Q.1 – Q.5 Carry ONE mark each.
1. “I cannot support this proposal. My ________ will not permit it.”
2. Courts : _______ : : Parliament : Legislature
(By word meaning)
3. What is the smallest number with distinct digits whose digits add up to 45?
4. In a class of 100 students,
(i) there are 30 students who neither like romantic movies nor comedy movies,
(ii) the number of students who like romantic movies is twice the number of students who like comedy movies, and
(iii) the number of students who like both romantic movies and comedy movies is 20.
How many students in the class like romantic movies?
5. How many rectangles are present in the given figure?
Q.6 – Q.10 Carry TWO marks Each
6. Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures that have claws, and some that do not. All creatures that have claws are ferocious.
Based only on the information provided above, which one of the following options can be logically inferred with certainty?
(A) All creatures with claws are animals.
(B) Some creatures with claws are non-ferocious.
(C) Some non-ferocious creatures have claws.
(D) Some ferocious creatures are creatures with claws.
7. Which one of the following options represents the given graph?
(A) f(x) = x2 2−|x|
(B) f(x) = x 2−|x|
(C) f(x) = |x|2−x
(D) f(x) = x 2−x
8. Which one of the following options can be inferred from the given passage alone?
When I was a kid, I was partial to stories about other worlds and interplanetary travel. I used to imagine that I could just gaze off into space and be whisked to another planet.
[Excerpt from The Truth about Stories by T. King]
(A) It is a child’s description of what he or she likes.
(B) It is an adult’s memory of what he or she liked as a child.
(C) The child in the passage read stories about interplanetary travel only in parts.
(D) It teaches us that stories are good for children.
9. Out of 1000 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to:
(i) Collect saliva samples from all 1000 individuals and randomly group them into sets of 5.
(ii) Mix the samples within each set and test the mixed sample for covid.
(iii) If the test done in (ii) gives a negative result, then declare all the 5 individuals to be covid negative.
(iv) If the test done in (ii) gives a positive result, then all the 5 individuals are separately tested for covid.
Given this strategy, no more than _______ testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.
10. A 100 cm × 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions 100 cm×1 cm.
The total number of creases visible when the sheet is unfolded is _______.
Q.11 – Q.35 Carry ONE mark Each
11. The major product formed in the given reaction is
12. The compound which gives a fragment at m/z = 124[M + H]+ is
13. The major product formed in the given reaction is
14. The major product formed in the given reaction is
15. On irradiation using UV light (>300 nm), compounds X and Y, predominantly, undergo
(A) X: Norrish type I reaction and Y: Norrish type II reaction
(B) X: Norrish type II reaction and Y: Norrish type I reaction
(C) Both X and Y: Norrish type I reaction
(D) Both X and Y: Norrish type II reaction
16. The topicity relationship of Ha and Hb in X, Y and Z are, respectively,
(A) Diastereotopic, Homotopic and Enantiotopic
(B) Homotopic, Enantiotopic and Enantiotopic
(C) Homotopic, Homotopic and Enantiotopic
(D) Diastereotopic, Enantiotopic and Homotopic
17. Compound P was prepared based on a four-component reaction at room temperature in methanol. The required starting materials for the synthesis are
18. The major product formed in the following reaction is
19. The reaction of Ph3PCl2 with PhNH2 primarily produces
20. Formation of [M(en)3]2+ from [M(H2O)6]2+ and three equivalents of ethylenediamine (en) is LEAST favored when M is
21. Wacker oxidation of alkenes is catalyzed by a combination of
(A) Pd(II) and Cu(II)
(B) Co(II) and Cu(II)
(C) Pd(II) and Ni(II)
(D) Pd(II) and Co(II)
22. For the conversion of [Pt(L)Cl3]− to trans-[Pt(L)Cl2(H2O)], the trans-effect is LEAST when the ligand L is
23. The tetracoordinated copper center in the oxidized and reduced forms of plastocyanin exhibits longest bond with
(A) cysteine-S and methionine-S, respectively
(B) methionine-S and cysteine-S, respectively
(C) cysteine-S and cysteine-S, respectively
(D) methionine-S and methionine-S, respectively
24. The packing efficiency (in %) of spheres for a body-centered cubic (bcc) lattice is approximately
25. The magnitudes of CFSE in [M(H2O)6]n+ for Mn and Fe ions satisfy the relations
(A) Mn2+ < Mn3+ and Fe2+ < Fe3+
(B) Mn2+ > Mn3+ and Fe2+ > Fe3+
(C) Mn2+ < Mn3+ and Fe2+ > Fe3+
(D) Mn2+ > Mn3+ and Fe2+ < Fe3+
26. The organometallic catalyst for the following transformation is
27. Point group of naphthalene (C10H8) is
28. The INCORRECT statement is
(A) Zero-point energy of a quantum mechanical harmonic oscillator of frequency v is hv/2
(B) Energy level of a quantum mechanical rigid rotor is inversely proportional to its moment of inertia
(C) The time independent Schrödinger equation for Li2+ cannot be solved exactly
(D) Total angular momentum of an atomic system is equal to the sum of orbital angular momentum and spin angular momentum
29. For an ideal gas, the molecular partition function in the canonical ensemble, that is proportional to the system volume (V), is the
(A) vibrational partition function
(B) rotational partition function
(C) electronic partition function
(D) translational partition function
30. Assertion (S): The total angular momentum for light atoms (low atomic number) is obtained by Russell-Saunders coupling, whereas jj-coupling is used for heavy atoms (high atomic number).
Reasoning (R): The spin-orbit interactions are weak in light atoms (low atomic number) and strong in heavy atoms (high atomic number).
The correct option is
(A) S and R are true; and R is the correct reason for S
(B) S and R are true; but R is NOT the correct reason for S
(C) S is true but R is false
(D) S is false but R is true
31. The acetolysis product(s) of the given reaction is(are)
32. Product(s) formed in the given reaction is(are)
33. The choice(s) that correctly identify radioisotopes (P, Q, R, S) shown in the following nuclear reaction is(are)
34. For the Lindemann-Hinshelwood mechanism of gas phase unimolecular reactions, the true statement(s) is(are)
(A) Only molecules with three or more atoms can follow the Lindemann-Hinshelwood mechanism
(B) Lindemann-Hinshelwood mechanism involves bimolecular elementary steps
(C) The overall reaction is of second order at low pressure
(D) The overall reaction is of second order at high pressure
35. The calculated magnetic moment of [Ce(NO3)5]2− is _______ BM. (rounded off to two decimal places)
(Given: atomic number of Ce is 58)
Q.36 – Q.65 Carry TWO marks Each
36. A compound, C15H16O2 , has the following spectral data;
1H NMR (ppm): 9.16 (s), 6.89 (d, J = 8 Hz), 6.64 (d, J = 8 Hz), 1.53 (s)
13C NMR (ppm): 154.7, 140.9, 127.1, 114.4, 40.7, 30.7
The structure of the compound is
37. The major product formed in the given reaction sequence is
38. E and F in the given reaction scheme are
39. M and N in the given reaction scheme are
40. In the 1H NMR spectrum, multiplicity of the signal (bold and underlined H atom) in the following species is
(A) I- pentet, II- quartet, III- doublet and IV- singlet
(B) I- pentet, II- singlet, III- singlet and IV- doublet
(C) I- triplet, II- triplet, III- doublet and IV- doublet
(D) I- singlet, II- quartet, III- singlet and IV- singlet
41. The major product obtained by the treatment of (η5-C5H5)2Ni with Na/Hg in ethanol is
(A) (η5-C5H5)( η3-C5H5)Ni
(C) (η5-C5H5)( η3-C5H7)Ni
42. The number of shared corners of the constituent SiO4 units in orthosilicate, pyrosilicate, cyclic silicate and sheet silicate, respectively, are
(A) 0, 1, 2 and 3
(B) 2, 3, 0 and 1
(C) 0, 3, 1 and 2
(D) 1, 2, 3 and 0
43. Concentration of Q in a consecutive reaction is given by where [P]0 is the initial concentration of P.
If the value of k2 = 25 s−1, the value of k1 that leads to the longest waiting time for Q to reach its maximum is
(A) k1 = 20 s−1
(B) k1 = 25 s−1
(C) k1 = 30 s−1
(D) k1 = 35 s−1
44. The wave function for Be3+ in a certain state is given by where N is the normalization constant, r is the distance of electron from the nucleus and 𝑎0 is the Bohr radius. The most probable distance of the electron from the nucleus in this state is
45. Match the following
(A) P→III, Q→I, R→IV, S→II
(B) P→III, Q→IV, R→II, S→I
(C) P→IV, Q→I, R→III, S→II
(D) P→II, Q→III, R→IV, S→I
46. In the scheme below,
Iα represents the intensity of the light absorbed. Assuming that the quantum yield of the first step is one, the steady state concentration of Q is given by
47. Product(s) formed in the given reaction sequence is(are)
48. Product(s) formed in the reaction below is(are)
49. The stereoisomer(s) of G giving the depicted product is(are)
50. Product(s) formed in the given reaction sequence is(are)
51. The reaction(s) in which inversion of configuration occur(s) is(are)
52. The correct statement(s) regarding myoglobin (Mb) and haemoglobin (Hb) is(are)
(A) At low partial pressure of O2 (e.g., 5 kPa), the O2 affinity of Hb lowers upon lowering the pH
(B) Binding of the first O2 molecule to Hb results in lower affinity for the binding of second O2 molecule
(C) Metal center in deoxy-Mb is low-spin whereas it is high-spin in the case of oxy-Mb
(D) One end of O2 binds to the metal center in oxy-Mb and the other end of the bound O2 is H-bonded with imidazole-NH of a distal histidine
53. The correct statement(s) regarding Co2(CO)8 is(are)
(A) It reacts with Na to give Na[Co(CO)4]
(B) It contains three bridging carbonyls
(C) It can be prepared by reductive carbonylation of Co(OAc)2·4H2O
(D) Two isomers exist in hexane solution
54. The compound(s) having [Xe]4f1 configuration is(are)
(Given the atomic numbers Ce:58, Lu:71, Pr:59 and Nd:60)
(D) Nd(NR2)3 (R = SiMe3)
55. The correct statement(s) for XeF2 is(are)
(A) Its bonding is best explained by classical 2-centered-2-electron bonds
(B) Its bonding is best explained by a non-classical 3-centered-4-electron bond
(C) It contains nine lone pairs of electrons
(D) Its point group is D∞h
56. For the non-dissociative adsorption of a gas on solid,
(i) the Freundlich isotherm is given by θ = kp1/n where θ is surface coverage, p is pressure, k and n are empirical constants; and
(ii) the BET isotherm is given by
where p* and c empirical constants, and p < p*.
