Q1 · Dec 2019 · 2 marks
A cube does not have the symmetry element
- (a) C_2
- (b) C_3
- (c) C_4
- (d) C_6
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Answer: (d)
CSIR NET Chemical Science — Group Theory previous year questions
29 questions · 2011–2019 · all with verified answer · last checked 2026-11-06
Q2 · June 2019 · 2 marks
The \pi-orbital p_1 + p_2 - p_3 - p_4 of cis-butadiene belongs to the irreducible representation
| \boldsymbol{C}_{\mathbf{2 v}} | E | \boldsymbol{C}_{\mathbf{2}} | \sigma_{v} | \sigma_{v}{ }^{\prime} |
| \boldsymbol{A}_{\mathbf{1}} | 1 | 1 | 1 | 1 |
| \boldsymbol{A}_{\mathbf{2}} | 1 | 1 | -1 | -1 |
| \boldsymbol{B}_{\mathbf{1}} | 1 | -1 | 1 | -1 |
| \boldsymbol{B}_{\mathbf{2}} | 1 | -1 | -1 | 1 |
- (a) A_1
- (b) A_2
- (c) B_1
- (d) B_2
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Answer: (b)
Q3 · Dec 2019 · 2 marks
For every atom that is NOT shifted under C_4 and \sigma symmetry operations, the characters are respectively.
- (a) -1, -1
- (b) 0, 0
- (c) 1, 1
- (d) -1, 1
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Answer: (c)
Q4 · Dec 2019 · 2 marks
The equivalent symmetry operations for S_6^3 and S_3^6 are, respectively
- (a) C_3 and C_2
- (b) \sigma_h and I
- (c) \sigma_h and E
- (d) i and E
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Answer: (d)
Q5 · Dec 2017 · 2 marks
The correct relation involving symmetry operations
- (a) S_{4}^{2}=S_{2}
- (b) \sigma(x z) \cdot \sigma(y z)=C_{2}(x)
- (c) S_{4}^{3}=C_{4}^{3}
- (d) S_{6}^{3}=S_{2}
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Answer: (d)
Q6 · Dec 2017 · 2 marks
The molecule with a C_2 axis of symmetry among the following is
- (a) \mathrm{BH_2Cl}
- (b) \mathrm{CH_3Cl}
- (c) \mathrm{NH_2Cl}
- (d) HOCl
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Answer: (a)
Q7 · June 2016 · 2 marks
The point group obtained by adding symmetry operation \sigma_h to the point group C_4 is
- (a) S_4
- (b) C_{4h}
- (c) D_{2h}
- (d) D_4
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Answer: (b)
Q8 · Dec 2011 · 2 marks
The symmetry point group of the most stable geometry of the following molecule \mathrm{Cl(H)C{=}C{=}C(H)Cl} is
- (a) C_2
- (b) C_1
- (c) C_{2v}
- (d) C_{2h}
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Answer: (a)
Q9 · Dec 2011 · 2 marks
The character table of C_{3v} point group is provided below, along with an additional reducible representation, \Gamma
\Gamma is given by
| E | 2 \mathrm{C}_{3} | 3 \sigma_{\mathrm{v}} | |
| \mathrm{A}_{1} | 1 | 1 | 1 |
| \mathrm{A}_{2} | 1 | 1 | -1 |
| E | 2 | -1 | 0 |
| Г | 6 | 0 | 2 |
- (a) A_1 + A_2 + E
- (b) 2A_1 + 2E
- (c) 2A_2 + 2E
- (d) 2A_1 + 2A_2 + E
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Answer: (b)
Q10 · Dec 2011 · 2 marks
The molecule that possesses symmetry S_4 element is
- (a) ethylene
- (b) allene
- (c) benzene
- (d) 1,3-butadiene
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Answer: (b)
Q11 · Dec 2011 · 2 marks
For H_{2} O molecule, the electronic transition from the ground state to an excited state of B_{1} symmetry is
| C_{2 v} | E | C_{2} | \sigma_{v} | \sigma_{v}^{\prime} | |
| A_{1} | 1 | 1 | 1 | 1 | z, z^{2}, x^{2}, y^{2} |
| A_{2} | 1 | 1 | -1 | -1 | x y |
| B_{1} | 1 | -1 | 1 | -1 | x, x z |
| B_{2} | 1 | -1 | -1 | 1 | y, y z |
- (a) not allowed
- (b) allowed with \boldsymbol{x} polarization
- (c) allowed with \boldsymbol{y} polarization
- (d) allowed with \boldsymbol{z} polarization
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Answer: (b)
Q12 · June 2015 · 2 marks
The product C_2^x \cdot \sigma_{xy} (C_2^x is the two-fold rotation axis around the x-axis and \sigma_{xy} is the xy mirror plane) is
