Q61. In Infrared spectroscopy the correct order of νC=O stretching absorption of the following compounds is:
[A] = Br–CH₂COOH
[B] = Cl₂CHCOOH
[C] = F₃C–COOH
A [A] < [B] < [C] B [A] > [B] > [C] C [A] < [C] < [B] D [C] > [A] > [B] E Question not attempted
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Correct answer: [A] < [B] < [C]
Q62. The non-haem iron protein which serves as oxygen carrier in some marine worms is:
A Haemoglobin B Ferradoxin C Haemerythrin D Myoglobin E Question not attempted
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Correct answer: Haemerythrin
Q63. Reaction with which of the following reagents indicates the presence of carbonyl group in glucose?
A HI B NH₂OH C (CH₃CO)₂O D H₂O E Question not attempted
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Correct answer: NH₂OH
Q64. What would be the λmax of the following compound, calculated as per Woodward-Fieser rule? [Chemical structure as shown in question paper]
A 304 nm B 313 nm C 343 nm D 368 nm E Question not attempted
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Correct answer: 343 nm
Q65. The monomer units of biodegradable polymer Nylon-2-Nylon-6 are:
A Glycine and amino-caproic acid B Glycine and adipic acid C Glycine and pthalic acid D Pthalic acid and amino-caproic acid E Question not attempted
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Correct answer: Glycine and amino-caproic acid
Q66. Which of the following is an example of antiseptic?
A Penicillin B Omeprazol C Novestrol D Bithionol E Question not attempted
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Correct answer: Bithionol
Q67. Which of the following compound was first synthesised by Acharya Prafulla Chandra Ray?
A Zinc sulphate B Sulphuric acid C Potassium nitrate D Mercurous nitrite E Question not attempted
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Correct answer: Mercurous nitrite
Q68. The deficiency of which vitamin causes bleeding gums?
A Thiamine B Riboflavin C Pyridoxine D Ascorbic acid E Question not attempted
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Correct answer: Ascorbic acid
Q69. The three sets of values for the spring constant (K), damping constant (b) and mass (m) for a lightly damped spring-mass harmonic oscillator are given below:
Set 1: K = 2K₀, b = b₀, m = 2m₀
Set 2: K = K₀, b = 6b₀, m = 4m₀
Set 3: K = 3K₀, b = 3b₀, m = m₀
Rank the sets in descending order according to the time required for the mechanical energy to decrease to one-fourth of its initial value:
A 1 > 2 > 3 B 3 > 1 > 2 C 2 > 3 > 1 D 1 > 3 > 2 E Question not attempted
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Correct answer: 1 > 2 > 3
Q70. A mass M travels at speed v₀ perpendicular to a stick of mass m and length l which is initially at rest (Fig. a). The mass collides completely inelastically with the stick at one of its ends (Fig. b). What is the resulting angular velocity ω of the system? [Figure as shown in question paper]
A v₀/(2l) B v₀/(4l) C 5v₀/(6l) D 6v₀/(5l) E Question not attempted
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Correct answer: 6v₀/(5l)
Q71. Four point charges are placed very close to each other as shown in the figure. The separation between the two charges on the y-axis is 'd'. The separation between the two charges on the x-axis is also 'd'. Find the electrostatic potential at a point P, which is located at a distance r from origin (r ≫ d). [Figure as shown in question paper]
A (Kqd/(2r²))(√3 − 1) B (Kqd/r²)(1 − √3) C 2Kqd/r² D (Kqd/r²)(√3 − 1) E Question not attempted
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Correct answer: (Kqd/(2r²))(√3 − 1)
Q72. Consider two identical bodies each with rest mass m₀, approaching each other at equal relativistic speeds v. The bodies collide and stick to each other. What is the ratio of final rest mass of the system to its initial rest mass?
A 1/√(1 − v²/c²) B 2/√(1 − v²/c²) C 1 D Insufficient information E Question not attempted
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Correct answer: 1/√(1 − v²/c²)
Q73. Consider the two concentric conducting spherical bodies shown in figure. Here, the inner sphere has a radius of 3 cm and a net charge of +12 μC. The outer spherical shell has inner radius of 6 cm and outer radius of 8 cm and a net charge of −6 μC. Now consider the following statements and choose the correct option:
A: The net charge on the inner surface of the outer shell is zero.
B: The electric field at a radial distance r = 7 cm from the centre is zero. [Figure as shown in question paper]
A Only the statement A is correct. B Only the statement B is correct. C Both the statements A and B are correct. D Both the statements A and B are wrong. E Question not attempted
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Correct answer: Only the statement B is correct.
Q74. For crystalline Sulphur the number of atoms per unit volume is 3.3 × 10²⁸/m³. If the electronic polarizability of Sulphur atom is 3.28 × 10⁻⁴⁰ Fm², the relative permittivity of Sulphur is nearly:
A 2 B 3 C 4 D 6 E Question not attempted
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Correct answer: 3
Q75. Read the following sentences regarding interference from two sources:
(A): If the waves from two sources are incoherent there would be no fringe pattern on the screen.
(B): The average intensity on the screen must be 2I₀ regardless of whether the sources are coherent or not.
(Here I₀ is intensity of the light on the screen from one slit (source) when other slit (source) is covered.)
A Both (A) & (B) are correct. B Only (A) is correct. C Only (B) is correct. D Both (A) & (B) are incorrect. E Question not attempted
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Correct answer: Both (A) & (B) are correct.
Q76. A beam of light of wavelength 590 nm is focussed by a converging lens of diameter 10 cm at a distance of 20 cm from it. The diameter of the disc image formed is (in cm):
A 2.8 × 10⁻⁵ B 2.8 × 10⁻⁴ C 1.4 × 10⁻⁴ D 1.4 × 10⁻⁶ E Question not attempted
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Correct answer: 2.8 × 10⁻⁴
Q77. Find the amplitude of the displacement current density adjacent to an antenna where the magnetic field intensity of an electromagnetic signal is Hₓ = 0.15 cos[4(3 × 10⁸t − y)] A/m. [Where symbols have their usual meaning]
A 0.3 A/m² B 0.6 A/m² C 0.3 μ₀ A/m² D 0.6 μ₀ A/m² E Question not attempted
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Correct answer: 0.6 A/m²
Q78. Suppose 145 moles of a monoatomic gas undergoes an isothermal expansion, as shown in figure. Now consider the following statements and select the correct option:
A: Due to lack of information the change in the temperature of the gas during the process can not be calculated.
B: Work done on the gas during expansion is 555 kJ. [Figure as shown in question paper]
A Only the statement A is correct. B Only the statement B is correct. C Both the statements A and B are correct. D Both the statements A and B are wrong. E Question not attempted
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Correct answer: Both the statements A and B are wrong.
Q79. There is a system of three polarizing sheets in the path of initially unpolarized light. The polarizing direction of the first sheet is parallel to the y-axis, that of the second sheet is at an angle of 60° counter clockwise from the y-axis and that of the third sheet is parallel to the x-axis. Approximately, the ratio of the initial intensity I₀ to light intensity after passing through the three-sheet system, is:
A 0.940 B 0.094 C 0.050 D 0.50 E Question not attempted
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Correct answer: 0.094
Q80. The number Ω of states accessible to N atoms of a monoatomic ideal gas with a volume V, when the energy of the gas is between E and E + dE is given by Ω = AVᴺ E³ᴺ/². Here factor A depends only on N. The entropy of gas as a function of V and E is given by: (k is Boltzmann constant)
A S = k ln A − k ln V + Nk ln E B S = k ln A − Nk ln V − Nk ln E C S = Nk ln A + Nk ln V + (3/2)Nk ln E D S = k ln A + Nk ln V + (3/2)Nk ln E E Question not attempted
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Correct answer: S = k ln A + Nk ln V + (3/2)Nk ln E