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GATE
2025
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.
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General Aptitude
Q.1 – Q.5 Carry ONE mark Each
Q.1 Courage : Bravery :: Yearning : __________
Select the most appropriate option to complete the analogy.
(A) Longing
(B) Yelling
(C) Yawning
(D) Glaring
Q.2 We __________ tennis in the lawn when it suddenly started to rain.
Select the most appropriate option to complete the above sentence.
(A) have been playing
(B) had been playing
(C) would have been playing
(D) could be playing
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Q.3 A 4 × 4 digital image has pixel intensities (𝑈) as shown in the figure. The number of
pixels with 𝑈 ≤ 4 is:
(A) 3
(B) 8
(C) 11
(D) 9
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Q.4 In the given figure, the numbers associated with the rectangle, triangle, and ellipse
are 1, 2, and 3, respectively. Which one among the given options is the most
appropriate combination of P, Q, and R ?
2
R
4
Q
1 P
3
(A) P = 6; Q = 5; R = 3
(B) P = 5; Q = 6; R = 3
(C) P = 3; Q = 6; R = 6
(D) P = 5; Q = 3; R = 6
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Q.5 A rectangle has a length L and a width W, where L > W. If the width, W, is increased
by 10%, which one of the following statements is correct for all values of L and W?
(A) Perimeter increases by 10%.
(B) Length of the diagonals increases by 10%.
(C) Area increases by 10%.
(D) The rectangle becomes a square.
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Q.6 – Q.10 Carry TWO marks Each
Q.6 Column-I has statements made by Shanthala; and, Column-II has responses given
by Kanishk.
Column-I Column-II
P. This house is in a mess. 1. Alright, I won’t bring it up during
our conversations.
Q. I am not happy with the marks 2. Well, you can easily look it up.
given to me.
R. Politics is a subject I avoid talking 3. No problem, let me clear it up for
about. you.
S. I don’t know what this word 4. Don’t worry, I will take it up with
means. your teacher.
Identify the option that has the correct match between Column-I and Column-II.
(A) P – 2; Q – 3; R – 1; S – 4
(B) P – 3; Q – 4; R – 1; S – 2
(C) P – 4; Q – 1; R – 2; S – 3
(D) P – 1; Q – 2; R – 4; S – 3
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Q.7 Weight of a person can be expressed as a function of their age. The function usually
varies from person to person. Suppose this function is identical for two brothers,
and it monotonically increases till the age of 50 years and then it monotonically
decreases. Let 𝑎1 and 𝑎2 (in years) denote the ages of the brothers and 𝑎1 < 𝑎2 .
Which one of the following statements is correct about their age on the day when
they attain the same weight?
(A) 𝑎1 < 𝑎2 < 50
(B) 𝑎1 < 50 < 𝑎2
(C) 50 < 𝑎1 < 𝑎2
(D) Either 𝑎1 = 50 or 𝑎2 = 50
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Q.8 A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius r
cm as shown in the figure. The side of the dodecagon is d cm. All the triangles
(numbered 1 to 12) in the figure are used to form squares of side r cm and each
numbered triangle is used only once to form a square.
The number of squares that can be formed and the number of triangles required to
form each square, respectively, are:
Note: The figure shown is representative.
(A) 3; 4
(B) 4; 3
(C) 3; 3
(D) 3; 2
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Q.9 2
𝑥2 𝑥 2𝑥
If a real variable 𝑥 satisfies 3 = 27 × 9 , then the value of 𝑥 2 is:
(2 )
(A) 2−1
(B) 20
(C) 23
(D) 215
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Q.10 The number of patients per shift (𝑋) consulting Dr. Gita in her past 100 shifts is
shown in the figure. If the amount she earns is ₹ 1000(𝑋 − 0.2), what is the average
amount (in ₹) she has earned per shift in the past 100 shifts?
Note: The figure shown is representative.