- (a) \sigma_{xz}
- (b) \sigma_{yz}
- (c) C_2^y
- (d) C_2^z
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Answer: (a)
Q13 · Dec 2015 · 2 marks
The product C_2^x.\sigma_{xy} (C_2^x is the two-fold rotation axis around the x-axis and \sigma_{xy} is the xy mirror plane) is
- (a) \sigma_{xz}
- (b) \sigma_{yz}
- (c) C_2^y
- (d) C_2^z
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Answer: (a)
Q14 · Dec 2015 · 2 marks
A molecular orbital of a diatomic molecule changes sign when it is rotated by 180° around the molecular axis. This orbital is
- (a) \sigma
- (b) \pi
- (c) \delta
- (d) \phi
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Answer: (b)
Q15 · Dec 2011 · 2 marks
The molecule diborane belongs to the symmetry point group
- (a) C_{2v}
- (b) C_{2h}
- (c) D_{2d}
- (d) D_{2h}
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Answer: (d)
Q16 · Dec 2011 · 2 marks
The irreducible representations of C_{2h} are A_g, B_g, A_u and B_u. The Raman active modes of trans-1,3-butadiene belong to the irreducible representations
- (a) A_g and B_g
- (b) A_g and A_u
- (c) A_u and B_g
- (d) B_g and B_u
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Answer: (a)
Q17 · Dec 2014 · 2 marks
The product \sigma^{xy}.S_4^z (S_4^z is the four fold improper axis of rotation around the z-axis, and \sigma^{xy} is the reflection in the xy plane) is
- (a) C_4^z
- (b) C_4^z.i
- (c) C_4^y
- (d) C_2^z
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Answer: (a)
Q18 · June 2011 · 2 marks
The symmetry point group of propyne is
- (a) C_3
- (b) C_{3v}
- (c) D_3
- (d) D_{3d}
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Answer: (b)
Q19 · June 2011 · 2 marks
Number of rotational symmetry axes for triclinic crystal system is
- (a) 4
- (b) 3
- (c) 1
- (d) 0
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Answer: (d)
Q20 · June 2011 · 2 marks
The E \times E direct product in D_3 point group contains the irreducible representations
| \mathrm{D}_{3} | E | 2 \mathrm{C}_{3} | 3 \mathrm{C}_{2} |
| \mathrm{A}_{1} | 1 | 1 | -1 |
| \mathrm{A}_{2} | 1 | 1 | -1 |
| \mathrm{E}_{2} | 2 | -1 | 0 |
- (a) \mathrm{A_1 + A_2 + E}
- (b) \mathrm{2A_1 + E}
- (c) \mathrm{2A_2 + E}
- (d) \mathrm{2A_1 + 2A_2}
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Answer: (a)
Q21 · June 2011 · 2 marks
The result of the product C_2(x)C_2(y) is
- (a) E
- (b) \sigma_{xy}
- (c) C_2(z)
- (d) i
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Answer: (c)
Q22 · Dec 2014 · 2 marks
The product \sigma^{xy}.S_4^z (S_4^z is the four fold improper axis of rotation around the z-axis, and \sigma^{xy} is the reflection in the xy plane) is
- (a) C_4^z
- (b) C_4^z.i
- (c) C_4^y
- (d) C_2^z
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Answer: (a)
Q23 · June 2013 · 2 marks
Identify the Mulliken notation for the following irreducible representation
| E | \mathrm{C}_{\mathrm{n}} | \mathrm{nC}_{2} | i | \sigma_{\mathrm{h}} |
| 1 | 1 | -1 | -1 | -1 |
- (a) A'_{1u}
- (b) A''_{2u}
- (c) B'_{2u}
- (d) A'_{2u}
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Answer: (b)
Q24 · June 2011 · 2 marks
A molecules contains the following symmetry operations: E, 2C_6, 2C_3, C_2, 3\sigma_d, 3\sigma_v. The number of classes and order of the symmetry point group is:
- (a) 3, 12
- (b) 5, 12
- (c) 6, 12
- (d) 6, 6
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Answer: (c)
Q25 · June 2011 · 2 marks
Among the following, the CORRECT statement is:
- (a) The number of irreducible representations is equal to classes of symmetry operations.
- (b) The number of irreducible representations is equal to the order of the symmetry point group.
- (c) The irreducible representations contained in any point group are always of one dimension.
- (d) A symmetry point group may not contain a totally symmetric irreducible representation.
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Answer: (a)
Q26 · June 2011 · 2 marks
A square pyramidal, \mathrm{MX_4}, molecule belongs to C_{4v} point group. The symmetry operations are: E, 2C_4, C_2, 2\sigma_v and 2\sigma_d. The trace for the reducible representation, when symmetry operations of C_{4v} applied to \mathrm{MX_4}, is:
- (c) 5 1 1 1 1
- (a) 5 1 1 1 3
- (b) 1 1 1 1 1
- (d) 4 1 1 1 3
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Answer: (a)
Q27 · June 2011 · 2 marks
Character table of C_{2v} point group is:
If the initial and final states belong to A_1 and B_1 irreducible representation respectively, the allowed electronic transition from A_1 to B_1 is:
| \mathrm{C}_{2}, | E | \mathrm{C}_{2} | \sigma, | \sigma_{v} | |
| \mathrm{A}_{1} | 1 | 1 | 1 | 1 | z |
| \mathrm{A}_{2} | 1 | 1 | -1 | -1 | 1 |
| \mathrm{B}_{1} | 1 | -1 | 1 | -1 | x |
| \mathrm{B}_{2} | 1 | -1 | -1 | 1 | y |
- (a) z-polarized
- (b) y-polarized
- (c) x-polarized
- (d) x, z-polarized
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Answer: (c)
Q28 · Dec 2012 · 2 marks
The number of IR active vibrational modes of pyridine is:
| \mathrm{C}_{2 \mathrm{v}} | \mathrm{E}_{2} | \mathrm{C}_{2} | \sigma_{\mathrm{v}} | \sigma_{\mathrm{v}} | |
| \mathrm{A}_{1} | 1 | 1 | 1 | 1 | Z |
| \mathrm{A}_{2} | 1 | 1 | -1 | -1 | \mathrm{R}_{2} |
| \mathrm{B}_{1} | 1 | -1 | 1 | -1 | \mathrm{x}, \mathrm{R}_{\mathrm{y}} |
| \mathrm{B}_{2} | 1 | -1 | -1 | 1 | y, \mathrm{R}_{\mathrm{x}} |
- (a) 12
- (b) 20
- (c) 24
- (d) 33
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Answer: (c)
Q29 · June 2011 · 2 marks
Refer to the character table of the point group C_{3v} given above. Find which of the following transition is forbidden
- (a) a_1 \leftrightarrow a_1
- (b) a_1 \leftrightarrow e
- (c) a_2 \leftrightarrow e
- (d) a_1 \leftrightarrow a_2
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Answer: (d)
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