The maximum value of the function $f(x)=3x^3-18x^2+27x-40$ on the set $S=\{x \in R : x^2+30 \leq 11x\}$ is

$\cos ^2\left(\frac{\pi}{6}+\theta\right)-\sin ^2\left(\frac{\pi}{6}-\theta\right)$ is equal to

Let $l_1$ and $l_2$ be two lines intersecting at $P$. If $A_1, B_1, C_1$ are points on $l_1$,and $A_2, B_2, C_2, D_2, E_2$ are points on $l_2$,and if none of these coincides with $P$,then the number of triangles formed by these eight points is:

$A$ capacitor $C = 100 \ \mu F$ is connected to three resistors,each of resistance $1 \ k\Omega$,and a battery of emf $9 \ V$. The switch $S$ has been closed for a long time to charge the capacitor. When switch $S$ is opened,the capacitor discharges with a time constant of.....$ms$.

The covalent alkaline earth metal halide $(X = Cl, Br, I)$ is

The area (in square units) of the circle which touches the lines $4x + 3y = 15$ and $4x + 3y = 5$ is