50
40
40
Number of shifts
30
30
20
20
10
10
0
5 6 7 8
Number of patients per shift (X)
(A) 6,100
(B) 6,300
(C) 6,000
(D) 6,500
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Q.11 – Q.35 Carry ONE mark Each
Q.11 The phosphazene compound that acts as a superbase is
(A)
(B)
(C)
(D)
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Q.12 The reaction for the synthesis of Me2SiCl2 through Rochow-Müller process is
(A)
(B)
(C)
(D)
Q.13 Upon cooling from room temperature, the magnetic susceptibility of MnO slowly
increases until 118 K, and then it decreases. This phenomenon is known as
(A) ferromagnetism
(B) paramagnetism
(C) antiferromagnetism
(D) ferrimagnetism
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Q.14 An aqueous solution of Co(ClO4)26H2O is light pink in colour. Addition of conc.
HCl results in an intense blue coloured solution due to the formation of a new
species. The new species among the following is
[Given: Atomic number of Co = 27]
(A) I
(B) II
(C) III
(D) IV
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Q.15 For an unambiguous single step synthesis of the following target molecule (TM),
the best bond disconnection in its retrosynthetic analysis is
(TM)
(A)
(B)
(C)
(D)
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Q.16 In the 1H-NMR spectrum of the following molecule, the signal of proton Ha
appears as
(A) singlet
(B) triplet
(C) quintet
(D) quartet
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Q.17 A disaccharide X does NOT show mutarotation in aqueous solution. Acidic
hydrolysis of X affords two different monosaccharides. The disaccharide X is
(A)
(B)
(C)
(D)
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Q.18 The symmetry element that does NOT belong to 𝐶4𝑣 point group is
(A) 𝐶4
(B) 𝐶2
(C) 𝑖
(D) 𝜎𝑣
Q.19 Rigid rotor wavefunctions are given by 𝑌𝑙,𝑚 (𝜃, 𝜙). The wavefunctions 𝑌1,0 (𝜃, 𝜙)
and 𝑌2,0 (𝜃, 𝜙) are given below
3 5
𝑌1,0 (𝜃, 𝜙) = √ cos 𝜃 𝑌2,0 (𝜃, 𝜙) = √ (3 𝑐𝑜𝑠 2 𝜃 − 1)
4𝜋 16𝜋
For a non-polar diatomic molecule, the value of transition dipole moment integral
for transition between 𝑌1,0 (𝜃, 𝜙) and 𝑌2,0 (𝜃, 𝜙) is equal to
(A) 1⁄√2𝜋
(B) 0
(C) 2
(D) 1⁄√4𝜋
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Q.20 The translational, vibrational, and rotational molecular partition functions for a
system containing ideal diatomic gas molecules in the canonical ensemble (N, V,
T) are written as, 𝑞𝑡𝑟𝑎𝑛𝑠 , 𝑞𝑣𝑖𝑏 , and 𝑞𝑟𝑜𝑡 , respectively. The option that correctly
defines their thermodynamic variable(s) dependency is
(A) 𝑞𝑡𝑟𝑎𝑛𝑠 (𝑇, 𝑉), 𝑞𝑣𝑖𝑏 (𝑇, 𝑉), 𝑞𝑟𝑜𝑡 (𝑇, 𝑉)
(B) 𝑞𝑡𝑟𝑎𝑛𝑠 (𝑇, 𝑉), 𝑞𝑣𝑖𝑏 (𝑇), 𝑞𝑟𝑜𝑡 (𝑇)
(C) 𝑞𝑡𝑟𝑎𝑛𝑠 (𝑇), 𝑞𝑣𝑖𝑏 (𝑇, 𝑉), 𝑞𝑟𝑜𝑡 (𝑇)
(D) 𝑞𝑡𝑟𝑎𝑛𝑠 (𝑇, 𝑉), 𝑞𝑣𝑖𝑏 (𝑇), 𝑞𝑟𝑜𝑡 (𝑇, 𝑉)
Q.21 The Vaska’s complex trans-IrCl(CO)(PPh3)2 shows a band at 1967 cm-1 for the
νCO stretching vibration in its infrared spectrum. The complex(es) that will show
an increase in the νCO stretching vibration from 1967 cm-1 is/are
(A)
(B)
(C)
(D)
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Q.22 Under the conditions mentioned for each reaction, the reaction(s) that would give
borazine (B3N3H6) as the major product is/are
(A)
(B)
(C)
(D)
Q.23 The essential symmetry(ies) for a monoclinic crystal system is/are the presence of
(A) one C3 axis
(B) one C2 axis
(C) one C4 axis
(D) one C6 axis
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Q.24 Compound(s) that show(s) an intense peak at m/z 120 in the EI mass spectrum
is/are
(A)
(B)
(C)
(D)
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Q.25 The correct option(s) of reagents and reaction sequences suitable for carrying out
the following transformation is/are
(A) (i) NBS, (PhCOO)2; (ii) aq. NaOH; (iii) active MnO2; (iv) Li/liq.NH3, t-BuOH
(B) (i) m-CPBA; (ii) BF3.Et2O
(C) (i) SeO2; (ii) Dess-Martin periodinane; (iii) K[BH(s-Bu)3] (K-selectride)
(D) (i) dil. KMnO4; (ii) NaIO4
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Q.26 Among the given options, the possible product(s) that can be obtained from the
following reaction is/are
(A)
(B)
(C)
(D)
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Q.27 Choose the correct option(s) with regard to mechanism of the following
transformation.
(A) It proceeds through divinyl cyclopropane rearrangement
(B) It involves a diradical intermediate
(C) It proceeds through di--methane rearrangement
(D) It proceeds through [2+2+2] cycloaddition reaction
Q.28 Consider two non-interacting particles confined to a one-dimensional box with
infinite potential barriers. Their wavefunctions are 𝜓1 and 𝜓2 and energies are 𝐸1
and 𝐸2 , respectively. The INCORRECT statement(s) about this system is/are
(A) The total energy is 𝐸1 + 𝐸2
(B) The total wavefunction is 𝜓1 + 𝜓2
(C) The total energy is 𝐸1 𝐸2
(D) The total wavefunction is 𝜓1 𝜓2
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Q.29 The thermodynamic criterion/criteria for a spontaneous process is/are
(A) ΔU > 0 at constant S and V
(B) ΔS > 0 at constant U and V
(C) Δ(H − TS) > 0 at constant T and P
(D) Δ(𝑈 − 𝑇𝑆) < 0 at constant T and V
Q.30 Xe and F2 in 1:1 molar ratio when mixed in a closed flask and kept in the sunlight
for a day, gave white crystals of a compound Q. Two equivalents of Q on reaction
with one equivalent of AsF5 gave an ionic compound X+Y‒ with the cation having
two Xe atoms. The total number of lone pairs present on the cation X+ is ______
(in integer).
Q.31 The total number of hyperfine lines expected in the EPR spectrum of •CH2OH
(radical) is ____ (in integer).
[Note: Consider all hydrogen atoms for calculation]
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Q.32 Partial hydrolysis of a pentapeptide yields all possible tripeptides and dipeptides.
The dipeptides that are obtained upon hydrolysis are given below.
Val-Ala, Gln-His, Phe-Val and Ala-Gln
The total number of tripeptides obtained that contain ‘Ala’ as one of the amino acids
is____ (in integer).
Q.33 The specific rotation of enantiomerically pure (S)-2-butanol is +14. The specific
rotation of enantiomeric mixture of 2-butanol obtained from an asymmetric
reduction of 2-butanone is found to be +7. The percentage of (R)-2-butanol present
in the reaction mixture is _____ (in integer).
Q.34 The ratio of the fundamental vibrational frequencies (𝜐13C 16O ⁄𝜐12C 16O ) of two
diatomic molecules 13C16O and 12C16O, considering their force constants to be the
same, is_______ (rounded off to two decimal places).
Q.35 The expressions for the vapour pressure of solid (𝑝1) and vapour pressure of liquid
(𝑝2 ) phases of a pure substance, respectively, are
2000 4000
ln 𝑝1 = − +5 and ln 𝑝2 = − + 10
𝑇 𝑇
The triple point temperature of this substance is ____ K (in integer).
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Q.36 – Q.65 Carry TWO marks Each
Q.36 The reaction that proceeds through an oxidative addition followed by a reductive
elimination is
[Given: Atomic numbers Ni = 28, Ta = 73, Zr = 40, Pt = 78]
(A)
(B)
(C)
(D)
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Q.37 The homogeneous catalyst whose metal ion does NOT undergo either oxidation or
reduction in any of the steps during the hydrogenation of terminal olefins is
(A) RhCl(PPh3)3
(B) HRuCl(PPh3)3
(C) [Ir(COD)(PCy3)(Py)]+ PF6− (COD = cyclooctadiene)
(D) [Rh(COD)(PPh3)2]+ PF6− (COD = cyclooctadiene)
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Q.38 The given zirconocene compound, (5-Cp)2ZrEt2, when heated in the presence of
an equimolar amount of PMe3 results in the formation of a compound X which
obeys the 18 electron rule. The reaction also resulted in the release of a saturated
hydrocarbon.
[Given: Atomic number of Zr = 40]
The structure of compound X is
(A)
(B)
(C)
(D)
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Q.39 The 1H NMR spectrum of the given iridium complex at room temperature gave a
single signal at 2.6 ppm, and its 31P NMR spectrum gave a single signal at
23.0 ppm. When the spectra were recorded at lower temperatures, both these signals
split into a complex pattern. The intra-molecular dynamic processes shown by this
molecule are
(A) Berry pseudo-rotation and rotation of the ethylene units along the C=C axis
(B) Berry pseudo-rotation and propeller type rotation of the ethylene units along the
Ir-alkene axis
(C) Ray-Dutt twist and rotation of the ethylene units along the C=C axis
(D) Ray-Dutt twist and propeller type rotation of the ethylene units along the
Ir-alkene axis
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Q.40 The effective magnetic moment, eff value for [Cr(H2O)6]3+ taking into account for
spin-orbit coupling is closest to
[Given: Atomic number of Cr = 24, spin-orbit coupling constant = 92 cm‒1, and
o = 17400 cm‒1]
(A) 3.79 B
(B) 3.87 B
(C) 4.05 B
(D) 3.60 B
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Q.41 The major products X and Y formed in the following reaction sequences are
(A)
(B)
(C)
(D)
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Q.42 Compound K displayed a strong band at 1680 cm-1 in its IR spectrum. Its
1
H-NMR spectral data are as follows: (ppm) 7.30 (d, J = 7.2 Hz, 2H),
6.8 (d, J = 7.2 Hz, 2H), 3.8 (septet, J = 7.0 Hz, 1H), 2.2 (s, 3H),
1.9 (d, J = 7.0 Hz, 6H). The correct structure of compound K is
(A)
(B)
(C)
(D)
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Q.43 The major product formed in the following reaction sequences is
(A)
(B)
(C)
(D)
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Q.44 In the following asymmetric transformation, the key aldol reaction involves the
attack of
(A) Si face of enolate on to the Re face of aldehyde
(B) Si face of enolate on to the Si face of aldehyde
(C) Re face of enolate on to the Re face of aldehyde
(D) Re face of enolate on to the Si face of aldehyde
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Q.45 The correct option with regard to the following statements is
(a) Time-independent Schrödinger equation can be exactly solved for Be2+.
(b) For a particle confined in a one-dimensional box of length l with infinite
3 1/2
potential barriers, the trial variation function 𝜙 = [( 3 ) 𝑥] is not an
𝑙
acceptable trial wavefunction for 0 ≤ 𝑥 ≤ 𝑙.
(c) Wavefunctions for system of Fermions must be anti-symmetric with respect
to exchange of any two Fermions in the system.
(d) Born-Oppenheimer approximation can be used to separate the vibrational
and rotational motion of a molecule.
(A) (a) True (b) False (c) False (d) True
(B) (a) True (b) True (c) False (d) False
(C) (a) False (b) True (c) True (d) False
(D) (a) False (b) True (c) True (d) True
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Q.46 The phase diagram of a single component system is given below.
