Which semi-dwarf variety of plant was developed by Nobel laureate Norman $E$. Borlaug?

The reagent used for the conversion of allyl alcohol to propenal is

The figure shows wave fronts in still water,moving in the direction of the arrow towards the interface $PQ$ between a shallow region and a deep (denser) region. Which of the lines shown may represent one of the wave fronts in the deep region?

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and $l^2+m^2-n^2=0$ is

If $X$ is a Poisson variate such that $P(X=1)=P(X=2)$, then $P(X=4)$ is equal to

Let $Z$ denote the set of integers. Define $f: Z \rightarrow Z$ by $f(x) = \begin{cases} \frac{x}{2}, & x \text{ is even} \\ 0, & x \text{ is odd} \end{cases}$. Then $f$ is: