F(x)={[z" fir ">=0],[z^(2)" if "x<0](NCERT)

Let Z denote the set of all integers and f: Z to Z defined by f(x) = {{:(x+2, ("x is even")),(0, ("x is odd")):} , Then f is:

If the system of equtions 2x-y+z=0,x-2y+z=0, tx-y+2z=0 has infinitely many solution and f(x) be a continuous function such that f(5+x)+f(x)=2, then f_(0)^(-2t) f(x) dx is equal to

If the system of equtions 2x-y+z=0,x-2y+z=0, tx-y+2z=0 has infinitely many solution and f(x) be a continuous function such that f(5+x)+f(x)=2, then f_(0)^(-2t) f(x) dx is equal to

Let f : Z to Z be given by f(x) = {((x)/(2) if"is even"),(0 if" is odd"):} Then f is

If the system of equations 2x-y+z=0,x-2y+z=0, tx-y+2z=0 has infinitely many solution and f(x) be a continuous function such that f(5+x)+f(x)=2 , then int_(0)^(-2t) f(x) dx is equal to

Let y = f(x) be a differentiable function, AA x in R and satisfies, f(x) = x+ int_(0)^(1)x^(2)z f(z) dz + int_(0)^(1)x z^(2) f(z) dz , then

Let f(x)=[x] and g(x)={0, x in Z x^2, x in R -Z then (where [.]denotest greatest integer funtion)

Let f(x)=[x] and g(x)={0, x in Z x^2, x in R -Z then (where [.]denotest greatest integer funtion)