


Q.2. If 23% of a number is 46, find the number.


Q.3 Arrange the rational numbers -7/10, 5/-8, 2/3 in ascending order.


Q.4. Find the value of 'a' if: - pqa = (3p + q)2 _ (3p-q) 2


Q.5. Factorize: - (25a2 + c2+ 1Oac2) - 49b2


Q.6. If the square of the hypotenuse of an isosceles right triangle is 200 cm2; find the length of each side.


Q.7. If a:b = 3:5 and b:c = 6:7, find a:b:c


Q.8. The age of Rakesh & Dinesh are in the ratio 5:7. After 5 years, the ratio of their age will be 5:6. Find their present age.


Q.9. A train, 360 mts long, is running at a speed of 45 kms/hr. How much time will it take to cross a bridge which is 140 mts long?


Q.10. The population of a town is 20,000. If the annual birth rate is 4% and the annual death rate is 2%, calculate the population after two years.


Q.11. Find the length of side of a square field whose area is equal to the area of a rectangular of length 225 m and breadth 144 m.


Q.12. If a driver takes one second to apply the brakes, how many times will the car travel once the drive applies the brakes, traveling at 40 km/hr?


Q.13. Construct a triangle ABC in which base BC=5.4 cm, altitude from A is 2.6 cm and medium dissecting BC is 3.5 cm and describe the steps of construction.


Q.14. Mahesh took a test which had 20 questions. The total grade was computed by awarding 10 points for each correct answer and deducting 5 points for each incorrect answer. Mahesh answered all 20 questions and received a score of 125. How many wrong answers did he have?


Q.15. Find the surface area of a cuboid whose length, breadth and height are respectively 13 cm, 9 cm and 2.5 cm.


Q.16. Use each of the digits 1, 2, 3, 4, 5 and 6 once only, in this multiplication problem to make it correct.



PART 'B' (20 X 5 Marks)


Q.21. Factorize: - (a) 4y2-4yx+ x2-9z2 (b) a2-2ab2+ b2-a + b.


Q.22. A steamer goes down stream from one point to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1km/hr, find the speed of the steamer in still water and the distance between the ports.


Q.23. The thickness of a metallic tube is 1 cm and the inner diameter of the tube is 12 cm. Find the weight of 1 meter long tube, if the density of the metal be 7.8 gm/cm3.


Q.24. How many sides has a regular polygon, each of whose angle measures 108o?


Q.25. 2 men and 7 boys can do a piece of work in 4 days. The same work is done by 4 men and 4 boys in 3 days. How long would it take 1 man and 1 boy to do the same?


Q.26. A wall 4.84 m long and 3.1 m high is to be covered with rectangular tiles of size 22cm x 10 cm. Find the total cost of the tiles at the rate of Rs. 2 per tile?


Q.27. The pie-chart represents the amount spent on different sports by a school. If the money spent on football is Rs. 9000, answer, the following questions:-


(a) What is the total amount spent on sports?

(b) How much extra amount is spent on hockey compared to football?

(c) What is the amount spent on cricket?



Q.28. A cistern can be filled by taps A and B in 10 minutes and 12 minutes respectively. A third tap C can empty this tank completely in 7 minutes. If all the three taps are turned on at the same time find the time taken to fill the cistern?


Q.29. Ram purchased rice worth Rs 500. He sold 3/4th of it at a loss of 10%, and the remainder at a gain of 10%. How much percent does he gain or lose on the whole transaction?


Q.30. In figure triangle PQR and SQR are isosceles. Find the following with reasons: