The function $$f(x) =$$ $$x$$ $$sinx$$ satisfies the following equation:
$$f$$"$$\left( x \right) + f\left( x \right) + t\,\cos \,x\,\, = \,\,0$$. The value of $$t$$ is ______ .

The value of the integral given below is $$$\int_0^\pi {{x^2}\,\cos \,x\,dx} $$$

Suppose you want to move from 0 to 100 on the number line. In each step, you either move right by a unit distance or you take a shortcut. A shortcut is simply a pre specified pair of integers i, j with i < j. Given a shortcut i, j if you are at position i on the number line, you may directly move to j. suppose T(k) denotes the smallest number of steps needed to move from k to 100. Suppose further that there is at most 1 shortcut involving any number, and in particular from 9 there is a shortcut to 15. Let y and z be such that T(9) = 1+ min(T(y),T(z)). Then the value of the product yz is _______.

Given $$i = \sqrt { - 1} ,$$ what will be the evaluation of the definite integral $$\int\limits_0^{\pi /2} {{{\cos x +i \sin x} \over {\cos x - i\,\sin x}}dx?} $$