The circuit given below is that of:

$A$ screen is placed $50\,cm$ from a single slit,which is illuminated with $6000 \mathring{A}$ light. If the distance between the first and third minima in the diffraction pattern is $3\,mm$,the width of the slit is.....$mm$.

Compound $A$ $(C_3H_6O)$ undergoes the following reactions to form $B$ and $C$. Identify $A$,$B$,and $C$.

Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$,while box $B$ contains one mole of helium at temperature $(7/3) T_0$. The boxes are then put into thermal contact with each other,and heat flows between them until the gases reach a common final temperature (Ignore the heat capacity of boxes). Then,the final temperature of gases,$T_f$,in terms of $T_0$ is

Two adjacent sides of a parallelogram $ABCD$ are given by $\overline{AB}=2 \hat{i}+10 \hat{j}+11 \hat{k}$ and $\overline{AD}=-\hat{i}+2 \hat{j}+2 \hat{k}$. The side $AD$ is rotated by an acute angle $\alpha$ in the plane of the parallelogram so that $AD$ becomes $AD^{\prime}$. If $AD^{\prime}$ makes a right angle with side $AB$,then the cosine of the angle $\alpha$ is given by

The most stable conformation of ethylene glycol is