Write down the Boolean expression for the output $Y$ of the system shown in the figure.

The angle between the lines $\vec{r}=(2 \hat{i}-3 \hat{j}+\hat{k})+\lambda(\hat{i}+4 \hat{j}+3 \hat{k})$ and $\vec{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(\hat{i}+2 \hat{j}-3 \hat{k})$ is

If $p$ and $q$ are the perpendicular distances from the origin to the straight lines $x \sec \theta - y \operatorname{cosec} \theta = a$ and $x \cos \theta + y \sin \theta = a \cos 2 \theta$,then

Two radioactive materials $X_1$ and $X_2$ have decay constants $10 \lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $1 / e$ after a time:

Which phylum is characterized by the presence of a central cavity known as the spongocoel?

Observe the following statements:
$1.$ Heavy water is harmful for the growth of animals.
$2.$ Heavy water reacts with $Al_4C_3$ and forms deuterated acetylene.
$3.$ $BaCl_2 \cdot 2D_2O$ is an example of interstitial deuterate.
The correct statements are: