If $f(x) = \frac{\cos^2 x + \sin^4 x}{\sin^2 x + \cos^4 x}$, for $x \in R$, then $f(2002)$ is equal to

Three rods $AB$,$BC$,and $BD$ made of the same material and having the same cross-section have been joined as shown in the figure. The ends $A$,$C$,and $D$ are held at temperatures of $20^{\circ}C$,$80^{\circ}C$,and $80^{\circ}C$ respectively. If each rod is of the same length,then the temperature at the junction $B$ of the three rods is: (in $^{\circ}C$)

If $A=\begin{bmatrix} 1 & -2 \\ 4 & 5 \end{bmatrix}$ and $f(t)=t^2-3t+7$,then $f(A)+\begin{bmatrix} 3 & 6 \\ -12 & -9 \end{bmatrix}$ is equal to

If the equation for the angular displacement of a particle moving on a circular path is given by $\theta(t) = 2t^3 + 0.5$,where $\theta$ is in radians and $t$ is in seconds,then the angular velocity of the particle after $2 \, s$ from its start is ......... $rad/s$.

Ethyl chloride reacts with sodium ethoxide to form a compound $A$. Which of the following reactions also yields $A$?

Which of the following statements is correct?