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Exam Details

Mathematics (MA) 2009

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Questions 60
Duration 180 mins
Package Mathematics (MA) - Previous Year Papers

Paper pattern & analysis

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Showing all 60 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 55 91.7%
Hard 5 8.3%

Question type distribution

Multiple Choices 55 91.7%
Fill in the blanks 5 8.3%

Instructions

Mathematics (MA) 2009 – Instructions
  • Total number of questions: 60
  • 20 questions carry one mark each
  • 40 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
2009 · Unclassified
Mathematics (MA) 2009
Q.1 – Q.20 carry one mark each.

The dimension of the vector space V = A = (aij)n×n : aij ∈ C, aij = aji over the field R is

A
n²
B
n² - 1
C
n² - n
D
n² / 2
2
2009 · Unclassified
Mathematics (MA) 2009

The minimal polynomial associated with the matrix is

A
x³ - x² - 2x - 3
B
x³ - x² + 2x - 3
C
x² - x³ - 3x - 3
D
x² - x³ + 3x - 3
3
2009 · Unclassified
Mathematics (MA) 2009

For the function f(z) = sin(1/cos(1/z)), the point z = 0 is

A
A removable singularity
B
A pole
C
An essential singularity
D
A non-isolated singularity
4
2009 · Unclassified
Mathematics (MA) 2009

Let f(z) = Σ zn for z ∈ C. If C : |z - i| = 2 then ∮ (f(z) dz / (z - i)5) =

A
2πi(1 + 15i)
B
2πi(1 - 15i)
C
4πi(1 + 15i)
D
2πi
5
2009 · Unclassified
Mathematics (MA) 2009

For what values of α and β, the quadrature formula ∫ f(x) dx ≈ α f(-1) + f(β) is exact for all polynomials of degree ≤ 1?

A
α = 1, β = 1
B
α = -1, β = 1
C
α = 1, β = -1
D
α = -1, β = -1
6
2009 · Unclassified
Mathematics (MA) 2009

Let f : [0,4] → R be a three times continuously differentiable function. Then the value of f [1,2,3,4] is

A
f⁽³⁾(ξ) / 3 for some ξ ∈ (0,4)
B
f⁽³⁾(ξ) / 2 for some ξ ∈ (0,4)
C
f⁽⁶⁾(ξ) / 3 for some ξ ∈ (0,4)
D
f⁽⁶⁾(ξ) / 6 for some ξ ∈ (0,4)