GATE CY year:2025 PYQs & Answers — Page 6

Questions 51–60 of 65. Imported answers require independent review unless marked reviewed.

The complex(es) having metal-metal bond order ≥3.5 is/are [Given: The atomic numbers of Mo, Cr, Mn, and Re are 42, 24, 25, and 75, respectively.]

Your answerSelect all correct options. You can choose more than one.

[Mo₂(μ-SO₄)₄(H₂O)₂]³⁻

[Mn₂(CO)₁₀]

[Cr₂(μ-O₂CCH₃)₄]

[Mo₂(μ-HPO₄)₄(H₂O)₂]²⁻

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Consider the following two reactions and their corresponding Hammett plots

Reaction M: Ar–C(CH₃)₂Cl →[S_N1, slow, kₓ] Ar–C⁺(CH₃)₂ →[H₂O, kₓ] Ar–C(CH₃)₂OH Reaction N: Ar–COOEt + OH⁻ →[H₂O, kₓ] Ar–COO⁻ + EtOH

Choose the option(s) that correctly match(es) the points on the graph given in Column-I with substituents X given in Column-II in accordance with their substituents constant σ

Your answerSelect all correct options. You can choose more than one.

s → σ_(X = Cl); t → σ_(X = OMe); u → σ_(X = NH₂); r → σ_(X = NO₂)

s → σ_(X = Me); u → σ_(X = NH₂); t → σ_(X = OMe); r → σ_(X = Br)

p → σ_(X = Me); q → σ_(X = CN); r → σ_(X = NO₂); t → σ_(X = OMe)

p → σ_(X = Cl); q → σ_(X = NO₂); r → σ_(X = CN); t → σ_(X = Me)

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The correct option(s) of reagents and reaction sequences suitable for carrying out the following transformation is/are

Your answerSelect all correct options. You can choose more than one.

(i) Li–C≡C–H, THF, −70 °C; (ii) cat. HgSO₄, H₂SO₄, H₂O; (iii) aqueous acid, Δ

(i)

Diagram for Chemistry question 53 (figure 2)

, NaH; (ii) aqueous acid, Δ

(i) LDA, TfNPh₂; (ii) cat. [(dppe)Pd(0)],

Diagram for Chemistry question 53 (figure 3)

; (iii) aqueous acid, Δ (dppe = diphenylphosphinoethane)

(i) H₃C–NO₂, NaOCH₃; (ii) sat. NaCl; (iii) TiCl₃, H₂O; (iv) aqueous acid, Δ

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The process(es) and/or intermediate(s) through which the following transformation proceeds is/are

Your answerSelect all correct options. You can choose more than one.

1,2-methide shift

1,3-methide shift

non-classical carbocation

tertiary carbocation

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For the following reaction, the possible product(s) is/are

Your answerSelect all correct options. You can choose more than one.

Diagram for Chemistry question 55 (figure 2)

Diagram for Chemistry question 55 (figure 3)

Diagram for Chemistry question 55 (figure 4)

Diagram for Chemistry question 55 (figure 5)

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Wavefunctions and energies for a particle confined in a cube box are

and

, respectively. The functions

, and

are written as linear combinations of

. Among these functions, the eigenfunction(s) of the Hamiltonian operator for this particle is/are

Your answerSelect all correct options. You can choose more than one.

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If a particle’s state function is an eigenfunction of the operator

with eigenvalue

, then the possible eigenvalue(s) of the operator

for the same state function is/are

Your answerSelect all correct options. You can choose more than one.

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An archaeological specimen containing

gives 45 counts per gram of carbon in 5 minutes. A specimen of freshly cut wood gives 20 counts per gram of carbon per minute. The counter used recorded a background count of 5 counts per minute in the absence of any

containing sample. The age of the specimen is _____ years (in integer).\n\n[Note:

= 5730 years]

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In the following reaction, 13.4 grams of aldehyde P gave a diastereomer mixture of alcohols Q and R in a ratio of 2:1.

If the yield of the reaction is 80%, then the amount of Q (in grams) obtained is _____ (in integer).

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The kinetic energies of an electron (

) and a proton (

) are

and

, respectively. Given that mass of a proton is 1836 times that of an electron, the ratio of their de Broglie wavelengths (

) is_____ (rounded off to two decimal places).

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GATE CY year:2025 PYQs

Question 51

Question 52

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60