The maximum and minimum values of the function $f: R \rightarrow R$ defined by $f(x)=5 \cos x+3 \cos \left(x+\frac{\pi}{3}\right)+8$ for all $x \in R$,are respectively

Write down the Boolean expression for the output $Y$ of the system shown in the figure.

$A$ coil of self-inductance $L$ is connected in series with a bulb $B$ and an $A.C.$ source. Brightness of the bulb decreases when

Consider the following statements $A$ and $B$ and identify the correct answer.
$A$. In an elastic collision,if a body suffers a head-on collision with another of the same mass at rest,then the first body comes to rest while the other starts moving with the velocity of the first one.
$B$. Two bodies of equal mass suffering a head-on elastic collision merely exchange their velocities.

If the position vectors of $A, B$ and $C$ are respectively $2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}$ and $3 \hat{i}-4 \hat{j}-4 \hat{k}$, then $\cos ^2 A$ is equal to

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