If $\omega$ is a complex cube root of unity,then $225+(3 \omega+8 \omega^2)^2+(3 \omega^2+8 \omega)^2$ is equal to:

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ $(\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ $(k > 0)$. The terminal speed of the ball is

$A$ whistle revolves in a circle with an angular speed of $20\, rad/s$ using a string of length $50\, cm$. If the frequency of sound from the whistle is $385\, Hz$,then what is the minimum frequency heard by an observer,who is far away from the centre in the same plane? (Speed of sound is $340\, m/s$)

$Fe_2Cr_2O_4 + Na_2CO_3 + O_2$ $\xrightarrow{\text{Fusion}} [X]$ $\xrightarrow[H_2O]{H^+} [Y]$ $\xrightarrow{H_2O_2/H^+} [Z]$
Which of the following statements is true for the compounds $[X], [Y]$ and $[Z]$?

The value of $a$ for which the equations $x^3+ax+1=0$ and $x^4+ax^2+1=0$ have a common root is

$A$ plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials with refractive indices $\mu_1$ and $\mu_2$ and $R$ is the radius of curvature of the curved surface of the lenses,then the focal length of the combination is: