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:

Consider the following statements:
$(a)$ $R_2SiO$ is the repeating unit of linear silicones.
$(b)$ $RSiCl_3$ on hydrolysis followed by dehydration gives linear silicones.
$(c)$ Silicones can be used as heat insulators.
$(d)$ Silica is soluble in $HF$.
The correct statement$(s)$ is/are:

What is the value of linear velocity,if $\vec \omega = 3\hat i - 4\hat j + \hat k$ and $\vec r = 5\hat i - 6\hat j + 6\hat k$?

The jawless vertebrate is

Which of the following reactions will not result in the formation of carbon-carbon bonds?

Let $P(6, 3)$ be a point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If the normal at point $P$ intersects the $x$-axis at $(9, 0)$,then the eccentricity of the hyperbola is: