In a game, 3 coins are tossed. A person is paid ₹ 7 /-, if he gets all heads or all tails; and he is supposed to pay ₹ 3 /-, if he gets one head or two heads. The amount he can expect to win on an average per game is ₹

$$\int \mathrm{e}^x\left(1-\cot x+\cot ^2 x\right) \mathrm{d} x=$$

The parametric equations of the circle $$x^2+y^2+2 x-4 y-4=0$$ are

In a triangle $$\mathrm{ABC}$$, with usual notations, if $$\mathrm{c}=4$$, then value of $$(a-b)^2 \cos ^2 \frac{C}{2}+(a+b)^2 \sin ^2 \frac{C}{2}$$ is