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Exam Details

Mathematics (MA) 2007

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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

Mathematics
84 Qs

Topic distribution

Real Analysis
16 Qs
Linear Algebra
10 Qs
Ordinary Differential Equations
9 Qs
Complex Analysis
8 Qs
Algebra
8 Qs
Calculus
7 Qs
Topology
6 Qs
Functional Analysis
6 Qs
Numerical Analysis
5 Qs
Partial Differential Equations
5 Qs
Linear Programming
4 Qs

Subtopic distribution

Function Sequences and Uniform Convergence
7 Qs
Functions of a complex variable
6 Qs
Vector Spaces and Linear Transformations
5 Qs
Metric Spaces and Continuity
5 Qs
Multiple Integrals and Change of Variables
5 Qs
Rings and Polynomial Domains
5 Qs
Topological Spaces and Constructions
4 Qs
Lebesgue Measure and Integration
4 Qs
Existence, Uniqueness and Linear Equations
4 Qs
Normed Spaces, Banach Spaces and Operators
4 Qs
Group Theory
3 Qs
Laplace Transforms and Series Solutions
3 Qs

Difficulty distribution

Medium 56 65.9%
Easy 25 29.4%
Hard 4 4.7%

Question type distribution

MCQ 85 100%

Syllabus

Full Syllabus

Sample questions from this paper

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

1
2007 · Mathematics · Topology · Topological Spaces and Constructions
Mathematics (MA) 2007
Consider \(\mathbb{R}^2\) with the usual topology. Let \(S = \{(x, y) \in \mathbb{R}^2 : x \text{ is an integer}\}\). Then \(S\) is
2
2007 · Mathematics · Real Analysis · Function Sequences and Uniform Convergence
Mathematics (MA) 2007
For a positive integer \(n\), let \(f_n : \mathbb{R} \to \mathbb{R}\) be defined by \[f_n(x) = \begin{cases} \frac{1}{4n+5}, & \text{if } 0 \le x \le n, \\ 0, & \text{otherwise}. \end{cases}\] Then \(\{f_n(x)\}\) converges to zero
3
2007 · Mathematics · Linear Algebra · Vector Spaces and Linear Transformations
Mathematics (MA) 2007
Let \(P_1\) and \(P_2\) be two projection operators on a vector space. Then
4
2007 · Mathematics · Numerical Analysis · Systems of linear equations
Mathematics (MA) 2007
Consider the system of linear equations \[\begin{aligned} x + y + z &= 3 \\ x - y - z &= 4 \\ x - 5y + kz &= 6. \end{aligned}\] Then the value of \(k\) for which this system has an infinite number of solutions is
5
2007 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2007
Let \(S = \{0\} \cup \left\{\frac{1}{4n+7} : n = 1, 2, \dots\right\}\). Then the number of analytic functions which vanish only on \(S\) is
6
2007 · Mathematics · Algebra · Group Theory
Mathematics (MA) 2007
The value of \(\alpha\) for which \(G = \{\alpha, 1, 3, 9, 19, 27\}\) is a cyclic group under multiplication modulo 56 is