A real valued function $f(x)$ satisfies the function equation $f(x - y) = f(x)f(y) - f(a - x)f(a + y)$ where a is a given constant and $f(0) = 1$, $f(2a - x)$ is equal to

Solve $|x\,-\,2| + |x\,-\,1| = x\,-\,3$

$f : R \to R$ is defined as

$f(x) = \left\{ {\begin{array}{*{20}{c}}
{{x^2} + 2mx - 1\,,}&{x \leq 0}\\
{mx - 1\,\,\,\,\,\,\,\,\,\,\,\,\,,}&{x > 0}
\end{array}} \right.$

 If $f (x)$ is one-one then the set of values of $'m'$ is

If $h\left( x \right) = \left[ {\ln \frac{x}{e}} \right] + \left[ {\ln \frac{e}{x}} \right]$ ,where [.] denotes greatest integer function, then which of the following is false ?

The function $f\left( x \right) = \left| {\sin \,4x} \right| + \left| {\cos \,2x} \right|$, is a periodic function with period

The maximum value of function $f(x) = \int\limits_0^1 {t\,\sin \,\left( {x + \pi t} \right)} dt,\,x \in \,R$ is