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Exam Details

Mathematics (MA) 2013

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Questions 65
Duration 180 mins
Package Mathematics (MA) - Previous Year Papers

Paper pattern & analysis

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Showing all 65 questions in this paper.

Subject distribution

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Topic distribution

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Subtopic distribution

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Difficulty distribution

Easy 52 80%
Hard 13 20%

Question type distribution

Multiple Choices 52 80%
Fill in the blanks 13 20%

Instructions

Mathematics (MA) 2013 – Instructions
  • Total number of questions: 65
  • 30 questions carry one mark each
  • 35 questions carry two marks each
  • Negative marking: 1/3 of the marks allotted to the question
  • Use of calculator is allowed
  • This is a proctored examination
  • All other browser applications will be automatically closed
  • After three warnings, the examination window will close automatically

Syllabus

Full Syllabus

Sample questions from this paper

Questions are selected across the paper subjects wherever the paper contains that variety.

1
2013 · Unclassified
Mathematics (MA) 2013
Q.1 – Q.25 carry one mark each.

The possible set of eigen values of a 4 × 4 skew-symmetric orthogonal real matrix is

A
±i
B
±i, ±1
C
±1
D
0, ±i
2
2013 · Unclassified
Mathematics (MA) 2013

The coefficient of (z − π)2 in the Taylor series expansion of f(z) = (sin z)/(z − π) if z ≠ π, 1 if z = π around π is

A
1/2
B
−1/2
C
1/6
D
−1/6
3
2013 · Unclassified
Mathematics (MA) 2013

Consider R2 with the usual topology. Which of the following statements are TRUE for all A, B ⊆ R2? P: A ∪ B = A̅ ∪ B̅. Q: A ∩ B = A̅ ∩ B̅. R: (A ∪ B)̅ = A̅ ∪ B̅. S: (A ∩ B)̅ = A̅ ∩ B̅.

A
P and R only
B
P and S only
C
Q and R only
D
Q and S only
4
2013 · Unclassified
Mathematics (MA) 2013

Let f: R → R be a continuous function with f(1) = 5 and f(3) = 11. If g(x) = ∫13 f(x + t)dt then g'(0) is equal to _____

Write your response
5
2013 · Unclassified
Mathematics (MA) 2013

Let P be a 2 × 2 complex matrix such that trace(P2) = 1 and det(P) = −6. Then, trace(P4 − P3) is _____

Write your response
6
2013 · Unclassified
Mathematics (MA) 2013

Suppose that R is a unique factorization domain and that a, b ∈ R are distinct irreducible elements. Which of the following statements is TRUE?

A
The ideal (1 + a) is a prime ideal
B
The ideal (a + b) is a prime ideal
C
The ideal (1 + ab) is a prime ideal
D
The ideal (a) is not necessarily a maximal ideal