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UGC NET CSE | June 2023 | Part 2: 31

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Let $G=\frac{R}{\{0\}}$ and $H=\{-1,1\}$ be groups under the multiplication. Then, the map $\phi: G \rightarrow H$ defined by $\phi(x)=\frac{x}{|x|}$ is

  1. Not a homomorphism
  2. A one-one homomorphism, which is not onto
  3. An onto homomorphism, which is not one to one
  4. An homomorphism
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UGC NET CSE | June 2023 | Part 2: 3
There are $M$ points on one straight line $A B$ and $n$ points on another straight line $A C$ none of them being $A$. How many triangles can be formed with these points as vertices? $m n(m+n-2)$ $\frac{1}{2} m n(m+n-2)$ $\frac{1}{2} m n(m+n-1)$ $m n(m+n-1)$
There are $M$ points on one straight line $A B$ and $n$ points on another straight line $A C$ none of them being $A$. How many triangles can be formed with these points a...
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