Let $X, N, Y$ and $Z$ be random variables. The variables $X$ and $N$ are independent of each other. $X$ is uniformly distributed between -1 and $1 ; N$ follows Normal distribution with zero mean and unity variance.

$Y$ and $Z$ are defined as, $Y=X+N$ and $Z=X^2+N$.

Which of the following pairs represents the values of correlation between $X$ and $Y$ and that between $X$ and $Z$ ?

Consider the square region $R$ in the $X-Y$ plane as shown with the dark shading in the Figure. The value of $\iint_R\left(x^2+y^2-1\right) d x d y$ is $\_\_\_\_$ .

(rounded off to two decimal places)

The address of the first location of a 256 kilo byte $(\mathrm{KB})$ memory is $(2500)_{\mathrm{H}}$. Choose the correct address of the last location of the memory.

The relation between the input current $(I)$ and the output voltage $(V)$ of a circuit is governed by the equation: $C \frac{d V}{d t}=I(t)-m(t)$. The circuit is excited by $I(t)=q \delta(t)$, where $q$ is a real valued constant. V at $t=0^{-}$is $V_0$.

Which of the following is an equivalent representation of the above case?