HBCSE Indian National Astronomy Olympiad Question Paper 2016
Name of the Organisation : HBCSE – Olympiads
Name of the paper : Indian National Astronomy Olympiad Question Paper
Year : 2016
Website : http://olympiads.hbcse.tifr.res.in/
Download Sample Question Paper: https://www.pdfquestion.in/uploads/8157olympiad.pdf
Indian National Astronomy Olympiad Question Paper :
Duration : 3Hrs
Please Note:
** Please write your roll number on top of this page in the space provided.
** Before starting, please ensure that you have received a copy of the question paper containing total 3 pages (5 sides).
Related : HBCSE Indian National Mathematical Olympiad INMO Previous Question Papers : www.pdfquestion.in/7250.html
** There are total 9 questions. Maximum marks are indicated in front of each question.
** For all questions, the process involved in arriving at the solution is more important than the answer itself. Valid assumptions / approximations are perfectly acceptable. Please write your method clearly, explicitly stating all reasoning.
** Blank spaces are provided in the question paper for the rough work. No rough work should be done on the answer-sheet.
** No computational aides like calculators, log tables, slide rule etc. are allowed.
** The answer-sheet must be returned to the invigilator. You can take this question booklet back with you.
** Please be advised that tentative dates for the next stage are as follows – Orientation Cum Selection Camp (Senior) 3rd May to 19th May 2016.
1. (9 marks) Satej is a twelve year old boy. He loves astronomy. Recently, he attended a sky observation workshop, organized by the Amateur Astronomers Club at a hill station. During the observation session, he was introduced to Hercules, Taurus, Scorpius, Orion, Ursa Major, Gemini, Draco, Leo, Serpens and Virgo constellations. He had sketched the stick figures of some of these constellations in his note book. Unfortunately, he forgot to write the names of the constellations and is finding it ifficult to identify the constellations. Can you help him to identify the constellations for his sketches?
2. (12 marks) In desperate times of depleting energy resources, Sandesh comes with an ingenious idea. He wishes to use methane on Neptune to satisfy Earth’s ever increas- ing energy needs but needs to work out a few details. Help him to see of his idea is a good one by solving the following questions.
(a) Estimate the total number of domestic LPG cylinders that can be filled up with methane from Neptune.
(b) Estimate the net domestic consumption of LPG cylinders in a year in India. Justify your approach in arriving at this number. We then extend the answer obtained to represent the earth.
(c) What is the approximate time-period, that methane brought from Neptune, can sustain the earth? Is Sandesh’s idea good enough to satisfy Earth’s energy needs?
3. (a) (5 marks) Anjali is quite particular about noting down the daily earnings she makes in her side business, run by her and her mother. She noticed that over a period of 5 consecutive days, the money she earned daily, was basically the date multiplied by 10. She found the total money earned over these 5 days to be Rs 630. What were the dates corresponding to those 5 consecutive days?
(b) (5 marks) What is the maximum value of n for which 100! is divisible by 2n
4. (10 marks) A boat is sailing on a river, parallel to a rectangular signboard propped up on the bank of the river. A search lamp on a flagpole on the top of the boat illuminates the signboard. The height of the lamp on the boat is such that complete shadow of the signboard is cast on the ground. As the boat moves, a sailor in the observation cabin of the boat starts seeing the clear shadow when the boat is at a distance of about 100 m from the signboard. The boat passes the signboard at a closest distance of 60 m. What will be the ratio of the minimum area of the shadow to that of the maximum area of the shadow as the boat passes by? Explain your answer using very clear diagram/s.