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Exam Details

Mathematics (MA) 2008

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Questions 85
Duration 180 mins
Package Mathematics (MA) - Previous Year Papers

Paper pattern & analysis

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Showing all 85 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 77 90.6%
Hard 8 9.4%

Question type distribution

Multiple Choices 77 90.6%
Fill in the blanks 8 9.4%

Instructions

Mathematics (MA) 2008 – Instructions
  • Total number of questions: 85
  • 20 questions carry one mark each
  • 65 questions carry two marks each
  • Negative marking: 1/4 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
2008 · Unclassified
Mathematics (MA) 2008
Q.1 – Q.20 carry one mark each.

Consider the subspace W = (aij) : aij = 0 if i is even of all 10×10 real matrices. Then the dimension of W is

A
25
B
50
C
75
D
100
2
2008 · Unclassified
Mathematics (MA) 2008

Let S be the open unit disk and f : S → C be a real-valued analytic function with f(0) = 1. Then the set z ∈ S : f(z) = 1 is

A
empty
B
nonempty finite
C
countably infinite
D
uncountable
3
2008 · Unclassified
Mathematics (MA) 2008

Let E = (x, y) ∈ R2 : 0 ≤ x ≤ 1, 0 ≤ y ≤ x. Then ∫(f(x + y) dy) dx is equal to

A
−1
B
0
C
1/2
D
1
4
2008 · Unclassified
Mathematics (MA) 2008

For (x, y) ∈ R2, let f(x, y) = 2xy / (x2 + y2) if (x, y) ≠ (0, 0), 0 if (x, y) = (0, 0) . Then

A
fx and fy exist at (0, 0), and f is continuous at (0, 0)
B
fx and fy exist at (0, 0), and f is discontinuous at (0, 0)
C
fx and fy do not exist at (0, 0), and f is continuous at (0, 0)
D
fx and fy do not exist at (0, 0), and f is discontinuous at (0, 0)
5
2008 · Unclassified
Mathematics (MA) 2008

Let y be a solution of y' = ex2 − 1 on [0, 1] which satisfies y(0) = 0. Then

A
y(x) > 0 for x > 0
B
y(x) < 0 for x > 0
C
y changes sign in [0, 1]
D
6
2008 · Unclassified
Mathematics (MA) 2008

For the equation x(x−1)y'' + sin(x)y' + 2x(x−1)y = 0, consider the following statements P: x = 0 is a regular singular point. Q: x = 1 is a regular singular point. Then

A
both P and Q are true
B
P is false but Q is true
C
P is true but Q is false
D
both P and Q are false