Identify $A$ in the following reaction.
$A + \text{Acetic anhydride} \xrightarrow{H^{+}} \text{Aspirin} + \text{Acetic acid}$

Let $a, b, c$ be distinct non-negative numbers. If the vectors $a \hat{i} + a \hat{j} + c \hat{k}$,$\hat{i} + \hat{k}$,and $c \hat{i} + c \hat{j} + b \hat{k}$ lie in a plane,then $c$ is:

Which of the following does not show mutarotation?

The moment of inertia of a uniform thin rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $\frac{L}{3}$ from one of its ends and perpendicular to the rod is:

An ovule which becomes curved so that the nucellus and embryo sac lie at right angles to the funicle is:

Half-life of a radioactive substance $A$ is two times the half-life of another radioactive substance $B$. Initially,the number of nuclei of $A$ and $B$ are $N_A$ and $N_B$ respectively. After three half-lives of $A$,the number of nuclei of both are equal. Then the ratio $\frac{N_A}{N_B}$ is