GATE-2021
CY: Chemistry
GA-General Aptitude
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Getting to the top is ___________than staying on top.
(A) more easy
(B) much easy
(C) easiest
(D) easier
2. The mirror image of the above text about the x-axis is
3. In a company, 35% of the employees drink coffee, 40% of the employees drink tea and 10% of the employees drink both tea and coffee. What % of employees drink neither tea nor coffee?
(A) 15
(B) 25
(C) 35
(D) 40
4. ⊕ and ⨀ are two operators on numbers p and q such that
If x ⊕ y = 2 ⊙ 2, then x =
(A) y/2
(B) y
(C) 3y/2
(D) 2y
5. Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be seated to the right of Q. The number of distinct seating arrangements possible is:
(A) 2
(B) 4
(C) 6
(D) 8
Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
6. Statement: Either P marries Q or X marries Y
Among the options below, the logical NEGATION of the above statement is:
(A) P does not marry Q and X marries Y.
(B) Neither P marries Q nor X marries Y.
(C) X does not marry Y and P marries Q.
(D) P marries Q and X marries Y.
7. Consider two rectangular sheets, Sheet M and Sheet N of dimensions 6 cm x 4 cm each.
Folding operation 1: The sheet is folded into half by joining the short edges of the current shape.
Folding operation 2: The sheet is folded into half by joining the long edges of the current shape.
Folding operation 1 is carried out on Sheet M three times.
Folding operation 2 is carried out on Sheet N three times.
The ratio of perimeters of the final folded shape of Sheet N to the final folded shape of Sheet M is ______.
(A) 13 : 7
(B) 3 : 2
(C) 7 : 5
(D) 5 : 13
8. Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above.
The value of θ, in degrees, is ______
(A) 36
(B) 45
(C) 72
(D) 108
9. A function, λ, is defined by
The value of the expression is:
(A) −1
(B) 0
(C) 16/3
(D) 16
10. Humans have the ability to construct worlds entirely in their minds, which don’t exist in the physical world. So far as we know, no other species possesses this ability. This skill is so important that we have different words to refer to its different flavors, such as imagination, invention and innovation.
Based on the above passage, which one of the following is TRUE?
(A) No species possess the ability to construct worlds in their minds.
(B) The terms imagination, invention and innovation refer to unrelated skills.
(C) We do not know of any species other than humans who possess the ability to construct mental worlds.
(D) Imagination, invention and innovation are unrelated to the ability to construct mental worlds.
Chemistry (CY)
Q.1 – Q.14 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. The rates of alkaline hydrolysis of the compounds shown below
follow the order:
(A) I > II > III
(B) II > I > III
(C) II > III > I
(D) III > I > II
2. The major product formed in the following reaction
is
3. The major product formed in the following reaction
is
4. The least acidic among the following compounds
is
(A) M
(B) N
(C) O
(D) P
5. The major product formed in the following reaction
is
6. The reagent(s) required for the conversion of hex-3-yne to (E)-hex-3-ene is/are:
(A) H2, Pd/BaSO4
(B) Bu3SnH
(C) Li / liquid NH3
(D) LiAlH0
7. An organic compound exhibits the [M]+, [M+2]+ and [M+4]+ peaks in the intensity ratio 1:2:1 in the mass spectrum, and shows a singlet at δ49 in the 1H NMR spectrum in CDCl3. The compound is:
(A) 1,4-dichlorobenzene
(B) 1,4-dibromobenzene
(C) 1,2-dibromobenzene
(D) 1,2-dichlorobenzene
8. Reaction of LiAlH4 with one equivalent of Me3N∙HCl gives a tetrahedral compound, which reacts with another equivalent of Me3N∙HCl to give compound N. The compound N and its geometry, respectively, are:
