## 08 JanNorth East/Assam State Level Eligibility Test (SLET) Mathematics/Statistics 2013

The Assam/North East state level eligibility test (SLET) for lecturership (Assistant Professor) was held lat month across the North Eastern state. The question papers for the Mathematics/Statistics (Mathematical Sciences) subject can be found below. Paper I Paper II Paper III [ad#ad-2]...

## 27 DecJoint CSIR UGC NET-JRF/LS Physical Sciences (December 2013)

The joint CSIR UGC National Eligibility Test for Junior Research Fellowship and Lecturer Ship was recently held nationwide on December 22nd, 2013. The question paper for Physical Sciences can be downloaded here. [ad#ad-2]...

## 27 DecJoint CSIR UGC NET-JRF/LS Mathematical Sciences (December 2013)

The joint CSIR UGC National Eligibility Test for Junior Research Fellowship and Lecturer Ship was recently held nationwide on December 22nd, 2013. The question paper for Mathematical Sciences can be downloaded here. [ad#ad-2]...

## 04 NovSET (N. E. Region) 2012 Exam Question Papers

[caption id="attachment_7349" align="alignleft" width="320"] Image Source : Shutterstock[/caption] The 2012 exam question papers of Mathematical Sciences, Assamese, English, Economics, Education, History, Philosophy, Political Science, Geography, Manipuri, Bodo, Bengali, Hindi, Anthropology, Sanskrit, Sociology, Commerce, Chemical Science, Life Science and Physical Science for SET conducted by SLET Commission, Assam...

## 16 AprThe Number of Solutions of a System of Linear Equations

The standard form of a linear equation in $$n$$ unknowns $$x_1,x_2,\dots ,x_n$$ is $$a_1x_1+a_2x_2+\dots +a_nx_n=b,$$ where $$a_1,a_2,\dots ,a_n$$ and $$b$$ are constants. Here constants mean some real numbers (these constants may come from any number field). A collection of one or more linear equations of same variables is called...

## 28 JanFind the Remainder

1) The remainder when $$3^{31}$$ is divided by 5 is A) 2 B) 3 C) 4 D) 1 (Hint: - gcd(3,5)=1 and $$\phi (5)=4,$$ thus $$3^4\equiv 1(mod 5).$$) 2) The reminder when $$5^{99}$$ is divided by 13 is A) 0 B) 8 C) 1 D) 4   3) The reminder when...

## 09 Nov15 questions on Real Analysis for NET and GATE aspirants

Find the correct option: 1. Let $$f:[2,4]\rightarrow R$$ be a continuous function such that $$f(2)=3$$ and $$f(4)=6.$$ The most we can say about the set $$f([2,4])$$ is that   A. It is a set which contains [3,6]. B. It is a closed interval. C. It is a set which contains 3 and 6. D....

Find the correct options:   1)  $$M=\left(\begin{array}{ccc}1 & 2 & 2 \\0 & 2 & 2 \\0 & 1 & 1 \end{array}\right)$$ and $$V={ Mx^{T} : x\in R^{3}}.$$ Then $$dim V$$ is (a)   0   (b)   1   (c)   2   (d)   3   2)  $$A^{2}-A=0,$$ where $$A$$ is a $$9\times 9$$ matrix....