## 22 Jun50 questions on linear algebra for NET and GATE aspirants

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....

## 10 JanApplications of Sylow Theorems

Sylow Theorem's is Group Theory are an important mathematical tool. Below we give a simple application of the theorems. Theorem: If $$H$$ and $$K$$ are subgroups of $$G$$ and $$Hleq N_G(K)$$, then $$HK$$ is a subgroup of $$G$$. In particular, if $$K$$ is normal is $$G$$...

## 05 AugGATE 2011 Question Paper

The Graduate Apptitute Test in Engineering (GATE) is jointly organised by the Indian Institutes of Technology (IITs) and the Indian Institute of Science (IISc). The mathematics paper of the 2011 test can be found here. We are grateful to Mr. Uday Bhaskar Sharma (The Institute of...

## 28 JulNET/GATE Questions

# Tick out the correct answers. More than one answer may be correct for a question. Tick out all.   1) The number of maximal ideals in $$frac{Z}{36Z}$$ is A) 1 B) 2 C) 3 D) 4.   2) The number of subfields of $$F_{2^{27}}$$ (distinct from $$F_{2^{27}}$$ itself) is A) 1 B) 2 C) 3 D)...