(A) LiAlH4NMe3 and trigonal bipyramidal
(B) Li2AlH4Cl and square pyramidal
(C) AlH3(NMe3)2 and trigonal bipyramidal
(D) AlH3(NMe3)2 and pentagonal
9. Which one of the following is a non-heme protein?
(A) hemoglobin
(B) hemocyanin
(C) myoglobin
(D) cytochrome P-450
10. A correct example of a nucleotide is:
(A) adenosine monophosphate (AMP)
(B) RNA
(C) uridine
(D) DNA
11. The equilibrium constant for the reaction
3 NO (g) ⇌ N2O (g) + NO2 (g)
at 25 °C is closest to:
[ΔG° = −104.18 kJ; R = 8.314 J mol−1 K−1]
(A) 1.043
(B) 1.8 × 108
(C) 1.651
(D) 5.7 × 10−19
12. The reaction of NiBr2 with two equivalents of PPh3 in CS2 at –78 °C gives a red-colored diamagnetic complex, [NiBr2(PPh3)2]. This transforms to a green-colored paramagnetic complex with the same molecular formula at 25 °C. The geometry and the number of unpaired electrons in the green-colored complex, respectively, are:
(A) tetrahedral and 1
(B) tetrahedral and 2
(C) square planar and 2
(D) square planar and 4
13. The rate of the substitution reaction of [Co(CN)5Cl]3– with OH– to give [Co(CN)5(OH)]3–
(A) depends on the concentrations of both [Co(CN)5Cl]3– and OH–
(B) depends on the concentration of [Co(CN)5Cl]3– only
(C) is directly proportional to the concentration of OH– only
(D) is inversely proportional to the concentration of OH–
14. The ∆o of [Cr(H2O)6]3+, [CrF6]3– and [Cr(CN)6]3– follows the order:
(A) [Cr(H2O)6]3+ > [CrF6]3– > Cr(CN)6]3–
(B) [CrF6]3– > [Cr(H2O)6]3+ > [Cr(CN)6]3–
(C) [Cr(CN)6]3– > [Cr(H2O)6]3+ > [CrF6]3–
(D) [CrF6]3– > [Cr(CN)6]3– > [Cr(H2O)6]3+
Q.15 – Q.18 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).
15. The phase diagram of CO2 is shown below:
The correct statement(s) about CO2 is/are:
(A) Below Tc, it does not exist in liquid state.
(B) Above Tc, it does not exist in liquid state.
(C) At Tc, it can exist in all three phases.
(D) Above T1, it does not exist in solid state.
16. Acceptable wavefunctions for a quantum particle must be:
(A) odd
(B) even
(C) single-valued
(D) continuous
17. The characters of E, C2, σv, and σ’v symmetry operations, in this order, for valid irreducible representation(s) of the C2v point group is/are:
(A) 1, 1, 1, 1
(B) −1, 1, 1, −1
(C) 1, −1, 1, −1
(D) 1, −1, −1, −1
18. The normal mode(s) of vibration of H2O is/are:
Q.19 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
19. A reversible heat engine absorbs 20 kJ of heat from a source at 500 K and dissipates it to the reservoir at 400 K. The efficiency of the heat engine is _______%.
20. Among the following eight compounds,
the number of compound(s) which can exhibit stereoisomerism is _______.
21. The Mo−Mo bond order in [(η5-C5H5)Mo(CO)2]2 which obeys the 18-electron rule is _______.
22. The change in enthalpy (ΔH) for the reaction
2 P (s) + 3 Br2 (l) → 2 PBr3 (l)
is −243 kJ. In this reaction, if the amount of phosphorus consumed is 3.1 g, the change in enthalpy (rounded off to two decimal places) is ______ kJ.
[Atomic Wt. of P = 31]
23. The number of signal(s) in the 1H NMR spectrum of the following compound
recorded at 25 °C in CDCl3 is __________.
24. A 5 V battery delivers a steady current of 1.5 A for a period of 2 h. The total charge that has passed through the circuit is ______ Coulombs.
25. The spin-only magnetic moment of [Co(H2O)6]2+ (rounded off to one decimal place) is _______ BM.
Q.26 – Q.42 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
26. The geometry and the number of unpaired electrons in tetrakis(1-norbornyl)Co
respectively, are:
(A) tetrahedral and one
(B) tetrahedral and five
(C) square planar and one
(D) square planar and three
27. The yellow color of an aqueous solution of K2CrO4 changes to red-orange upon the addition of a few drops of HCl. The red-orange complex, the oxidation state of its central element(s), and the origin of its color, respectively, are:
(A) chromium chloride, +3, d-d transition
(B) dichromate ion, +6 and +6, charge transfer
(C) perchlorate ion, +7, charge transfer
(D) chromic acid, +6, charge transfer
28. The shapes of the compounds
ClF3, XeOF2, N3− and XeO3F2
respectively, are:
(A) T-shape, T-shape, linear and trigonal bipyramidal
(B) trigonal planar, T-shape, V-shape and square pyramidal
(C) T-shape, trigonal planar, linear and square pyramidal
(D) trigonal planar, trigonal planar, V-shape and trigonal bipyramidal
29. The metal borides that contain isolated boron atoms are:
(A) Tc7B3 and Re7B3
(B) Cr5B3 and V3B2
(C) Ti4B4 and V3B4
(D) TiB and HfB
30. The major product formed in the following reaction
is
(A) non-6-yn-2-one
(B) non-3-yn-8-one
(C) non-2-yn-6-one
(D) non-3-en-8-one
31. The major product formed in the following reaction
is:
32. The major product formed in the following reaction
is:
33. In the following reaction sequence
the major products P and Q, respectively, are:
34. In an electrochemical cell, Ag+ ions in AgNO3 are reduced to Ag metal at the cathode and Cu is oxidized to Cu2+ at the anode. A current of 0.7 A is passed through the cell for 10 min. The mass (in grams) of silver deposited and copper dissolved, respectively, are:
[Faraday Constant = 96,485 C mol−1, Atomic Weight of Ag = 107.9, Atomic Weight of Cu = 63.55]
(A) 0.469 and 0.138
(B) 0.235 and 0.138
(C) 0.469 and 0.069
(D) 0.235 and 0.069
35. Among the following
the compounds which can be prepared by nucleophilic substitution reaction are:
(A) III, IV, and V
(B) I, II, and VI
(C) II, IV, and VI
(D) I, III, and V
36. In the following reaction
the major products X and Y, respectively, are:
37. The major products P and Q formed in the following reactions
respectively, are:
38. The major product formed in the reaction of (2R,3R)-2-bromo-3-methylpentane with NaOMe is:
(A) (Z)-3-methylpent-2-ene
(B) (E)-3-methylpent-2-ene
(C) (2R,3R)-2-methoxy-3-methylpentane
(D) (2S,3R)-2-methoxy-3-methylpentane
39. The major product formed in the following reaction
is:
40. Hexane and heptane are completely miscible. At 25 °C, the vapor pressures of hexane and heptane are 0.198 atm and 0.06 atm, respectively. The mole fractions of hexane and heptane in the vapor phase for a solution containing 4 M hexane and 6 M heptane, respectively, are:
(A) 0.688 and 0.312
(B) 0.400 and 0.600
(C) 0.312 and 0.688
(D) 0.600 and 0.400
41. The correct order of Lewis acid strengths of BF2Cl, BFClBr, BF2Br and BFBr2 is:
(A) BF2Cl > BFClBr > BF2Br > BFBr2
(B) BFBr2 > BFClBr > BF2Br > BF2Cl
(C) BF2Cl > BF2Br > BFClBr > BFBr2
(D) BFClBr > BFBr2 > BF2Cl > BF2Br
42. The correct order of increasing intensity (molar absorptivity) of the UV-visible absorption bands for the ions [Ti(H2O)6]3+, [Mn(H2O)6]2+, [CrO4]2–, and [NiCl4]2– is:
(A) [Ti(H2O)6]3+ < [Mn(H2O)6]2+ < [CrO4]2– < [NiCl4]2–
(B) [Mn(H2O)6]2+ < [Ti(H2O)6]3+ < [NiCl4]2– < [CrO4]2–
(C) [NiCl4]2– < [Ti(H2O)6]3+ < [Mn(H2O)6]2+ < [CrO4]2–
(D) [Ti(H2O)6]3+ < [NiCl4]2– < [CrO4]2– < [Mn(H2O)6]2+
Q.43 – Q.44 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
43. The correct statement(s) about the concentration of Na+ and K+ ions in animal cells is/are:
(A) [K+] inside the cell > [K+] outside the cell
(B) [Na+] inside the cell > [Na+] outside the cell
(C) [Na+] inside the cell < [Na+] outside the cell
(D) [K+] inside the cell < [K+] outside the cell
44. The correct statement(s) about actinides is/are:
(A) The 5f electrons of actinides are bound less tightly than the 4f electrons.
