JAM Mathematics (MA) - Previous Year Papers Previous Year Questions

1

2012 · Unclassified

Mathematics (MA) 2012

Let \(\{x_n\}\) be the sequence \(+\sqrt{1}, -\sqrt{1}, +\sqrt{2}, -\sqrt{2}, +\sqrt{3}, -\sqrt{3}, +\sqrt{4}, -\sqrt{4},....\) If \[y_n = \frac{x_1+x_2+\cdots+x_n}{n} \text{ for all } n \in \mathbb{N},\] then the sequence \(\{y_n\}\) is

A

monotonic

B

NOT bounded

C

bounded but NOT convergent

D

convergent

Open complete paper

2

2013 · Unclassified

Mathematics (MA) MA2013

Let \(A=\begin{pmatrix}1 & 1 & 1\\ 3 & -1 & 1\\ 1 & 5 & 3\end{pmatrix}\) and \(V\) be the vector space of all \(X\in\mathbb{R}^3\) such that \(AX=0\). Then \(\dim(V)\) is

A

1

B

2

C

3

Open complete paper

3

2014 · Unclassified

Mathematics (MA) MA2014

Let \(f(x)=|x^2-25|\) for all \(x \in \mathbb{R}\). The total number of points of \(\mathbb{R}\) at which \(f\) attains a local extremum (minimum or maximum) is

A

1

B

2

C

3

D

4

Open complete paper

4

2015 · Unclassified

Mathematics (MA) MA2015

Suppose \(N\) is a normal subgroup of a group \(G\). Which one of the following is true?

A

If \(G\) is an infinite group then \(G/N\) is an infinite group

B

If \(G\) is a nonabelian group then \(G/N\) is a nonabelian group

C

If \(G\) is a cyclic group then \(G/N\) is an abelian group

D

If \(G\) is an abelian group then \(G/N\) is a cyclic group

Open complete paper

5

2016 · Unclassified

Mathematics (MA) 2016

The sequence \(\{s_n\}\) of real numbers given by \[s_n = \frac{\sin \frac{\pi}{2}}{1\cdot 2} + \frac{\sin \frac{\pi}{2^2}}{2\cdot 3} + \cdots + \frac{\sin \frac{\pi}{2^n}}{n\cdot(n+1)}\] is

A

a divergent sequence

B

an oscillatory sequence

C

not a Cauchy sequence

D

a Cauchy sequence

Open complete paper

6

2017 · Unclassified

Mathematics (MA) 2017

Consider the function \( f(x,y) = 5 - 4\sin x + y^2 \) for \( 0 < x < 2\pi \) and \( y \in \mathbb{R} \). The set of critical points of \( f(x,y) \) consists of

A

a point of local maximum and a point of local minimum

B

a point of local maximum and a saddle point

C

a point of local maximum, a point of local minimum and a saddle point

D

a point of local minimum and a saddle point

Open complete paper