The correct statement(s) is(are)
(A) At low surface coverage, the Langmuir isotherm reduces to the Freundlich isotherm with n = 1
(B) At high surface coverage, the Langmuir isotherm reduces to the Freundlich isotherm with n = ∞
(C) At very low pressure (p << p*), the BET isotherm reduces to the Langmuir isotherm
(D) At very high pressure (p → p*), the BET isotherm reduces to the Langmuir isotherm
57. Two different enzyme catalysis reactions I and II have identical Y-intercepts for the Lineweaver-Burke (equation given below) plots. The slope for reaction I is twice than that of reaction II.
If the initial concentrations of enzymes in I and II are same, the correct statement(s) is(are)
where v and vmax are rate and maximum rate; KM is Michaelis-Menten constant, and [S] is substrate concentration.
(A) Reactions I and II have same turn over number
(B) Michaelis-Menten constants for reactions I and II are identical
(C) Michaelis-Menten constant for reaction I is twice than that of reaction II
(D) The rates of the elementary steps for reactions I and II are identical
58. The enthalpy change for the exothermic reaction between BeI2 and HgF2 is _______kJ mol−1 (rounded off to the nearest integer)
(Given: Bond dissociation energy (in kJ mol−1) for Be−F = 632, Be−I = 289, Hg−F = 268 and Hg−I = 145)
59. Number of carbon atoms connected to the metal center in [W(C60)(CO)5] is _______ (rounded off to the nearest integer)
(Given: atomic number of W is 74)
60. Two-component solid-liquid system of naphthalene-benzene forms a simple eutectic mixture. Assuming that naphthalene-benzene forms an ideal solution, the mole fraction of naphthalene in benzene at 300 K and 1 bar is _______ (rounded off to two decimal places)
(Given: Freezing point (Tfp) and enthalpy of fusion (∆Hfus) of naphthalene are 353 K and 19.28 kJ mol−1, respectively and gas constant (R) =8.31 J K−1 mol−1)
61. The intrinsic viscosity of a sample of polystyrene in toluene is 84 cm3 g−1 at 30° It follows Mark-Houwink equation with empirical constant values of K = 1.05 × 10−2 cm3 g−1 and a = 0.75. The molecular weight of the polymer is ________ × 103 g mol−1 (rounded off to the nearest integer)
62. According to Debye-Hückel limiting law, the mean molal activity coefficient for 0.87 g K2SO4 (molar mass = 174 g mol−1) in 1 kg of water at 25°C is _________ (rounded off to two decimal places)
63. A solution is prepared by dissolving 128 g of naphthalene (C10H8) in 780 g of benzene (C6H6). The vapor pressure of pure benzene is 12.6 kPa at 25° Assuming that naphthalene in benzene is an ideal solution, the partial vapor pressure of benzene is _________ kPa (rounded off to two decimal places)
64. For the galvanic cell: H2 (g) | HCl (aq) | Cl2 (g)
the standard electromotive force (E0) value is given by
E0 = 1.73 – (1.25 × 10−3)T + (1.00 × 10−6)T2
where E0 is in Volts and T is in Kelvin.
For the cell reaction, the standard enthalpy change (∆rH0) at 300 K is _________ kJ mol−1(rounded off to the nearest integer)
(Given: Faraday constant, F = 96500 C mol−1)
65. A solution of three non-interacting compounds P, Q, and R is taken in a cuvette of 1 cm path length. Their concentrations are [P] = 1 × 10−6 M, [Q] = 2 × 10−6 M, [R] = 3 × 10−6 M and the molar extinction coefficients at 300 nm are εP =1 × 105 M−1 cm−1, εQ = 2 × 105 M−1 cm−1 and εR = 3 × 105 M−1 cm−1. The % transmittance at 300 nm is __________ (rounded off to two decimal places)
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