The option with the correct number of degrees of freedom corresponding to the
labelled points i, j, and k, respectively, is
(A) 0, 1, 2
(B) 3, 2, 1
(C) 2, 0, 1
(D) 0, 2, 1
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Q.47 An approximate partition function 𝑄(𝑁, 𝑉, 𝑇) of a gas is given below.
1 2𝜋𝑚𝑘𝐵 𝑇 3𝑁/2
𝑄(𝑁, 𝑉, 𝑇) = ( ) (𝑉 − 𝑁𝑏)𝑁
𝑁! ℎ2
The equation of state(s) for this gas is/are
[Note: 𝑏 is a parameter independent of volume.]
(A) 𝑃(𝑉 − 𝑁𝑏) = 𝑁𝑘𝐵 𝑇
(B) 𝑃𝑉 (𝑁−𝑏) = 𝑘𝐵 𝑇
(C) 𝑃𝑉 = 𝑁𝑘𝐵 𝑇
(D) 𝑃(𝑉 − 𝑁𝑏) = 𝑁𝑘𝐵
Q.48 The compound(s) having structure similar to that of B2H6 is/are
(A) I2Cl6
(B) Si2Cl6
(C) Al2Cl6
(D) Cl2O6
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Q.49 The UV-visible spectrum of [Ni(en)3]2+ (en = ethylenediamine) shows absorbance
maxima at 11200 cm‒1, 18350 cm‒1, and 29000 cm‒1.
Absorbance maximum Electronic transition
(a) 11200 cm‒1 (i) 3
A2g → 3T1g (F)
(b) 18350 cm‒1 (ii) 3
A2g → 3T2g
(c) 29000 cm‒1 (iii) 3
A2g → 3T1g (P)
[Given: Atomic number of Ni = 28]
The correct match(es) between absorbance maximum and electronic transition
is/are
(A) (a) → (ii)
(B) (b) → (i)
(C) (a) → (iii)
(D) (c) → (iii)
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Q.50 Cytochrome P450 (CYP) enzymes catalyze stereoselective C‒H hydroxylation of
hydrocarbons in the presence of O2. The correct statement(s) about the structure
and activity of CYP is/are
(A) A thiolate group is coordinated to the Fe center at one of the axial positions
around Fe.
(B) While one of the oxygen atoms of O2 is inserted into a C‒H bond of a
hydrocarbon, the other oxygen atom gets reduced to water.
(C) An imidazole group is coordinated to the Fe center at one of the axial positions
around Fe.
(D) An iron-oxo species acts as a key oxidant in the catalytic cycle of CYP.
Q.51 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.]
(A) [Mo2(-SO4)4(H2O)2]3‒
(B) [Mn2(CO)10]
(C) [Cr2(-O2CCH3)4]
(D) [Mo2(-HPO4)4(H2O)2]2‒
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Q.52 Consider the following two reactions and their corresponding Hammett plots
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
Column-I (points on the graph) Column-II (substituent X)
p NH2
q NO2
r OMe
s Cl
t Me
u CN
(A) s → σ(X = Cl) ; t → σ(X = OMe) ; u → σ(X = NH2) ; r → σ(X = NO2)
(B) s → σ(X = Me) ; u → σ(X = NH2 ) ; t → σ(X = OMe) ; r → σ(X = Br)
(C) p → σ(X = Me) ; q → σ(X = CN) ; r → σ(X = NO2) ; t → σ(X = OMe)
(D) p → σ(X = Cl) ; q → σ(X = NO2) ; r → σ(X = CN) ; t → σ(X = Me)
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Q.53 The correct option(s) of reagents and reaction sequences suitable for carrying out
the following transformation is/are
(A)
(B)
(C)
(D)
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Q.54 The process(es) and/or intermediate(s) through which the following
transformation proceeds is/are
(A) 1,2-methide shift
(B) 1,3-methide shift
(C) non-classical carbocation
(D) tertiary carbocation
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Q.55 For the following reaction, the possible product(s) is/are
