For the following questions answer them individually
If $$180^\circ < A < 270^\circ, 90^\circ < B < 180^\circ, \tan A = \sqrt{3}$$ and $$\sin B = \frac{\sqrt{3}}{2}$$, then the value of $$\sin(A - B)$$
$$\frac{4 \cosec 150^\circ + 3 \sec^2 210^\circ}{5 \tan 225^\circ + 6 \cot^2 330^\circ} =$$
A person on walking 20 metres towards a chimney in a horizontal line through its base observes that its angle of elevation of the top of the chimney changes from $$30^\circ$$ to $$45^\circ$$. Then the height(in metres) of the chimney is
A polynomial in x leaves remainders 2 and 3 when divided by x + 1 and x - 1 respectively. Then the remainder we get when that polynomial is divided by $$x^2 - 1$$ is