A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length $$x$$. The maximum area enclosed by the park is

If $$A$$ and $$B$$ are square matrices of size $$n\, \times \,n$$ such that
$${A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right),$$ then which of the following will be always true?

Let $$A = \left( {\matrix{ 1 & 2 \cr 3 & 4 \cr } } \right)$$ and $$B = \left( {\matrix{ a & 0 \cr 0 & b \cr } } \right),a,b \in N.$$ Then

$$\int\limits_0^\pi {xf\left( {\sin x} \right)dx} $$ is equal to