Three rods each of length $L$ and mass $M$ are placed along $X$,$Y$,and $Z$-axes such that one end of each rod is at the origin. The moment of inertia of this system about the $Z$-axis is:

The reaction $A \xrightarrow{k}$ Product is zero order,while the reaction $B \xrightarrow{k}$ Product is a first order reaction. For what initial concentration of $A$ are the half-lives of the two reactions equal?

Which of the following is responsible for mechanical support, enzyme transport and protein synthesis?

$A$ sinusoidal carrier voltage of frequency $1.5\,MHz$ and amplitude $50\,V$ is amplitude modulated by a sinusoidal voltage of frequency $10\,kHz$ producing $50\%$ modulation. The lower and upper side-band frequencies in $kHz$ are:

$A$ small mass $m$ is attached to a massless string whose other end is fixed at $P$ as shown in the figure. The mass is undergoing circular motion in the $x-y$ plane with center $O$ and constant angular speed $\omega$. If the angular momentum of the system,calculated about $O$ and $P$ is denoted by $\vec L_o$ and $\vec L_p$ respectively,then:

In any $\triangle ABC$,the expression $\frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4b^2c^2}$ is equal to: