DUET 2021 Question Paper Ph.D in Chemistry

DU PhD in Chemistry
Topic:‐ CHEM PHD

1) With reference to the figure below, which represents the Gibbs free energy along a reaction path for a single phase
transformation from state 1 to state 2,

[Question ID = 51]
1. rate = C exp(‐ΔG1/RT)

[Option ID = 201]
2. rate = C exp(‐ΔG2/RT)

[Option ID = 202]
3. rate = C exp(‐{ΔG1+ ΔG2}/RT)

[Option ID = 203]
4. rate = C exp(‐{ΔG1‐ ΔG2}/RT)

[Option ID = 204]

2) The degeneracy of a particle in a cubic box having energy three times that of the lowest energy state is[Question ID =
52]
1. 1 [Option ID = 205]
2. 2 [Option ID = 206]
3. 3 [Option ID = 207]
4. 4 [Option ID = 208]

3) Which of the following functions is an eigenfunction of the operator d/dx? k is a constant.

[Question ID = 53]
1. exp(ikx)

[Option ID = 209]
2. kx2

[Option ID = 210]
3. sinkx

[Option ID = 211]
4. exp(kx2)

[Option ID = 212]

4) Three non‐interacting particles, each with spin ½, are moving in a one dimensional box of length L. The energy of the
lowest energy state of the system is

[Question ID = 54]

1.

[Option ID = 213]

2.

[Option ID = 214]

3.

[Option ID = 215]

4.

[Option ID = 216]

5) The order of the N‐O bond strengths in NO, NO+, and NO‐ is[Question ID = 55]
1. NO > NO+ > NO¯ [Option ID = 217]

2. NO+ > NO > NO¯ [Option ID = 218]
3. NO+ > NO¯ > NO [Option ID = 219]
4. NO¯ > NO > NO+ [Option ID = 220]

6) If the energy of a particle can be either 1, 2, 3, 4 or 5 units with probability 1/15, 2/15, 3/15/ 4/15 and 5/15,
respectively, the average energy of the particle is[Question ID = 56]
1. 0.5 [Option ID = 221]
2. 3.0 [Option ID = 222]
3. 3.7 [Option ID = 223]
4. 4.3 [Option ID = 224]

7) In terms of the partition function Z of a system of particles, the average energy <E> is expressed as

[Question ID = 57]
1.

[Option ID = 225]

2.

[Option ID = 226]

3.

[Option ID = 227]

4.

[Option ID = 228]

8) State which of the following statements about Bose‐Einstein (BE) statistics is FALSE[Question ID = 58]
1. BE statistics is for particles with integral spin. [Option ID = 229]
2. BE statistics can be applied to photons. [Option ID = 230]
3. Bosons obey Pauli’s Exclusion Principle. [Option ID = 231]
4. The wave function of bosons is symmetric. [Option ID = 232]

9) The equation for the evaluation of β in the Maxwell‐Boltzmann distribution law is

[Question ID = 59]
1. β = 1/kT.

[Option ID = 233]
2. β = ‐1/kT.

[Option ID = 234]
3. β = kT.

[Option ID = 235]
4. β = 2/kT.

[Option ID = 236]

10) According to the Debye‐Hückel limiting law, if the concentration of a dilute aqueous solution of KCl is increased 4‐fold,
the value of logγ ± will

[Question ID = 60]
1. decrease by a factor of 2

[Option ID = 237]
2. increase by a factor of 2

[Option ID = 238]
3. decrease by a factor of 4

[Option ID = 239]
4. increase by a factor of 4

[Option ID = 240]

11) In the first excited state, S1, acetylene has a trans bent configuration compared to its linear S0 ground state, and its CC
bond length also increases from 1.21 Å to 1.34 Å. The S1 ← S0 absorption spectrum will show

[Question ID = 61]
1. no vibrational coarse structure.

[Option ID = 241]
2. a sharp peak.

[Option ID = 242]
3. a continuum.

[Option ID = 243]
4. a broad vibrational progression.

[Option ID = 244]

12) ClO2 molecule was trapped in a solid. Its ground electronic state is known to be B1. Light polarized parallel to the y‐axis
excited the molecule to an upper state. The upper state is

[Question ID = 62]
1. A1

[Option ID = 245]
2. A2

[Option ID = 246]
3. B1

[Option ID = 247]
4. B2

[Option ID = 248]

13) The term symbol for the ground state of B2+ is 2Σg +. The total spin and total orbital angular momentum are,
respectively,

[Question ID = 63]
1. ½, 0

[Option ID = 249]
2. ¾, 0

[Option ID = 250]
3. √3/2, 0

[Option ID = 251]
4. 2, 1

[Option ID = 252]

14) Interpret the observed IR and Raman frequencies for an XY2 molecule

V/CM‐1 IR Raman
2224 vs, PR s, depol
1285 vs, PR vs, pol
568 s, PQR ­

The structure is

[Question ID = 64]
1. linear XYY

[Option ID = 253]
2. linear YXY

[Option ID = 254]
3. bent XYY

[Option ID = 255]
4. bent YXY

[Option ID = 256]

15) Assuming that the force constants of double and triple bonds are roughly two and three times, respectively, that of
single bonds, the ratio of the stretching frequencies of the C‐C, C=C and C≡C bonds is

[Question ID = 65]
1. 1:2:3

[Option ID = 257]
2. 1:1.4:1.7

[Option ID = 258]
3. 3:2:1

[Option ID = 259]

4. 1:4:9

[Option ID = 260]

16) The mean time for the 2p → 1s spectral transition is 1.6×10‐9 s, while the mean time for the 2s → 1s transition is 0.14
s. This is because

[Question ID = 66]
1. the 2p → 1s transition is forbidden, but 2s → 1s is allowed.

[Option ID = 261]
2. the 2p → 1s transition is allowed, but 2s → 1s is forbidden.

[Option ID = 262]
3. the 2p → 1s transition is allowed, and 2s → 1s is also allowed.

[Option ID = 263]
4. the 2p → 1s transition is forbidden, and the 2s → 1s transition is also forbidden.

[Option ID = 264]

17) The vibrations of diatomic molecules are usually modelled by a harmonic potential. If the potential is given by x2, the
correct statement is:

[Question ID = 67]
1. The force constant is 2 and the force is 2x.

[Option ID = 265]
2. The force constant is 2 and the force is ‐2x.

[Option ID = 266]
3. The force constant is ‐1 and the force is ‐2x.

[Option ID = 267]
4. The force constant is 1 and the force is 2x.

[Option ID = 268]

18) Major product of the following reaction is:

[Question ID = 68]

1.

[Option ID = 269]

2.

[Option ID = 270]

3.

[Option ID = 271]

4.

[Option ID = 272]

19) Which of the following conformer(s) will predominate(s) in dimethylsulfoxide (DMSO) solvent?

[Question ID = 69]
1. (B) only

[Option ID = 273]
2. (A) only

[Option ID = 274]
3. (B) is 50% and (A) in 50 %

[Option ID = 275]
4. (B) is 78% and (A) is 22%

[Option ID = 276]

20) Consider the following reaction:

[Question ID = 70]

1.

[Option ID = 277]

2.

[Option ID = 278]

3.

[Option ID = 279]

4.

[Option ID = 280]

21) Which one of the following reducing reagents will not give below given product?

[Question ID = 71]
1. 9‐Borobicyclo[3,3,1]nonane (9‐BBN), THF, 0°C

[Option ID = 281]
2. NaBH4, CeCl3, MeOH

[Option ID = 282]
3. LiAlH(OMe)3, THF, 0°C

[Option ID = 283]
4. NaBH4, EtOH, 0°C

[Option ID = 284]

22) The major product formed in the following reaction is:

[Question ID = 72]

1.

[Option ID = 285]

2.

[Option ID = 286]

3.

[Option ID = 287]

4.

[Option ID = 288]

23) Consider the following reaction

The products A and B are:

[Question ID = 73]

1.

[Option ID = 289]

2.

[Option ID = 290]

3.

[Option ID = 291]

4.

[Option ID = 292]

24) The following reaction is known as:

[Question ID = 74]
1. Suzuki reaction

[Option ID = 293]
2. Heck reaction

[Option ID = 294]
3. Stille coupling

[Option ID = 295]
4. Sonogashira coupling

[Option ID = 296]

25) Which one of the following products will be major product in the below given reaction?

[Question ID = 75]

1.

[Option ID = 297]

2.

[Option ID = 298]

3.

[Option ID = 299]

4.

[Option ID = 300]

26) Which one of the following is suitable reagent for the below given reaction?

[Question ID = 76]
1. t‐BuOOH, Ti(OiPr)4, (+)‐Diethyl tartrate

[Option ID = 301]
2. t‐BuOOH, (+)‐Diethyl tartrate

[Option ID = 302]
3. t‐BuOOH, Ti(OiPr)4, (‐)‐Diethyl tartrate

[Option ID = 303]
4. t‐BuOOH, Ti(OiPr)4

[Option ID = 304]

27) Consider the following addition reaction:

The least favored produt is:

[Question ID = 77]
1. 3‐Bromo‐3‐methyl‐1‐butene

[Option ID = 305]
2. 1‐Bromo‐3‐methyl ‐2‐butene

[Option ID = 306]
3. 3‐Bromo‐2‐methyl‐1‐butene

[Option ID = 307]
4. 4‐Bromo‐2‐methyl‐1‐butene

[Option ID = 308]

28) Which one is the correct order of potential effetiveness as leaving group in the nuleophilic substitution reaction?

[Question ID = 78]
1. II > I > III > IV

[Option ID = 309]
2. I > III > II> IV

[Option ID = 310]
3. IV > II > III > I

[Option ID = 311]
4. III > I > II > IV

[Option ID = 312]

29) Nitration of cinnamic acid will give the product(s):

[Question ID = 79]
1. 2‐Nitro‐cinnamic acid only

[Option ID = 313]
2. 3‐Nitro‐cinnamic acid only

[Option ID = 314]
3. 4‐Nitro‐cinnamic acid only

[Option ID = 315]
4. 2‐nitro‐cinnamic acid and 4‐nitro‐cinnamic acid formed more than 3‐nitro‐cinnamic acid

[Option ID = 316]

30) An organic compound having molecular formula C5H10O and it shows peak at 3410 cm‐1 in FT‐IR. 1H‐NMR (300 MHz,
CDCl3): = 6.05 (dd, 1H), 5.02 (dd, 1H), 4.09 (dd, 1H), 2.80 (s, D2O exchangeable), 1.3 (s, 6H) ppm. 13C‐NMR: =150,
110, 70, 29 ppm. Dept‐135: = 150(+), 110 (‐), 29 (+). The structure of the compound will be:

[Question ID = 80]

1.

[Option ID = 317]

2.

[Option ID = 318]

3.

[Option ID = 319]

4.

[Option ID = 320]

31) Cyclohexanone and cyclopetanone give one common m/z base peak. The value of the peak in m/z is:

[Question ID = 81]
1. 84

[Option ID = 321]
2. 42

[Option ID = 322]
3. 55

[Option ID = 323]
4. 83

[Option ID = 324]

32) The principal product of the following reaction is:

[Question ID = 82]

1.

[Option ID = 325]

2.

[Option ID = 326]

3.

[Option ID = 327]

4.

[Option ID = 328]

33) In the following reaction A and C are interconvered under thermal conditions through cyclobutane B.

[Question ID = 83]
1. Ring closure of A and ring opening of B both will be conrotatory proccesses

[Option ID = 329]
2. Ring closure of A will be disrotatory process and ring opening of B will be conrotatory proccess

[Option ID = 330]
3. Ring closure of A and ring opening of B both will be disrotatory proccesses

[Option ID = 331]
4. Ring closure of A will be conrotatory proccess and ring opening of B will be disrotatory process

[Option ID = 332]

34) The absolute configuration of below given compunds will be:

[Question ID = 84]
1. R

[Option ID = 333]
2. S

[Option ID = 334]
3. R, S

[Option ID = 335]
4. S, S

[Option ID = 336]

35) Which ordering correctly shows the variation in rates of water exchange in high spin aqua complexes [M(OH2) 6]?

[Question ID = 85]
1. Co2+ > Cr2+

[Option ID = 337]
2. V2+ > Co2+

[Option ID = 338]
3. Cr3+ > Fe3+

[Option ID = 339]
4. Cr2+ > Cr3+

[Option ID = 340]

36) The principal axis C4 is present in

[Question ID = 86]
1. BF3

[Option ID = 341]
2. SnO2

[Option ID = 342]
3. BrF5

[Option ID = 343]
4. C6H 6

[Option ID = 344]

37) Which one of the following sentence is false about EDTA?

[Question ID = 87]
1. Alkali medium is required for complexation because EDTA will ionize better in alkali medium.

[Option ID = 345]
2. EDTA form complexes with all metal ions.

[Option ID = 346]
3. Solubility of EDTA is lower than its disodium counterpart.

[Option ID = 347]
4. Alkali medium is required for complexation because EDTA will ionize more in acidic medium.

[Option ID = 348]

38) The non‐covalent interaction present in the Na+ ‐crown ether complex is due to,

[Question ID = 88]
1. ion‐ion

[Option ID = 349]
2. ion‐dipole

[Option ID = 350]
3. dipole‐dipole

[Option ID = 351]
4. hydrogen bonding

[Option ID = 352]

39) The series identifying the thiophilic heavy metal ions,

[Question ID = 89]
1. Cu1+, Hg2+, Tl1+

[Option ID = 353]
2. Ti4+, La3+, Si4+

[Option ID = 354]
3. V5+, Te6+, Y3+

[Option ID = 355]
4. Nb5+, Sc3+, B3+

[Option ID = 356]

40) A metal X on heating in nitrogen gas gives Y. Y on treatment with H2O gives a colourless gas which when passed
through CuSO4 solution gives blue colour. Y is

[Question ID = 90]
1. Mg(NO3)2

[Option ID = 357]
2. Mg3N2

[Option ID = 358]
3. MgCl2

[Option ID = 359]
4. MgO

[Option ID = 360]

41) Which of the following statement is true for the diffraction pattern in the crystal lattice?

[Question ID = 91]
1. Diffraction patterns are linear space.

[Option ID = 361]
2. Diffraction patterns possess a center of symmetry

[Option ID = 362]
3. Diffraction pattern does not have center of symmetry

[Option ID = 363]
4. Diffraction patterns contain α‐rays.

[Option ID = 364]

42) Which is the sequence showing the correct order of increasing intensity for the d‐d transition?

[Question ID = 92]
1. CoCl42‐ > [Co(NH3)6]3+ > [Co(NH3)6]2+ > [Co(H2O)6]2+

[Option ID = 365]
2. [Co(H2O)6]2+ > [Co(NH3)6]3+ > CoCl42‐ > [Co(NH3)6]2+

[Option ID = 366]
3. [Co(NH3)6]2+ > [Co(H2O)6]2+ > CoCl42‐ > [Co(NH3)6]3+

[Option ID = 367]
4. [Co(NH3)6]3+ > [Co(NH3)6]2+ > CoCl42‐ > [Co(H2O)6]2+

[Option ID = 368]

43) The equilibrium shift towards the products in Cr2O 72‐ ⇋ CrO42‐

[Question ID = 93]
1. occurs in acidic medium

[Option ID = 369]
2. occurs in basic medium

[Option ID = 370]
3. occurs in neutral medium

[Option ID = 371]
4. does not exist

[Option ID = 372]

44) Which one of the following ion shows kinetic masking?

[Question ID = 94]
1. Co2+

[Option ID = 373]
2. Cu2+

[Option ID = 374]
3. Cr3+

[Option ID = 375]
4. Fe3+

[Option ID = 376]

45) The p5 electronic configuration is equivalent to the term in ground state

[Question ID = 95]
1. 3P

[Option ID = 377]
2. 2P

[Option ID = 378]
3. 3F

[Option ID = 379]
4. 4P

[Option ID = 380]

46) The molecule which has an inversion center and S6‐axis is

[Question ID = 96]
1. Chlorobenzene

[Option ID = 381]
2. p‐dichlorobenzene

[Option ID = 382]
3. 1,3, 5‐ trichlorobenzene

[Option ID = 383]
4. Chair form of cyclohexane

[Option ID = 384]

47) The type of intermolecular interaction present in the herring bone packing of benzene,

[Question ID = 97]
1. Cation – π

[Option ID = 385]
2. anion – π

[Option ID = 386]
3. dipole‐ion

[Option ID = 387]
4. π – π

[Option ID = 388]

48) Which one of the following statement is correct?

[Question ID = 98]
1. A dissociative mechanism is a 2‐step mechanism with the leaving group departing in the second step.

[Option ID = 389]
2. An associative mechanism is a 2‐step mechanism; the intermediate has a lower coordination number than the starting complex.

[Option ID = 390]
3. In a dissociative interchange mechanism, bond breaking dominates over bond formation

[Option ID = 391]
4. In an associative interchange mechanism, the entering group associates with the substrate after the leaving group has departed.

[Option ID = 392]

49) Which one of the following cannot show linkage isomerism?

[Question ID = 99]
1. Cl‐

[Option ID = 393]
2. SCN‐

[Option ID = 394]
3. CN‐

[Option ID = 395]
4. NH3

[Option ID = 396]

50) Match List I with List II based on the molecular symmetry

Choose the correct answer from the options given below:

[Question ID = 100]
1. A ‐ III, B ‐ I , C ‐ IV , D ‐II

[Option ID = 397]
2. A ‐ II , B ‐ III , C ‐I , D ‐ II

[Option ID = 398]
3. A ‐ IV, B ‐ I , C ‐ III , D ‐ II

[Option ID = 399]
4. A ‐ IV, B ‐ III , C ‐ II , D ‐ I

[Option ID = 400]