Matching exercise choose the correct one out of the alternatives $$A, B, C, D$$

Group $$-$$ $${\rm I}$$
$$P.$$ $${2^{nd}}$$ order differential equations
$$Q.$$ Non-linear algebraic equations
$$R.$$ Linear algebraic equations
$$S.$$ Numerical integration

Group $$-$$ $${\rm II}$$
$$(1)$$ Runge $$-$$ Kutta method
$$(2)$$ Newton $$-$$ Raphson method
$$(3)$$ Gauss Elimination
$$(4)$$ Simpson's Rule

If a complex number $$z = {{\sqrt 3 } \over 2} + i{1 \over 2}$$ then z⁴ is

Two cards are drawn at random in succession with replacement from a deck of $$52$$ well shuffled cards Probability of getting both 'Aces' is

The random variable $$X$$ takes on the values $$1,$$ $$2$$ (or) $$3$$ with probabilities $$\,{{2 + 5P} \over 5},{{1 + 3P} \over 5}\,\,$$ and $$\,\,{{1.5 + 2P} \over 5}\,\,$$ respectively the values of $$P$$ and $$E(X)$$ are respectively