(B) The trans uranium elements are prepared artificially.
(C) All the actinides are radioactive.
(D) Actinides do not exhibit actinide contraction.
Q.45 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).
45. The number of photons emitted per nanosecond by a deuterium lamp (400 nm) having a power of 1 microwatt (rounded off to the nearest integer) is ______.
[h = 6.626 × 10−34 kg m2s−1; c = 3.0 108 m s−1]
46. Given the initial weight of 1 mg of radioactive (half-life = 5.27 years), the amount disintegrated in 1 year (rounded off to two decimal places) is _______mg.
47. The de Broglie wavelength of an argon atom (mass = 40 amu) traveling at a speed of 250 ms−1 (rounded off to one decimal place) is __________ picometers.
[N = 6.022 × 1023; h = 6.626 × 10−34 kg m2s−1]
48. The molar absorption coefficient of a substance dissolved in cyclohexane is 1710 L mol−1 cm−1 at 500 nm. The reduction in intensity of light of the same wavelength that passes through a cell of 1 mm path length containing a 2 m mol L−1solution (rounded off to one decimal place) is ___________%.
49. The fundamental vibrational frequency of 1H127I is 2309 cm−1. The force constant for this molecule (rounded off to the nearest integer) is _____N m−1.
[N = 6.022 × 1023, c = 3.0 × 108 m s−1]
50. A laser Raman spectrometer operating at 532 nm is used to record the vibrational spectrum of Cl2 having its fundamental vibration at 560 cm−1. The Stokes line corresponding to this vibration will be observed at _______ cm−1. (Rounded off to the nearest integer)
51. The vapor pressure of toluene (Mol. Wt. = 92) is 0.13 atm at 25°C. If 6 g of a hydrocarbon is dissolved in 92 g of toluene, the vapor pressure drops to 0.12 atm. The molar mass of the hydrocarbon (rounded off to the nearest integer) is _______.
52. The reaction
CO (g) + Cl2 (g) ⇌ COCl2 (g)
at 500°C, with initial pressures of 0.7 bar of CO and 1.0 bar of Cl2, is allowed to reach equilibrium. The partial pressure of COCl2 (g) at equilibrium is 0.15 bar. The equilibrium constant for this reaction at 500°C (rounded off to two decimal places) is ________.
53. The rate constants for the decomposition of a molecule in the presence of oxygen are 0.237 × 10−4 L mol−1 s−1 at 0 °C and 2.64 × 10−4 L mol−1 s−1 at 25 °C (R = 8.314 J mol−1 K−1).
The activation energy for this reaction (rounded off to one decimal place) is ___________ kJ mol−1.
54. 2 L of a gas at 1 atm pressure is reversibly heated to reach a final volume of 3.5 L. The absolute value of the work done on the gas (rounded off to the nearest integer) is _______ Joules.
55. The quantity of the cobalt ore [Co3(AsO4)2∙H2O] required to obtain 1 kg of cobalt (rounded off to two decimal places) is _________ kg.
[Atomic Wt. of Co = 59, As = 75, O = 16, H = 1]