The correct answer is (d) Impulse response is zero for negative values of n
To explain: Let us consider a LTI system having an output at time n=n0 given by the convolution formula
y(n)=\(\sum_{k=-{\infty}}^{\infty}h(k)x(n_0-k)\)
We split the summation into two intervals.
=>y(n)=\(\sum_{k=-{\infty}}^{-1}h(k)x(n_0-k)+\sum_{k=0}^{\infty}h(k)x(n_0-k)\)
=(h(0)x(n0)+h(1)x(n0-1)+h(2)x(n0-2)+….)+(h(-1)x(n0+1)+h(-2)x(n0+2)+…)
As per the definition of the causality, the output should depend only on the present and past values of the input. So, the coefficients of the terms x(n0+1), x(n0+2)…. should be equal to zero.
that is, h(n)=0 for n<0 .