The combined equation of the lines passing through the origin and having slopes $\frac{2}{3}$ and $-\frac{2}{3}$ is

Which of the following exhibits a haplontic life cycle?

Two full turns of the circular scale of a screw gauge cover a distance of $1\,mm$ on the main scale. The total number of divisions on the circular scale is $50$. Further,it is found that the screw gauge has a zero error of $+0.03\,mm$. While measuring the diameter of a thin wire,a student notes the main scale reading of $3\,mm$ and the number of the circular scale division in line with the main scale is $35$. The diameter of the wire is .......... $mm$.

Freundlich adsorption isotherms for the physical adsorption of a gas at temperatures $T_1$,$T_2$,and $T_3$ are shown in the graph given below. The correct relationship between $T_1$,$T_2$,and $T_3$ is:

$A$ metal salt gives a yellow precipitate with potassium chromate in acetic acid and a white precipitate with dilute sulfuric acid. However,it does not give a precipitate with sodium chloride or iodide. What will be the composition of the white precipitate formed when sodium carbonate is added to the solution of the metal salt?

If the position vectors of $A, B$ and $C$ are respectively $2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}$ and $3 \hat{i}-4 \hat{j}-4 \hat{k}$, then $\cos ^2 A$ is equal to