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TIFR 2013 Maths Paper Answer Key

This is TIFR 2013 Maths Paper Answer Key.

  1. These answers are unofficial. If you have an alternative answer, feel free to suggest it in the comment section.

  2. This is a work in progress. We are modifying and adding discussions. Please revisit soon (you may also click the follow button).

TIFR 2013 Unofficial Answer Key

Part A

1. D
2. B
3. C
4. C
5. D
6. C
7. D
8. A
9. C
10. B
11. D
12. C
13. B
14. B
15. D
16. D
17. B
18. C
19. B
20. D

Let C denote the cube [-1, 1]^3 \subset \mathbb{R}   . How many rotations are there in \mathbb{R}^3 which take C to itself?

A. 6; B. 12 C. 18. D. 24

Discussion:

Theorem: A finite subgroup of SO_3 is one of the following groups:

  • C_k : the cyclic group of rotations by multiples of \frac {2 \pi } {k} about a line, with k arbitrary
  • D_k : the Dihedral group of symmetries of a regular k-gon, with k arbitrary
  • T the tetrahedral group of 12 rotational symmetries of a tetrahedron;
  • O : the octahedral group of 24 rotational symmetries of a cube or an octahedron
  • I : the icosahedral group of 60 rotational symmetries of a dodecahedron or an icosahedron

Part B

21. C
22. A
23.
24. D
25. A
26. B
27. D
28. A
29. A
30. B

(courtesy: Tattwamasi Amrutam)

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