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# TIFR GS 2021 Sample Papers Graduate School Admissions : Tata Institute of Fundamental Research

Organisation : Tata Institute of Fundamental Research (TIFR)
Exam Name : Graduate School Admissions (GS-2021)
Announcement : Sample Papers

Contents :

Tata Institute of Fundamental Research (TIFR), Graduate School Admissions (GS-2021) Sample Papers

## TIFR GS Sample Papers

1. N particles are distributed amongst three levels having energies 0, kT and 2kT. If the total equilibrium energy of the system is approximately 425kT, what is the value of N?

[a] 1001
[b] 335
[c] 425
[d] 390
[e] 181

2. Charged particles are beamed into a region having a uniform electric field of 103Newton/Coulomb and a uniform magnetic field of 10-2 Newton/(ampere meter). The electric and magnetic fields are at right angles to each other and the beam of particles is directed perpendicular to both of them, so that the electrical and magnetic forces on an ion oppose each other. The speed of those ions that are unaffected through this region is:

[a] 104 m/s
[b] 105 m/s
[c] 106 m/s

3. In a magnetic field of 1.17 Tesla, a proton absorbs energy at a frequency of 50 MHz. For the same field, an electron absorbs at a frequency of: (Bohr Magneton = 9.27×10-24JT-1, Nuclear Magneton = 5.05×10-27JT-1)

[a] 50 MHz
[b] 92.5 MHz
[c] 500 MHz
[d] 25 GHz
[e] 92.5 GHz
[f] none of the above

4. Assuming no degeneracy in the genetic code, the number of amino acids that would have to exist if the code is four units long could be:

[a] 20
[b] 64
[c] 128
[d] 256

5. 10 ml of 0.4M CuSO4 solution is electrolyzed with a current of 1.93 A for 5 min. Assuming that the volume of the solution does not change during electrolysis, the molar concentration of Cu2+after electrolysis is:

[a] 0.05 M
[b] 0.1 M
[c] 0.2 M
[d] 0.3 M

6. The pK of histidine is 6.0. A 60 mM solution of histidine is adjusted to a pH of 5.0. The concentration of protonated form (in mM) will be:

[a] 54.6
[b] 30.0
[c] 5.46

7. The maximum height of a rooted binary tree (all nodes have either two children or none) with N nodes is

(a) N
(b) logN
(c) (N-1)/2
(d) (N2)/2
(e)N(N-1)/2.

8. If a graph G has n vertices and medges then the depth first traversal of G canbe carried out in time

(a) O(n+m)
(b) O (nm) but not O(n+m)
(c) O (n2) but not O(n+m)
(d) O (n)(e) O(m)

9. What is the matrix A called ?
(a) Anti-symmetric
(b) Sparse
(c) Upper triangular
(d) Toeplitz
(e) Irregular.

10.logb(logbx) equals
(a) (ln lnx-ln lnb)/lnb
(b) (lnx-lnb)/lnb
(c) (ln lnx-ln lnb)
(d) (lnx-lnb)/[(lnx)(lnb)]
(e) None of the Above