(A)
(B)
(C)
(D)
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Q.56 Wavefunctions and energies for a particle confined in a cubic box are 𝜓𝑛𝑥 ,𝑛𝑦 ,𝑛𝑧
and 𝐸𝑛𝑥 ,𝑛𝑦 ,𝑛𝑧 , respectively. The functions 𝜙1 , 𝜙2 , 𝜙3 , and 𝜙4 are written as linear
combinations of 𝜓𝑛𝑥 ,𝑛𝑦 ,𝑛𝑧 . Among these functions, the eigenfunction(s) of the
Hamiltonian operator for this particle is/are
1 1
𝜙1 = 𝜓1,4,1 − 𝜓2,2,3
√2 √2
1 1
𝜙2 = 𝜓1,5,1 + 𝜓3,3,3
√2 √2
1 1
𝜙3 = 𝜓1,3,8 + 𝜓3,8,1
√2 √2
1 √3
𝜙4 = 𝜓3,3,1 + 𝜓
2 2 2,4,1
(A) 𝜙2
(B) 𝜙4
(C) 𝜙3
(D) 𝜙1
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Q.57 If a particle’s state function is an eigenfunction of the operator 𝐿̂2 with eigenvalue
30ħ2 , then the possible eigenvalue(s) of the operator 𝐿̂2𝑧 for the same state function
is/are
(A) 10ħ2
(B) 16ħ2
(C) 25ħ2
(D) 0
Q.58 An archaeological specimen containing 14C 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 14C containing sample. The age of the specimen is_____ years
(in integer).
[Note: t1/2 of 14C = 5730 years]
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Q.59 In the following reaction, 13.4 grams of aldehyde P gave a diastereomeric 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).
Q.60 The kinetic energies of an electron (𝑒) and a proton (𝑝) are 𝐸 and 3𝐸,
respectively. Given that mass of a proton is 1836 times that of an electron, the
ratio of their de Broglie wavelengths (𝜆𝑒 ⁄𝜆𝑝 ) is_____ (rounded off to two decimal
places).
Q.61 If a molecule emitting a radiation of frequency 3.100 × 109 Hz approaches an
observer with a relative speed of 5.000 × 106 m s-1, then the observer detects a
frequency of ____ × 109 Hz. (rounded off to three decimal places)
[Given: Speed of light 𝑐 = 3.000 × 108 m s-1]
Q.62 The mean energy of a molecule having two available energy states at 𝜀 = 0 J and
𝜀 = 4.14 × 10‒21 J at 300 K is _____× 10‒21 J (rounded off to two decimal places).
[Given: Boltzmann constant (𝑘𝐵 ) = 1.38 × 10-23 J K-1]
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Q.63 For the cell reaction,
Hg2Cl2 (s) + H2 (1 atm) → 2Hg (l) + 2H+ (a = 1) + 2Cl‒ (a = 1)
𝜕ℰ 0
The standard cell potential is ℰ 0 = 0.2676 V, and ( 𝜕𝑇 ) = ‒3.19 × 10‒4 V K‒1.
𝑃
The standard enthalpy change of the reaction (∆𝑟 𝐻 0 ) at 298 K is ‒𝒙 kJ mol‒1.
The value of 𝒙 is _____ (rounded off to two decimal places).
[Given: Faraday constant 𝐹 = 96500 C mol‒1]
Q.64 Consider a Carnot engine with a hot source kept at 500 K. From the hot source,
100 J of energy (heat) is withdrawn at 500 K. The cold sink is kept at 300 K. The
efficiency of the Carnot engine is _____ (rounded off to one decimal place).
Q.65 The Lineweaver-Burk plot for an enzyme obeying the Michaelis-Menten
mechanism is given below.
The slope of the line is 0.36 × 10-2 s, and the y-intercept is 1.20 mol‒1 L s. The
value of the Michaelis constant (KM) is____× 10-3 mol L‒1 (in integer).
[Note: 𝑣 is the initial rate, and [𝑆]0 is the substrate concentration]
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