GATE CY Group theory PYQs & Answers

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Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

Questions 1–10 of 12. Imported answers require independent review unless marked reviewed.

Topic practice 12 questionsPage 1 of 2

The point group of CH₂=C=CH₂ is

Your answerChoose one option.

D₂h

C₂h

C₂v

D₂d

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The total number of symmetry operations (order, h) present in the point group of [PdCl₆]²⁻ is x and that in trans-[PdBr₂Cl₄]²⁻ is y. The value of x − y is _____ (in integer).

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The symmetry element that does NOT belong to

point group is

Your answerChoose one option.

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The order and the number of classes present in a group with the irreducible representations A₁, A₂, B₁, B₂, E₁, and E₂, are, respectively,

Your answerChoose one option.

6 and 6

12 and 6

6 and 3

12 and 3

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Among the following, the correct statement(s) is (are):

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

C₂ symmetry element is present in H₂O and H₂O₂ but NOT in PCl₅.

both C₂ and C₃ symmetry elements are present in CCl₄ and SF₆.

one σₕ and three σᵈ symmetry elements are present in benzene.

σᵥ symmetry element is present in NH₃ but NOT in BF₃.

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Point group of naphthalene (C₁₀H₈) is

Your answerChoose one option.

D₂d

D₂h

D₃d

D₃h

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The point group of SF

Your answerChoose one option.

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A point originally at

was subjected to a symmetry operation

that shifted the point to

. Subsequently, the point at

was subjected to another symmetry operation

that shifted this point to

. The symmetry operators

and

are, respectively,

Your answerChoose one option.

and

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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:

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

1, 1, 1, 1

−1, 1, 1, −1

1, −1, 1, −1

1, −1, −1, −1

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The character table for a pyramidal AB₃ molecule of C₃ᵥ point group is given below:

C₃ᵥ | E | 2C₃ | 3σᵥ | A₁ | 1 | 1 | 1 | z | x² + y², z² A₂ | 1 | 1 | −1 | Rz | E | 2 | −1 | 0 | (x,y) (Rx,Ry) | (x²−y², xy) (xz, yz)

The reducible representation of pyramidal AB₃ is

C₃ᵥ | E | 2C₃ | 3σᵥ Γ | 12 | 0 | 2

The CORRECT option representing all the normal Raman active modes of pyramidal AB₃ is:

Your answerChoose one option.

A₁ + A₂ + 2E

3A₁ + A₂ + E

2A₁ + 2E

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GATE CY Group theory PYQs

How to practice Group theory

Question 18

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Question 15