If `f(x) = p|sinx| + q e^|x| + r |x|^3` and it is derivable at x=0 then which of the following is complete solution for p,q and r

If f(x)=p|sin x|+qe^(|x|)+r|x|^(3) and it is derivable at x=0 then which of the following is complete solution for p,p,q and r

1) Infinite 2)2 33If f(x)=p|sin x + qelxl+r|x|3 and f(x) isdifferentiable at x=0, then1) q+r=0; p is any real number2)p+q=0; r is any real number3) q=0, r=0; p is any real number4) r=0,p=0; q is any real number

The pair of equations (p^(2) -1)x + (q^(2) -1) y + r=0 and (p+1) x + (q-1) y + r=0 have infinitely many solutions, then which of the following is true ?

If the function g(x) {{:((e^(px) + log _(e) (1+4x)+q)/(x^(3))","x ne 0),(r"," x=0):} continuous at x=0 , then find the values of p,q and r.

If P={x in R : f(x)=0} and Q={x in R : g(x)=0 } , then PuuQ is